A Signal Transmission Technique for Stability Analysis of Multivariable Non-Linear Control Systems
NASA Technical Reports Server (NTRS)
Jackson, Mark; Zimpfer, Doug; Adams, Neil; Lindsey, K. L. (Technical Monitor)
2000-01-01
Among the difficulties associated with multivariable, non-linear control systems is the problem of assessing closed-loop stability. Of particular interest is the class of non-linear systems controlled with on/off actuators, such as spacecraft thrusters or electrical relays. With such systems, standard describing function techniques are typically too conservative, and time-domain simulation analysis is prohibitively extensive, This paper presents an open-loop analysis technique for this class of non-linear systems. The technique is centered around an innovative use of multivariable signal transmission theory to quantify the plant response to worst case control commands. The technique has been applied to assess stability of thruster controlled flexible space structures. Examples are provided for Space Shuttle attitude control with attached flexible payloads.
Identification of discontinuous nonlinear systems via a multivariate Padé approach
NASA Astrophysics Data System (ADS)
Keshavarzzadeh, V.; Masri, S. F.
2016-02-01
We present a nonlinear system identification technique based on multi-dimensional rational polynomials. A multi-dimensional Padé-Legendre approximation is developed to circumvent challenges in dealing with sharp shocks. The purpose of this paper is to investigate the accuracy of such approximations for identification of various nonlinear systems, particularly systems with a non-smooth response surface. This identification approach utilizes the generalized form of a Padé-Legendre approximation for studying multivariable functions. In the studied problems, the nonlinearity is a function of state variables (displacement and velocity), which requires multi-dimensional formulation. Furthermore, a spatial filter is applied to minimize the effects of the singular points in the applicable rational function of the response surface. This study presents different types of nonlinearities including smooth, irregular, and hysteretic functions, in order to demonstrate the performance of the approach under different conditions. In order to study the robustness of the method in comparison to other identification techniques based on plain polynomial representation, a nonlinear system with a sharp discontinuous restoring force surface is considered. The performance of both approaches is investigated for different degrees of "sharpness". In addition, the accuracy of the identified models to represent the nonlinear system is verified by comparing the output of the system (computed on the basis of the identified model) from data sets corresponding to different excitations than those used for identification purposes. It is shown that the proposed approach provides a robust identification technique for a broad class of highly-nonlinear systems, and it is particularly advantageous to use when dealing with systems incorporating discontinuous properties.
Constructing networks from a dynamical system perspective for multivariate nonlinear time series.
Nakamura, Tomomichi; Tanizawa, Toshihiro; Small, Michael
2016-03-01
We describe a method for constructing networks for multivariate nonlinear time series. We approach the interaction between the various scalar time series from a deterministic dynamical system perspective and provide a generic and algorithmic test for whether the interaction between two measured time series is statistically significant. The method can be applied even when the data exhibit no obvious qualitative similarity: a situation in which the naive method utilizing the cross correlation function directly cannot correctly identify connectivity. To establish the connectivity between nodes we apply the previously proposed small-shuffle surrogate (SSS) method, which can investigate whether there are correlation structures in short-term variabilities (irregular fluctuations) between two data sets from the viewpoint of deterministic dynamical systems. The procedure to construct networks based on this idea is composed of three steps: (i) each time series is considered as a basic node of a network, (ii) the SSS method is applied to verify the connectivity between each pair of time series taken from the whole multivariate time series, and (iii) the pair of nodes is connected with an undirected edge when the null hypothesis cannot be rejected. The network constructed by the proposed method indicates the intrinsic (essential) connectivity of the elements included in the system or the underlying (assumed) system. The method is demonstrated for numerical data sets generated by known systems and applied to several experimental time series.
Constructing networks from a dynamical system perspective for multivariate nonlinear time series.
Nakamura, Tomomichi; Tanizawa, Toshihiro; Small, Michael
2016-03-01
We describe a method for constructing networks for multivariate nonlinear time series. We approach the interaction between the various scalar time series from a deterministic dynamical system perspective and provide a generic and algorithmic test for whether the interaction between two measured time series is statistically significant. The method can be applied even when the data exhibit no obvious qualitative similarity: a situation in which the naive method utilizing the cross correlation function directly cannot correctly identify connectivity. To establish the connectivity between nodes we apply the previously proposed small-shuffle surrogate (SSS) method, which can investigate whether there are correlation structures in short-term variabilities (irregular fluctuations) between two data sets from the viewpoint of deterministic dynamical systems. The procedure to construct networks based on this idea is composed of three steps: (i) each time series is considered as a basic node of a network, (ii) the SSS method is applied to verify the connectivity between each pair of time series taken from the whole multivariate time series, and (iii) the pair of nodes is connected with an undirected edge when the null hypothesis cannot be rejected. The network constructed by the proposed method indicates the intrinsic (essential) connectivity of the elements included in the system or the underlying (assumed) system. The method is demonstrated for numerical data sets generated by known systems and applied to several experimental time series. PMID:27078382
NASA Technical Reports Server (NTRS)
Aires, Filipe; Rossow, William B.; Hansen, James E. (Technical Monitor)
2001-01-01
A new approach is presented for the analysis of feedback processes in a nonlinear dynamical system by observing its variations. The new methodology consists of statistical estimates of the sensitivities between all pairs of variables in the system based on a neural network modeling of the dynamical system. The model can then be used to estimate the instantaneous, multivariate and nonlinear sensitivities, which are shown to be essential for the analysis of the feedbacks processes involved in the dynamical system. The method is described and tested on synthetic data from the low-order Lorenz circulation model where the correct sensitivities can be evaluated analytically.
Hwang, Chih-Lyang; Jan, Chau
2016-02-01
At the beginning, an approximate nonlinear autoregressive moving average (NARMA) model is employed to represent a class of multivariable nonlinear dynamic systems with time-varying delay. It is known that the disadvantages of robust control for the NARMA model are as follows: 1) suitable control parameters for larger time delay are more sensitive to achieving desirable performance; 2) it only deals with bounded uncertainty; and 3) the nominal NARMA model must be learned in advance. Due to the dynamic feature of the NARMA model, a recurrent neural network (RNN) is online applied to learn it. However, the system performance becomes deteriorated due to the poor learning of the larger variation of system vector functions. In this situation, a simple network is employed to compensate the upper bound of the residue caused by the linear parameterization of the approximation error of RNN. An e -modification learning law with a projection for weight matrix is applied to guarantee its boundedness without persistent excitation. Under suitable conditions, the semiglobally ultimately bounded tracking with the boundedness of estimated weight matrix is obtained by the proposed RNN-based multivariable adaptive control. Finally, simulations are presented to verify the effectiveness and robustness of the proposed control.
He, Shouling
2002-10-01
In this paper multilayer neural networks (MNNs) are used to control the balancing of a class of inverted pendulums. Unlike normal inverted pendulums, the pendulum discussed here has two degrees of rotational freedom and the base-point moves randomly in three-dimensional space. The goal is to apply control torques to keep the pendulum in a prescribed position in spite of the random movement at the base-point. Since the inclusion of the base-point motion leads to a non-autonomous dynamic system with time-varying parametric excitation, the design of the control system is a challenging task. A feedback control algorithm is proposed that utilizes a set of neural networks to compensate for the effect of the system's nonlinearities. The weight parameters of neural networks updated on-line, according to a learning algorithm that guarantees the Lyapunov stability of the control system. Furthermore, since the base-point movement is considered unmeasurable, a neural inverse model is employed to estimate it from only measured state variables. The estimate is then utilized within the main control algorithm to produce compensating control signals. The examination of the proposed control system, through simulations, demonstrates the promise of the methodology and exhibits positive aspects, which cannot be achieved by the previously developed techniques on the same problem. These aspects include fast, yet well-maintained damped responses with reasonable control torques and no requirement for knowledge of the model or the model parameters. The work presented here can benefit practical problems such as the study of stable locomotion of human upper body and bipedal robots.
Nonlinear aerodynamic modeling using multivariate orthogonal functions
NASA Technical Reports Server (NTRS)
Morelli, Eugene A.
1993-01-01
A technique was developed for global modeling of nonlinear aerodynamic coefficients using multivariate orthogonal functions based on the data. Each orthogonal function retained in the model was decomposed into an expansion of ordinary polynomials in the independent variables, so that the final model could be interpreted as selectively retained terms from a multivariable power series expansion. A predicted squared-error metric was used to determine the orthogonal functions to be retained in the model; analytical derivatives were easily computed. The approach was demonstrated on the Z-body axis aerodynamic force coefficient (Cz) wind tunnel data for an F-18 research vehicle which came from a tabular wind tunnel and covered the entire subsonic flight envelope. For a realistic case, the analytical model predicted experimental values of Cz very well. The modeling technique is shown to be capable of generating a compact, global analytical representation of nonlinear aerodynamics. The polynomial model has good predictive capability, global validity, and analytical differentiability.
Multi-application controls: Robust nonlinear multivariable aerospace controls applications
NASA Technical Reports Server (NTRS)
Enns, Dale F.; Bugajski, Daniel J.; Carter, John; Antoniewicz, Bob
1994-01-01
This viewgraph presentation describes the general methodology used to apply Honywell's Multi-Application Control (MACH) and the specific application to the F-18 High Angle-of-Attack Research Vehicle (HARV) including piloted simulation handling qualities evaluation. The general steps include insertion of modeling data for geometry and mass properties, aerodynamics, propulsion data and assumptions, requirements and specifications, e.g. definition of control variables, handling qualities, stability margins and statements for bandwidth, control power, priorities, position and rate limits. The specific steps include choice of independent variables for least squares fits to aerodynamic and propulsion data, modifications to the management of the controls with regard to integrator windup and actuation limiting and priorities, e.g. pitch priority over roll, and command limiting to prevent departures and/or undesirable inertial coupling or inability to recover to a stable trim condition. The HARV control problem is characterized by significant nonlinearities and multivariable interactions in the low speed, high angle-of-attack, high angular rate flight regime. Systematic approaches to the control of vehicle motions modeled with coupled nonlinear equations of motion have been developed. This paper will discuss the dynamic inversion approach which explicity accounts for nonlinearities in the control design. Multiple control effectors (including aerodynamic control surfaces and thrust vectoring control) and sensors are used to control the motions of the vehicles in several degrees-of-freedom. Several maneuvers will be used to illustrate performance of MACH in the high angle-of-attack flight regime. Analytical methods for assessing the robust performance of the multivariable control system in the presence of math modeling uncertainty, disturbances, and commands have reached a high level of maturity. The structured singular value (mu) frequency response methodology is presented
Multivariable nonlinear identification of smart buildings
NASA Astrophysics Data System (ADS)
Kim, Yeesock; Kim, Young Hoon; Lee, Seongsoo
2015-10-01
This paper presents a new multi-input-multi-output (MIMO) fuzzy model for nonlinear system identification (SI) of smart structures under a variety of random forces. The fuzzy SI model is developed through the integration of wavelet transform (WT), multiple MIMO linear autoregressive exogenous (ARX) input models, Takagi-Sugeno (TS) fuzzy model, weighted linear least squares, and data clustering algorithms: MIMO WARX-TS fuzzy model. To demonstrate the effectiveness of the MIMO WARX-TS fuzzy model, a three-story building equipped with a magnetorheological (MR) damper under a variety of random signals is investigated. To train the proposed model, an artificial earthquake and control forces are used as input signals while displacement and acceleration responses are used as outputs. To validate the trained model, four real recorded earthquake signals are used. It is shown from the simulation that the proposed MIMO WARX-TS fuzzy identification algorithm is effective in estimating nonlinear behavior of a building-MR damper system under a variety of seismic excitations.
Guaranteed robustness properties of multivariable nonlinear stochastic optimal regulators
NASA Technical Reports Server (NTRS)
Tsitsiklis, J. N.; Athans, M.
1984-01-01
The robustness of optimal regulators for nonlinear, deterministic and stochastic, multi-input dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.
Guaranteed robustness properties of multivariable, nonlinear, stochastic optimal regulators
NASA Technical Reports Server (NTRS)
Tsitsiklis, J. N.; Athans, M.
1983-01-01
The robustness of optimal regulators for nonlinear, deterministic and stochastic, multi-input dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.
NASA Technical Reports Server (NTRS)
Callier, F. M.; Desoer, C. A.
1973-01-01
A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.
NASA Technical Reports Server (NTRS)
Leininger, G. G.
1981-01-01
Using nonlinear digital simulation as a representative model of the dynamic operation of the QCSEE turbofan engine, a feedback control system is designed by variable frequency design techniques. Transfer functions are generated for each of five power level settings covering the range of operation from approach power to full throttle (62.5% to 100% full power). These transfer functions are then used by an interactive control system design synthesis program to provide a closed loop feedback control using the multivariable Nyquist array and extensions to multivariable Bode diagrams and Nichols charts.
ERIC Educational Resources Information Center
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
NASA Astrophysics Data System (ADS)
Kannan, Rohit; Tangirala, Arun K.
2014-06-01
Identification of directional influences in multivariate systems is of prime importance in several applications of engineering and sciences such as plant topology reconstruction, fault detection and diagnosis, and neurosciences. A spectrum of related directionality measures, ranging from linear measures such as partial directed coherence (PDC) to nonlinear measures such as transfer entropy, have emerged over the past two decades. The PDC-based technique is simple and effective, but being a linear directionality measure has limited applicability. On the other hand, transfer entropy, despite being a robust nonlinear measure, is computationally intensive and practically implementable only for bivariate processes. The objective of this work is to develop a nonlinear directionality measure, termed as KPDC, that possesses the simplicity of PDC but is still applicable to nonlinear processes. The technique is founded on a nonlinear measure called correntropy, a recently proposed generalized correlation measure. The proposed method is equivalent to constructing PDC in a kernel space where the PDC is estimated using a vector autoregressive model built on correntropy. A consistent estimator of the KPDC is developed and important theoretical results are established. A permutation scheme combined with the sequential Bonferroni procedure is proposed for testing hypothesis on absence of causality. It is demonstrated through several case studies that the proposed methodology effectively detects Granger causality in nonlinear processes.
Multivariable control systems with saturating actuators antireset windup strategies
NASA Technical Reports Server (NTRS)
Kapasouris, P.; Athans, M.
1985-01-01
Preliminary, promising, results for introducing antireset windup (ARW) properties in multivariable feedback control systems with multiple saturating actuator nonlinearities and integrating actions are presented. The ARW method introduces simple nonlinear feedback around the integrators. The multiloop circle criterion is used to derive sufficient conditions for closed-loop stability that employ frequency-domain singular value tests. The improvement in transient response due to the ARW feedback is demonstrated using a 2-input 2-outpurt control system based upon F-404 jet engine dynamics.
[A multivariate nonlinear model for quantitative analysis in laser-induced breakdown spectroscopy].
Chen, Xing-Long; Fu, Hong-Bo; Wang, Jing-Ge; Ni, Zhi-Bo; He, Wen-Gan; Xu, Jun; Rao Rui-zhong; Dong, Rui-Zhong
2014-11-01
Most quantitative models used in laser-induced breakdown spectroscopy (LIBS) are based on the hypothesis that laser-induced plasma approaches the state of local thermal equilibrium (LTE). However, the local equilibrium is possible only at a specific time segment during the evolution. As the populations of each energy level does not follow Boltzmann distribution in non-LTE condition, those quantitative models using single spectral line would be inaccurate. A multivariate nonlinear model, in which the LTE is not required, was proposed in this article to reduce the signal fluctuation and improve the accuracy of quantitative analysis. This multivariate nonlinear model was compared with the internal calibration model which is based on the LTE condition. The content of Mn in steel samples was determined by using the two models, respectively. A minor error and a minor relative standard deviation (RSD) were observed in multivariate nonlinear model. This result demonstrates that multivariate nonlinear model can improve measurement accuracy and repeatability.
Data-based virtual unmodeled dynamics driven multivariable nonlinear adaptive switching control.
Chai, Tianyou; Zhang, Yajun; Wang, Hong; Su, Chun-Yi; Sun, Jing
2011-12-01
For a complex industrial system, its multivariable and nonlinear nature generally make it very difficult, if not impossible, to obtain an accurate model, especially when the model structure is unknown. The control of this class of complex systems is difficult to handle by the traditional controller designs around their operating points. This paper, however, explores the concepts of controller-driven model and virtual unmodeled dynamics to propose a new design framework. The design consists of two controllers with distinct functions. First, using input and output data, a self-tuning controller is constructed based on a linear controller-driven model. Then the output signals of the controller-driven model are compared with the true outputs of the system to produce so-called virtual unmodeled dynamics. Based on the compensator of the virtual unmodeled dynamics, the second controller based on a nonlinear controller-driven model is proposed. Those two controllers are integrated by an adaptive switching control algorithm to take advantage of their complementary features: one offers stabilization function and another provides improved performance. The conditions on the stability and convergence of the closed-loop system are analyzed. Both simulation and experimental tests on a heavily coupled nonlinear twin-tank system are carried out to confirm the effectiveness of the proposed method.
Estimating the decomposition of predictive information in multivariate systems
NASA Astrophysics Data System (ADS)
Faes, Luca; Kugiumtzis, Dimitris; Nollo, Giandomenico; Jurysta, Fabrice; Marinazzo, Daniele
2015-03-01
In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of conditional mutual information, to the present target process. Moreover, it computes all information-theoretic quantities using a nearest-neighbor technique designed to compensate the bias due to the different dimensionality of individual entropy terms. The resulting estimators of prediction entropy, storage entropy, transfer entropy, and partial transfer entropy are tested on simulations of coupled linear stochastic and nonlinear deterministic dynamic processes, demonstrating the superiority of the proposed approach over the traditional estimators based on uniform embedding. The framework is then applied to multivariate physiologic time series, resulting in physiologically well-interpretable information decompositions of cardiovascular and cardiorespiratory interactions during head-up tilt and of joint brain-heart dynamics during sleep.
NASA Astrophysics Data System (ADS)
Bayati, Basil S.; Eckhoff, Philip A.
2012-12-01
We perform a high-order analytical expansion of the epidemiological susceptible-infectious-recovered multivariate master equation and include terms up to and beyond single-particle fluctuations. It is shown that higher order approximations yield qualitatively different results than low-order approximations, which is incident to the influence of additional nonlinear fluctuations. The fluctuations can be related to a meaningful physical parameter, the basic reproductive number, which is shown to dictate the rate of divergence in absolute terms from the ordinary differential equations more so than the total number of persons in the system. In epidemiological terms, the effect of single-particle fluctuations ought to be taken into account as the reproductive number approaches unity.
Nonlinear systems in medicine.
Higgins, John P.
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107
An Integrated Multivariable Artificial Pancreas Control System
Turksoy, Kamuran; Quinn, Lauretta T.; Littlejohn, Elizabeth
2014-01-01
The objective was to develop a closed-loop (CL) artificial pancreas (AP) control system that uses continuous measurements of glucose concentration and physiological variables, integrated with a hypoglycemia early alarm module to regulate glucose concentration and prevent hypoglycemia. Eleven open-loop (OL) and 9 CL experiments were performed. A multivariable adaptive artificial pancreas (MAAP) system was used for the first 6 CL experiments. An integrated multivariable adaptive artificial pancreas (IMAAP) system consisting of MAAP augmented with a hypoglycemia early alarm system was used during the last 3 CL experiments. Glucose values and physical activity information were measured and transferred to the controller every 10 minutes and insulin suggestions were entered to the pump manually. All experiments were designed to be close to real-life conditions. Severe hypoglycemic episodes were seen several times during the OL experiments. With the MAAP system, the occurrence of severe hypoglycemia was decreased significantly (P < .01). No hypoglycemia was seen with the IMAAP system. There was also a significant difference (P < .01) between OL and CL experiments with regard to percentage of glucose concentration (54% vs 58%) that remained within target range (70-180 mg/dl). Integration of an adaptive control and hypoglycemia early alarm system was able to keep glucose concentration values in target range in patients with type 1 diabetes. Postprandial hypoglycemia and exercise-induced hypoglycemia did not occur when this system was used. Physical activity information improved estimation of the blood glucose concentration and effectiveness of the control system. PMID:24876613
An integrated multivariable artificial pancreas control system.
Turksoy, Kamuran; Quinn, Lauretta T; Littlejohn, Elizabeth; Cinar, Ali
2014-05-01
The objective was to develop a closed-loop (CL) artificial pancreas (AP) control system that uses continuous measurements of glucose concentration and physiological variables, integrated with a hypoglycemia early alarm module to regulate glucose concentration and prevent hypoglycemia. Eleven open-loop (OL) and 9 CL experiments were performed. A multivariable adaptive artificial pancreas (MAAP) system was used for the first 6 CL experiments. An integrated multivariable adaptive artificial pancreas (IMAAP) system consisting of MAAP augmented with a hypoglycemia early alarm system was used during the last 3 CL experiments. Glucose values and physical activity information were measured and transferred to the controller every 10 minutes and insulin suggestions were entered to the pump manually. All experiments were designed to be close to real-life conditions. Severe hypoglycemic episodes were seen several times during the OL experiments. With the MAAP system, the occurrence of severe hypoglycemia was decreased significantly (P < .01). No hypoglycemia was seen with the IMAAP system. There was also a significant difference (P < .01) between OL and CL experiments with regard to percentage of glucose concentration (54% vs 58%) that remained within target range (70-180 mg/dl). Integration of an adaptive control and hypoglycemia early alarm system was able to keep glucose concentration values in target range in patients with type 1 diabetes. Postprandial hypoglycemia and exercise-induced hypoglycemia did not occur when this system was used. Physical activity information improved estimation of the blood glucose concentration and effectiveness of the control system.
Multivariate, non-linear trend analysis of heterogeneous water quality monitoring data
NASA Astrophysics Data System (ADS)
Lischeid, Gunnar; Kalettka, Thomas; Steidl, Jörg; Merz, Christoph; Lehr, Christian
2014-05-01
Comprehensive water quality monitoring is considered a necessary prerequisite for sound water resources management and a valuable source for science. In practice, however, use of large monitoring data sets is often limited due to heterogeneous data sources, spatially and temporally variable monitoring schemes, non-equidistant sampling, large natural variability, and, last but not least, by the sheer size of the data sets that makes identification of unexpected peculiarities a tedious task. As a consequence, any initiation of gradual long-term system shifts can hardly be detected, especially as long as it is restricted to a small fraction of sampling sites. In addition, trends might be limited to a rather small subset of sampling sites or to certain periods of time and might thus escape attention. Usually, numerous solutes are monitored in parallel, but trend analyses are performed for each solute separately. However, in water quality samples trends are hardly restricted to single solutes, but affect various solutes synchronously in a characteristic way. Thus performing joint multivariate trend analyses would not only save effort and time, but would yield more robust assessments of system shifts. We present a non-linear multivariate data visualization approach that allows a rapid assessment of non-linear, possibly local trends and unexpected behaviour in large water quality monitoring data sets. It consists of a combination of Self-Organizing Maps and Sammon's Mapping (SOM-SM). The approach was applied to a data set of 2900 water samples, each comprising 13 solutes, compiled from various monitoring programs in the Federal State of Brandenburg (Germany). In total, 128 stream water, groundwater and small pond sites had been sampled between 1994 and 2012 at different and irregular time intervals. The SOM-SM product is a graph where every sample is represented by a symbol. Location of the symbols in the graph is optimized such that the distance between any two symbols
Uniform approach to linear and nonlinear interrelation patterns in multivariate time series.
Rummel, Christian; Abela, Eugenio; Müller, Markus; Hauf, Martinus; Scheidegger, Olivier; Wiest, Roland; Schindler, Kaspar
2011-06-01
Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.
Uniform approach to linear and nonlinear interrelation patterns in multivariate time series
NASA Astrophysics Data System (ADS)
Rummel, Christian; Abela, Eugenio; Müller, Markus; Hauf, Martinus; Scheidegger, Olivier; Wiest, Roland; Schindler, Kaspar
2011-06-01
Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.
Non-linear multivariate curve resolution analysis of voltammetric pH titrations.
Díaz Cruz, José Manuel; Sanchís, Josep; Chekmeneva, Elena; Ariño, Cristina; Esteban, Miquel
2010-07-01
A new chemometric approach is put forward, dealing with the non-linear behaviour observed in the multivariate curve resolution (MCR) analysis of certain overlapping voltammetric signals obtained in titrations of metal complexes where pH is progressively changed. In such cases, non-reversible reduction signals move along the potential axis as a consequence of the involvement of H(+)-ions in the electrochemical process and cause a dramatic loss of linearity, which hinders accurate MCR analysis. The method proposed is based on the least-squares fitting of peak potential vs. pH datasets to parametric linear and sigmoid functions through the decomposition of the data matrix into both a concentration profile matrix and a unit signal matrix, in a similar way as in the alternating least-squares algorithm of MCR (ALS). Such calculations are carried out through several home-made Matlab programs which are freely available as Supplementary Material of the present work. The fitted parameters, along with the evolution of resolved concentrations and potential shifts with pH, provide valuable information on the complexation/reduction processes. The method is tested first on the relatively simple Cd(II)-NTA system and then applied to the study of the binding of Cd(II)-ions by glutathione (gamma-Glu-Cys-Gly, GSH) and the phytochelatin PC(2) ((gamma-Glu-Cys)(2)-Gly).
Apparatus and system for multivariate spectral analysis
Keenan, Michael R.; Kotula, Paul G.
2003-06-24
An apparatus and system for determining the properties of a sample from measured spectral data collected from the sample by performing a method of multivariate spectral analysis. The method can include: generating a two-dimensional matrix A containing measured spectral data; providing a weighted spectral data matrix D by performing a weighting operation on matrix A; factoring D into the product of two matrices, C and S.sup.T, by performing a constrained alternating least-squares analysis of D=CS.sup.T, where C is a concentration intensity matrix and S is a spectral shapes matrix; unweighting C and S by applying the inverse of the weighting used previously; and determining the properties of the sample by inspecting C and S. This method can be used by a spectrum analyzer to process X-ray spectral data generated by a spectral analysis system that can include a Scanning Electron Microscope (SEM) with an Energy Dispersive Detector and Pulse Height Analyzer.
Multivariate and Multiscale Data Assimilation in Terrestrial Systems: A Review
Montzka, Carsten; Pauwels, Valentijn R. N.; Franssen, Harrie-Jan Hendricks; Han, Xujun; Vereecken, Harry
2012-01-01
More and more terrestrial observational networks are being established to monitor climatic, hydrological and land-use changes in different regions of the World. In these networks, time series of states and fluxes are recorded in an automated manner, often with a high temporal resolution. These data are important for the understanding of water, energy, and/or matter fluxes, as well as their biological and physical drivers and interactions with and within the terrestrial system. Similarly, the number and accuracy of variables, which can be observed by spaceborne sensors, are increasing. Data assimilation (DA) methods utilize these observations in terrestrial models in order to increase process knowledge as well as to improve forecasts for the system being studied. The widely implemented automation in observing environmental states and fluxes makes an operational computation more and more feasible, and it opens the perspective of short-time forecasts of the state of terrestrial systems. In this paper, we review the state of the art with respect to DA focusing on the joint assimilation of observational data precedents from different spatial scales and different data types. An introduction is given to different DA methods, such as the Ensemble Kalman Filter (EnKF), Particle Filter (PF) and variational methods (3/4D-VAR). In this review, we distinguish between four major DA approaches: (1) univariate single-scale DA (UVSS), which is the approach used in the majority of published DA applications, (2) univariate multiscale DA (UVMS) referring to a methodology which acknowledges that at least some of the assimilated data are measured at a different scale than the computational grid scale, (3) multivariate single-scale DA (MVSS) dealing with the assimilation of at least two different data types, and (4) combined multivariate multiscale DA (MVMS). Finally, we conclude with a discussion on the advantages and disadvantages of the assimilation of multiple data types in a
Multivariate and multiscale data assimilation in terrestrial systems: a review.
Montzka, Carsten; Pauwels, Valentijn R N; Franssen, Harrie-Jan Hendricks; Han, Xujun; Vereecken, Harry
2012-11-26
More and more terrestrial observational networks are being established to monitor climatic, hydrological and land-use changes in different regions of the World. In these networks, time series of states and fluxes are recorded in an automated manner, often with a high temporal resolution. These data are important for the understanding of water, energy, and/or matter fluxes, as well as their biological and physical drivers and interactions with and within the terrestrial system. Similarly, the number and accuracy of variables, which can be observed by spaceborne sensors, are increasing. Data assimilation (DA) methods utilize these observations in terrestrial models in order to increase process knowledge as well as to improve forecasts for the system being studied. The widely implemented automation in observing environmental states and fluxes makes an operational computation more and more feasible, and it opens the perspective of short-time forecasts of the state of terrestrial systems. In this paper, we review the state of the art with respect to DA focusing on the joint assimilation of observational data precedents from different spatial scales and different data types. An introduction is given to different DA methods, such as the Ensemble Kalman Filter (EnKF), Particle Filter (PF) and variational methods (3/4D-VAR). In this review, we distinguish between four major DA approaches: (1) univariate single-scale DA (UVSS), which is the approach used in the majority of published DA applications, (2) univariate multiscale DA (UVMS) referring to a methodology which acknowledges that at least some of the assimilated data are measured at a different scale than the computational grid scale, (3) multivariate single-scale DA (MVSS) dealing with the assimilation of at least two different data types, and (4) combined multivariate multiscale DA (MVMS). Finally, we conclude with a discussion on the advantages and disadvantages of the assimilation of multiple data types in a
NASA Astrophysics Data System (ADS)
Sarhadi, Ali; Burn, Donald H.; Johnson, Fiona; Mehrotra, Raj; Sharma, Ashish
2016-05-01
Accurate projection of global warming on the probabilistic behavior of hydro-climate variables is one of the main challenges in climate change impact assessment studies. Due to the complexity of climate-associated processes, different sources of uncertainty influence the projected behavior of hydro-climate variables in regression-based statistical downscaling procedures. The current study presents a comprehensive methodology to improve the predictive power of the procedure to provide improved projections. It does this by minimizing the uncertainty sources arising from the high-dimensionality of atmospheric predictors, the complex and nonlinear relationships between hydro-climate predictands and atmospheric predictors, as well as the biases that exist in climate model simulations. To address the impact of the high dimensional feature spaces, a supervised nonlinear dimensionality reduction algorithm is presented that is able to capture the nonlinear variability among projectors through extracting a sequence of principal components that have maximal dependency with the target hydro-climate variables. Two soft-computing nonlinear machine-learning methods, Support Vector Regression (SVR) and Relevance Vector Machine (RVM), are engaged to capture the nonlinear relationships between predictand and atmospheric predictors. To correct the spatial and temporal biases over multiple time scales in the GCM predictands, the Multivariate Recursive Nesting Bias Correction (MRNBC) approach is used. The results demonstrate that this combined approach significantly improves the downscaling procedure in terms of precipitation projection.
KINETIC ANALYSIS OF HIGH-NITROGEN ENERGETIC MATERIALS USING MULTIVARIATE NONLINEAR REGRESSION
Campbell, M. S.; Rabie, R. L.; Diaz-Acosta, I.; Pulay, P.
2001-01-01
New high-nitrogen energetic materials were synthesized by Hiskey and Naud. J. Opfermann reported a new tool for finding the probable model of the complex reactions using multivariate non-linear regression analysis of DSC and TGA data from several measurements run at different heating rates. This study is to take the kinetic parameters from the different steps and discover which reaction step is responsible for the runaway reaction by comparing predicted results from the Frank-Kamenetsckii equation with the critical temperature found experimentally using the modified Henkin test.
Gries, J M; Verotta, D
2000-08-01
In a frequently performed pharmacokinetics study, different subjects are given different doses of a drug. After each dose is given, drug concentrations are observed according to the same sampling design. The goal of the experiment is to obtain a representation for the pharmacokinetics of the drug, and to determine if drug concentrations observed at different times after a dose are linear in respect to dose. The goal of this paper is to obtain a representation for concentration as a function of time and dose, which (a) makes no assumptions on the underlying pharmacokinetics of the drug; (b) takes into account the repeated measure structure of the data; and (c) detects nonlinearities in respect to dose. To address (a) we use a multivariate adaptive regression splines representation (MARS), which we recast into a linear mixed-effects model, addressing (b). To detect nonlinearity we describe a general algorithm that obtains nested (mixed-effect) MARS representations. In the pharmacokinetics application, the algorithm obtains representations containing time, and time and dose, respectively, with the property that the bases functions of the first representation are a subset of the second. Standard statistical model selection criteria are used to select representations linear or nonlinear in respect to dose. The method can be applied to a variety of pharmacokinetics (and pharmacodynamic) preclinical and phase I-III trials. Examples of applications of the methodology to real and simulated data are reported.
NASA Technical Reports Server (NTRS)
Meyer, George
1997-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
NASA Technical Reports Server (NTRS)
Meyer, George; Null, Cynthia H. (Technical Monitor)
1996-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordination, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
Ecological prediction with nonlinear multivariate time-frequency functional data models
Yang, Wen-Hsi; Wikle, Christopher K.; Holan, Scott H.; Wildhaber, Mark L.
2013-01-01
Time-frequency analysis has become a fundamental component of many scientific inquiries. Due to improvements in technology, the amount of high-frequency signals that are collected for ecological and other scientific processes is increasing at a dramatic rate. In order to facilitate the use of these data in ecological prediction, we introduce a class of nonlinear multivariate time-frequency functional models that can identify important features of each signal as well as the interaction of signals corresponding to the response variable of interest. Our methodology is of independent interest and utilizes stochastic search variable selection to improve model selection and performs model averaging to enhance prediction. We illustrate the effectiveness of our approach through simulation and by application to predicting spawning success of shovelnose sturgeon in the Lower Missouri River.
NASA Astrophysics Data System (ADS)
Okou, Francis A.; Akhrif, Ouassima; Dessaint, Louis A.; Bouchard, Derrick
2013-05-01
This papter introduces a decentralized multivariable robust adaptive voltage and frequency regulator to ensure the stability of large-scale interconnnected generators. Interconnection parameters (i.e. load, line and transormer parameters) are assumed to be unknown. The proposed design approach requires the reformulation of conventiaonal power system models into a multivariable model with generator terminal voltages as state variables, and excitation and turbine valve inputs as control signals. This model, while suitable for the application of modern control methods, introduces problems with regards to current design techniques for large-scale systems. Interconnection terms, which are treated as perturbations, do not meet the common matching condition assumption. A new adaptive method for a certain class of large-scale systems is therefore introduces that does not require the matching condition. The proposed controller consists of nonlinear inputs that cancel some nonlinearities of the model. Auxiliary controls with linear and nonlinear components are used to stabilize the system. They compensate unknown parametes of the model by updating both the nonlinear component gains and excitation parameters. The adaptation algorithms involve the sigma-modification approach for auxiliary control gains, and the projection approach for excitation parameters to prevent estimation drift. The computation of the matrix-gain of the controller linear component requires the resolution of an algebraic Riccati equation and helps to solve the perturbation-mismatching problem. A realistic power system is used to assess the proposed controller performance. The results show that both stability and transient performance are considerably improved following a severe contingency.
Steady-state decoupling and design of linear multivariable systems
NASA Technical Reports Server (NTRS)
Thaler, G. J.
1974-01-01
A constructive criterion for decoupling the steady states of a linear time-invariant multivariable system is presented. This criterion consists of a set of inequalities which, when satisfied, will cause the steady states of a system to be decoupled. Stability analysis and a new design technique for such systems are given. A new and simple connection between single-loop and multivariable cases is found. These results are then applied to the compensation design for NASA STOL C-8A aircraft. Both steady-state decoupling and stability are justified through computer simulations.
Fixed order dynamic compensation for multivariable linear systems
NASA Technical Reports Server (NTRS)
Kramer, F. S.; Calise, A. J.
1986-01-01
This paper considers the design of fixed order dynamic compensators for multivariable time invariant linear systems, minimizing a linear quadratic performance cost functional. Attention is given to robustness issues in terms of multivariable frequency domain specifications. An output feedback formulation is adopted by suitably augmenting the system description to include the compensator states. Either a controller or observer canonical form is imposed on the compensator description to reduce the number of free parameters to its minimal number. The internal structure of the compensator is prespecified by assigning a set of ascending feedback invariant indices, thus forming a Brunovsky structure for the nominal compensator.
Design of multivariable feedback control systems via spectral assignment
NASA Technical Reports Server (NTRS)
Mielke, R. R.; Tung, L. J.; Marefat, M.
1983-01-01
The applicability of spectral assignment techniques to the design of multivariable feedback control systems was investigated. A fractional representation design procedure for unstable plants is presented and illustrated with an example. A computer aided design software package implementing eigenvalue/eigenvector design procedures is described. A design example which illustrates the use of the program is explained.
NASA Astrophysics Data System (ADS)
Zhang, Wei; Wang, Yagang; Liu, Yurong; Zhang, Weidong
2016-01-01
In this paper, an H2 analytical decoupling control scheme with multivariable disturbance observer for both stable and unstable multi-input/multi-output (MIMO) systems with multiple time delays is proposed. Compared with conventional control strategies, the main merit is that the proposed control scheme can improve the system performances effectively when the MIMO processes with severe model mismatches and strong external disturbances. Besides, the design method has three additional advantages. First, the derived controller and observer are given in analytical forms, the design procedure is simple. Second, the orders of the designed controller and observer are low, they can be implemented easily in practice. Finally, the performance and robustness can be adjusted easily by tuning the parameters in the designed controller and observer. It is useful for practical application. Simulations are provided to illustrate the effectiveness of the proposed control scheme.
Reconstructing embedding spaces of coupled dynamical systems from multivariate data.
Boccaletti, S; Valladares, D L; Pecora, Louis M; Geffert, Hite P; Carroll, T
2002-03-01
A method for reconstructing dimensions of subspaces for weakly coupled dynamical systems is offered. The tool is able to extrapolate the subspace dimensions from the zero coupling limit, where the division of dimensions as per the algorithm is exact. Implementation of the proposed technique to multivariate data demonstrates its effectiveness in disentangling subspace dimensionalities also in the case of emergent synchronized motions, for both numerical and experimental systems.
Nonlinear input-output systems
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Luksic, Mladen; Su, Renjeng
1987-01-01
Necessary and sufficient conditions that the nonlinear system dot-x = f(x) + ug(x) and y = h(x) be locally feedback equivalent to the controllable linear system dot-xi = A xi + bv and y = C xi having linear output are found. Only the single input and single output case is considered, however, the results generalize to multi-input and multi-output systems.
A method for designing robust multivariable feedback systems
NASA Technical Reports Server (NTRS)
Milich, David Albert; Athans, Michael; Valavani, Lena; Stein, Gunter
1988-01-01
A new methodology is developed for the synthesis of linear, time-invariant (LTI) controllers for multivariable LTI systems. The aim is to achieve stability and performance robustness of the feedback system in the presence of multiple unstructured uncertainty blocks; i.e., to satisfy a frequency-domain inequality in terms of the structured singular value. The design technique is referred to as the Causality Recovery Methodology (CRM). Starting with an initial (nominally) stabilizing compensator, the CRM produces a closed-loop system whose performance-robustness is at least as good as, and hopefully superior to, that of the original design. The robustness improvement is obtained by solving an infinite-dimensional, convex optimization program. A finite-dimensional implementation of the CRM was developed, and it was applied to a multivariate design example.
Bilgel, Murat; Prince, Jerry L; Wong, Dean F; Resnick, Susan M; Jedynak, Bruno M
2016-07-01
It is important to characterize the temporal trajectories of disease-related biomarkers in order to monitor progression and identify potential points of intervention. These are especially important for neurodegenerative diseases, as therapeutic intervention is most likely to be effective in the preclinical disease stages prior to significant neuronal damage. Neuroimaging allows for the measurement of structural, functional, and metabolic integrity of the brain at the level of voxels, whose volumes are on the order of mm(3). These voxelwise measurements provide a rich collection of disease indicators. Longitudinal neuroimaging studies enable the analysis of changes in these voxelwise measures. However, commonly used longitudinal analysis approaches, such as linear mixed effects models, do not account for the fact that individuals enter a study at various disease stages and progress at different rates, and generally consider each voxelwise measure independently. We propose a multivariate nonlinear mixed effects model for estimating the trajectories of voxelwise neuroimaging biomarkers from longitudinal data that accounts for such differences across individuals. The method involves the prediction of a progression score for each visit based on a collective analysis of voxelwise biomarker data within an expectation-maximization framework that efficiently handles large amounts of measurements and variable number of visits per individual, and accounts for spatial correlations among voxels. This score allows individuals with similar progressions to be aligned and analyzed together, which enables the construction of a trajectory of brain changes as a function of an underlying progression or disease stage. We apply our method to studying cortical β-amyloid deposition, a hallmark of preclinical Alzheimer's disease, as measured using positron emission tomography. Results on 104 individuals with a total of 300 visits suggest that precuneus is the earliest cortical region to
Topics in complex nonlinear systems
NASA Astrophysics Data System (ADS)
Ying, Linghang
In the dissertation, I include two topics of my research in nonlinear dynamic systems. In the first topic, we use numerical optimization techniques to investigate the behavior of the success rates for two- and three-qubit entangling gates, first for perfect fidelity, and then extended to imperfect gates. We find that as the perfect fidelity condition is relaxed, the maximum attainable success rates increase in a predictable fashion depending on the size of the system, and we compare that rate of increase for several gates. Finally, we propose an experiment to test our imperfect LOQC gates using number-resolving photon detectors. We suggest a relatively simple physical apparatus capable of producing CZ gates with controllable fidelity less than 1 and success rates higher than the current theoretical maximum (S=2/27) for perfect fidelity. These experimental setups are within the reach of many experimental groups and would provide an interesting experiment in photonic quantum computing. In the second topic, we quantitatively study nonlinear effects on the evolution of surface gravity waves on the ocean, to explore systematically the effects of various input parameters on the probability of rogue wave formation. The fourth-order current-modified nonlinear Schrodinger equation (CNLS4) is employed to describe the wave evolution. First, we show that when the average wave steepness is small and nonlinear wave effects are subleading, the wave height distribution is well explained by a single "freak index" parameter, which describes the strength of (linear) wave scattering by random currents relative to the angular spread of the incoming random sea. When the average steepness is large, the wave height distribution takes a very similar functional form, but the key variables determining the probability distribution are the steepness, and the angular and frequency spread of the incoming waves. Then, we obtain quantitative predictions for the wave height distribution as a
Noise in Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Moss, Frank; McClintock, P. V. E.
2009-08-01
List of contributors; Preface; Introduction to volume three; 1. The effects of coloured quadratic noise on a turbulent transition in liquid He II J. T. Tough; 2. Electrohydrodynamic instability of nematic liquid crystals: growth process and influence of noise S. Kai; 3. Suppression of electrohydrodynamic instabilities by external noise Helmut R. Brand; 4. Coloured noise in dye laser fluctuations R. Roy, A. W. Yu and S. Zhu; 5. Noisy dynamics in optically bistable systems E. Arimondo, D. Hennequin and P. Glorieux; 6. Use of an electronic model as a guideline in experiments on transient optical bistability W. Lange; 7. Computer experiments in nonlinear stochastic physics Riccardo Mannella; 8. Analogue simulations of stochastic processes by means of minimum component electronic devices Leone Fronzoni; 9. Analogue techniques for the study of problems in stochastic nonlinear dynamics P. V. E. McClintock and Frank Moss; Index.
Robust Decentralized Nonlinear Control for a Twin Rotor MIMO System
Belmonte, Lidia María; Morales, Rafael; Fernández-Caballero, Antonio; Somolinos, José Andrés
2016-01-01
This article presents the design of a novel decentralized nonlinear multivariate control scheme for an underactuated, nonlinear and multivariate laboratory helicopter denominated the twin rotor MIMO system (TRMS). The TRMS is characterized by a coupling effect between rotor dynamics and the body of the model, which is due to the action-reaction principle originated in the acceleration and deceleration of the motor-propeller groups. The proposed controller is composed of two nested loops that are utilized to achieve stabilization and precise trajectory tracking tasks for the controlled position of the generalized coordinates of the TRMS. The nonlinear internal loop is used to control the electrical dynamics of the platform, and the nonlinear external loop allows the platform to be perfectly stabilized and positioned in space. Finally, we illustrate the theoretical control developments with a set of experiments in order to verify the effectiveness of the proposed nonlinear decentralized feedback controller, in which a comparative study with other controllers is performed, illustrating the excellent performance of the proposed robust decentralized control scheme in both stabilization and trajectory tracking tasks. PMID:27472338
Kuramoto, Lisa; Cragg, Jacquelyn; Nandhagopal, Ramachandiran; Mak, Edwin; Sossi, Vesna; de la Fuente-Fernández, Raul; Stoessl, A. Jon; Schulzer, Michael
2013-01-01
Background To date, statistical methods that take into account fully the non-linear, longitudinal and multivariate aspects of clinical data have not been applied to the study of progression in Parkinson’s disease (PD). In this paper, we demonstrate the usefulness of such methodology for studying the temporal and spatial aspects of the progression of PD. Extending this methodology further, we also explore the presymptomatic course of this disease. Methods Longitudinal Positron Emission Tomography (PET) measurements were collected on 78 PD patients, from 4 subregions on each side of the brain, using 3 different radiotracers. Non-linear, multivariate, longitudinal random effects modelling was applied to analyze and interpret these data. Results The data showed a non-linear decline in PET measurements, which we modelled successfully by an exponential function depending on two patient-related covariates duration since symptom onset and age at symptom onset. We found that the degree of damage was significantly greater in the posterior putamen than in the anterior putamen throughout the disease. We also found that over the course of the illness, the difference between the less affected and more affected sides of the brain decreased in the anterior putamen. Younger patients had significantly poorer measurements than older patients at the time of symptom onset suggesting more effective compensatory mechanisms delaying the onset of symptoms. Cautious extrapolation showed that disease onset had occurred some 8 to 17 years prior to symptom onset. Conclusions Our model provides important biological insights into the pathogenesis of PD, as well as its preclinical aspects. Our methodology can be applied widely to study many other chronic progressive diseases. PMID:24204641
Investigation of a Nonlinear Control System
NASA Technical Reports Server (NTRS)
Flugge-Lotz, I; Taylor, C F; Lindberg, H E
1958-01-01
A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.
On stability theory. [of nonlinear feedback control systems
NASA Technical Reports Server (NTRS)
Safonov, M. G.; Athans, M.
1979-01-01
It is found that under mild assumptions, feedback system stability can be concluded if one can 'topologically separate' the infinite-dimensional function space containing the system's dynamical input-output relations into two regions, one region containing the dynamical input-output relation of the 'feedforward' element of the system and the other region containing the dynamical output-input relation of the 'feedback' element. Nonlinear system stability criteria of both the input-output type and the state-space (Liapunov) type are interpreted in this context. The abstract generality and conceptual simplicity afforded by the topological separation perspective clarifies some of the basic issues underlying stability theory and serves to suggest improvements in existing stability criteria. A generalization of Zames' (1966) conic-relation stability criterion is proved, laying the foundation for improved multivariable generalizations of the frequency-domain circle stability criterion for nonlinear systems.
A direct approach to the design of linear multivariable systems
NASA Technical Reports Server (NTRS)
Agrawal, B. L.
1974-01-01
Design of multivariable systems is considered and design procedures are formulated in the light of the most recent work on model matching. The word model matching is used exclusively to mean matching the input-output behavior of two systems. The term is used in the frequency domain to indicate the comparison of two transfer matrices containing transfer functions as elements. Design methods where non-interaction is not used as a criteria were studied. Two design methods are considered. The first method of design is based solely upon the specification of generalized error coefficients for each individual transfer function of the overall system transfer matrix. The second design method is called the pole fixing method because all the system poles are fixed at preassigned positions. The zeros of terms either above or below the diagonal are partially fixed via steady state error coefficients. The advantages and disadvantages of each method are discussed and an example is worked to demonstrate their uses. The special cases of triangular decoupling and minimum constraints are discussed.
A canonical form for nonlinear systems
NASA Technical Reports Server (NTRS)
Su, R.; Hunt, L. R.
1986-01-01
The concepts of transformation and canonical form have been used in analyzing linear systems. These ideas are extended to nonlinear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form. For control design involving a nonlinear system, one approach is to put the system in its canonical form and approximate by that part having only feedback paths.
NASA Astrophysics Data System (ADS)
Hussain, Mirza Zahid; Li, Fuguo; Wang, Jing; Yuan, Zhanwei; Li, Pan; Wu, Tao
2015-07-01
The present study comprises the determination of constitutive relationship for thermo-mechanical processing of INCONEL 718 through double multivariate nonlinear regression, a newly developed approach which not only considers the effect of strain, strain rate, and temperature on flow stress but also explains the interaction effect of these thermo-mechanical parameters on flow behavior of the alloy. Hot isothermal compression experiments were performed on Gleeble-3500 thermo-mechanical testing machine in the temperature range of 1153 to 1333 K within the strain rate range of 0.001 to 10 s-1. The deformation behavior of INCONEL 718 is analyzed and summarized by establishing the high temperature deformation constitutive equation. The calculated correlation coefficient ( R) and average absolute relative error ( AARE) underline the precision of proposed constitutive model.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Du, Jiajia
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results. PMID:24592160
Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory
NASA Technical Reports Server (NTRS)
Silva, Walter A.
1999-01-01
The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.
A nonlinear model with latent process for cognitive evolution using multivariate longitudinal data.
Proust, Cécile; Jacqmin-Gadda, Hélène; Taylor, Jeremy M G; Ganiayre, Julien; Commenges, Daniel
2006-12-01
Cognition is not directly measurable. It is assessed using psychometric tests, which can be viewed as quantitative measures of cognition with error. The aim of this article is to propose a model to describe the evolution in continuous time of unobserved cognition in the elderly and assess the impact of covariates directly on it. The latent cognitive process is defined using a linear mixed model including a Brownian motion and time-dependent covariates. The observed psychometric tests are considered as the results of parameterized nonlinear transformations of the latent cognitive process at discrete occasions. Estimation of the parameters contained both in the transformations and in the linear mixed model is achieved by maximizing the observed likelihood and graphical methods are performed to assess the goodness of fit of the model. The method is applied to data from PAQUID, a French prospective cohort study of ageing.
Multivariable Techniques for High-Speed Research Flight Control Systems
NASA Technical Reports Server (NTRS)
Newman, Brett A.
1999-01-01
This report describes the activities and findings conducted under contract with NASA Langley Research Center. Subject matter is the investigation of suitable multivariable flight control design methodologies and solutions for large, flexible high-speed vehicles. Specifically, methodologies are to address the inner control loops used for stabilization and augmentation of a highly coupled airframe system possibly involving rigid-body motion, structural vibrations, unsteady aerodynamics, and actuator dynamics. Design and analysis techniques considered in this body of work are both conventional-based and contemporary-based, and the vehicle of interest is the High-Speed Civil Transport (HSCT). Major findings include: (1) control architectures based on aft tail only are not well suited for highly flexible, high-speed vehicles, (2) theoretical underpinnings of the Wykes structural mode control logic is based on several assumptions concerning vehicle dynamic characteristics, and if not satisfied, the control logic can break down leading to mode destabilization, (3) two-loop control architectures that utilize small forward vanes with the aft tail provide highly attractive and feasible solutions to the longitudinal axis control challenges, and (4) closed-loop simulation sizing analyses indicate the baseline vane model utilized in this report is most likely oversized for normal loading conditions.
Nonlinear Mode-Coupling in Nanomechanical Systems
Matheny, M. H.; Villanueva, L. G.; Karabalin, R. B.; Sader, J. E.; Roukes, M. L.
2013-01-01
Understanding and controlling nonlinear coupling between vibrational modes is critical for the development of advanced nanomechanical devices; it has important implications for applications ranging from quantitative sensing to fundamental research. However, achieving accurate experimental characterization of nonlinearities in nanomechanical systems (NEMS) is problematic. Currently employed detection and actuation schemes themselves tend to be highly nonlinear, and this unrelated nonlinear response has been inadvertently convolved into many previous measurements. In this Letter we describe an experimental protocol and a highly linear transduction scheme, specifically designed for NEMS, that enables accurate, in situ characterization of device nonlinearities. By comparing predictions from Euler–Bernoulli theory for the intra- and intermodal nonlinearities of a doubly clamped beam, we assess the validity of our approach and find excellent agreement. PMID:23496001
Nonlinear Dynamics of Parametrically Excited Gyroscopic Systems
Namachchivaya. N.S.
2001-06-01
The primary objective of this project is to determine how some of the powerful geometric methods of dynamical systems can be applied to study nonlinear gyroscopic systems. We proposed to develop techniques to predict local and global behavior and instability mechanisms and to analyze the interactions between noise, stability, and nonlinearities inherent in gyroscopic systems. In order to obtain these results we use the method of normal forms, global bifurcation techniques, and various other dynamical systems tools.
Nonlinear model for building-soil systems
McCallen, D.B.; Romstad, K.M.
1994-05-01
A finite-element based, numerical analysis methodology has been developed for the nonlinear analysis of building-soil systems. The methodology utilizes a reduced-order, nonlinear continuum model to represent the building, and the soil is represented with a simple nonlinear two-dimensional plane strain finite element. The foundation of the building is idealized as a rigid block and the interface between the soil and the foundation is modeled with an interface contract element. The objectives of the current paper are to provide the theoretical development of the system model, with particular emphasis on the modeling of the foundation-soil contact, and to demonstrate the special-purpose finite-element program that has been developed for nonlinear analysis of the building-soil system. Examples are included that compare the results obtained with the special-purpose program with the results of a general-purpose nonlinear finite-element program.
On controllability of nonlinear stochastic systems
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Kim, J.-H.; Mahmudov, N. I.
2006-12-01
In this paper, complete controllability for nonlinear stochastic systems is studied. First this paper addresses the problem of complete controllability of nonlinear stochastic systems with standard Brownian motion. Then this result is extended to establish complete controllability criterion for stochastic systems with fractional Brownian motion. A fixed point approach is employed for achieving the required result. The solutions are given by a variation of constants formula which allows us to study the complete controllability for nonlinear stochastic systems. In this paper, we prove the complete controllability of nonlinear stochastic system under the natural assumption that the associated linear control system is completely controllable. Finally, an illustrative example is provided to show the usefulness of the proposed technique.
Nonlinear waves in PT -symmetric systems
NASA Astrophysics Data System (ADS)
Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.
2016-07-01
Recent progress on nonlinear properties of parity-time (PT )-symmetric systems is comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying PT symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a PT -symmetric system. The natural inclusion of nonlinearity into these PT systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above PT -symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear PT -symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of PT symmetry are pointed out.
NASA Technical Reports Server (NTRS)
Liberty, S. R.; Mielke, R. R.; Tung, L. J.
1981-01-01
Applied research in the area of spectral assignment in multivariable systems is reported. A frequency domain technique for determining the set of all stabilizing controllers for a single feedback loop multivariable system is described. It is shown that decoupling and tracking are achievable using this procedure. The technique is illustrated with a simple example.
ERIC Educational Resources Information Center
Hsieh, Fushing; Ferrer, Emilio; Chen, Shuchun; Mauss, Iris B.; John, Oliver; Gross, James J.
2011-01-01
We present an approach for evaluating coherence in multivariate systems that considers all the variables simultaneously. We operationalize the multivariate system as a network and define coherence as the efficiency with which a signal is transmitted throughout the network. We illustrate this approach with time series data from 15…
NASA Technical Reports Server (NTRS)
Kriegler, F.; Marshall, R.; Lampert, S.; Gordon, M.; Cornell, C.; Kistler, R.
1973-01-01
The MIDAS system is a prototype, multiple-pipeline digital processor mechanizing the multivariate-Gaussian, maximum-likelihood decision algorithm operating at 200,000 pixels/second. It incorporates displays and film printer equipment under control of a general purpose midi-computer and possesses sufficient flexibility that operational versions of the equipment may be subsequently specified as subsets of the system.
NASA Technical Reports Server (NTRS)
Young, G.
1982-01-01
A design methodology capable of dealing with nonlinear systems, such as a controlled ecological life support system (CELSS), containing parameter uncertainty is discussed. The methodology was applied to the design of discrete time nonlinear controllers. The nonlinear controllers can be used to control either linear or nonlinear systems. Several controller strategies are presented to illustrate the design procedure.
Nonlinear dynamics enabled systems design and control
NASA Astrophysics Data System (ADS)
Lacarbonara, Walter
2012-08-01
There is a growing interest towards design of high-performance structures and devices by seeking ways to exploit advantageously different nonlinearities at different scales rather than constraining operations to avoid nonlinear phenomena. Tools of robust nonlinear modeling and analysis are shown to be turned into design tools for achieving high levels of vibration control authority and synthesis of engineered systems and materials. A brief overview of methods and results on active resonance cancellation and passive nonlinear hysteretic vibration absorbers is illustrated. Recent results on the diffused hysteresis exhibited at the nano-microscale in nanocomposites due to the powerful nonlinear stick-slip mechanism exhibited by carbon nanotubes dispersed in a hosting matrix are discussed. The optimization of the main microstructural parameters is shown to lead to unprecedented levels of damping capacity in next-generation nanostructured materials tailored for wide-band vibrational energy dissipation.
A System of Multivariable Krawtchouk Polynomials and a Probabilistic Application
NASA Astrophysics Data System (ADS)
Grünbaum, F. Alberto; Rahman, Mizan
2011-12-01
The one variable Krawtchouk polynomials, a special case of the 2F1 function did appear in the spectral representation of the transition kernel for a Markov chain studied a long time ago by M. Hoare and M. Rahman. A multivariable extension of this Markov chain was considered in a later paper by these authors where a certain two variable extension of the F1 Appel function shows up in the spectral analysis of the corresponding transition kernel. Independently of any probabilistic consideration a certain multivariable version of the Gelfand-Aomoto hypergeometric function was considered in papers by H. Mizukawa and H. Tanaka. These authors and others such as P. Iliev and P. Tertwilliger treat the two-dimensional version of the Hoare-Rahman work from a Lie-theoretic point of view. P. Iliev then treats the general n-dimensional case. All of these authors proved several properties of these functions. Here we show that these functions play a crucial role in the spectral analysis of the transition kernel that comes from pushing the work of Hoare-Rahman to the multivariable case. The methods employed here to prove this as well as several properties of these functions are completely different to those used by the authors mentioned above.
Nonlinear dynamical system approaches towards neural prosthesis
Torikai, Hiroyuki; Hashimoto, Sho
2011-04-19
An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.
Arnautovic, D.; Medanic, J.
1987-12-01
A methodology for the design of decentralized multivariable excitation and controllers in multimachine power systems is developed using projective controls. The existing methodology, is extended to permit the coordinated design of AVR and PSS controllers in power systems.
Nonlinear identification of ionic polymer actuator systems
NASA Astrophysics Data System (ADS)
Kothera, Curt S.; Lacy, Seth L.; Erwin, R. Scott; Leo, Donald J.
2004-07-01
Ionic polymers are a class of electromechanically coupled materials that can be used as flexible transducers. When set up in the cantilever configuration, the actuators exhibit a large bending deflection when an electric field is applied across their thickness. Being a relatively new research topic, the governing physical and chemical mechanisms are not yet fully understood. Experimental results have demonstrated nonlinear dynamic behavior. The nonlinear dynamics can be seen in the response of current, displacement, and velocity of the actuator. This work presents results for the nonlinear identification of ionic polymer actuator systems driven at a specific frequency. Identification results using a 5th-degree Volterra expansion show that the nonlinear distortion can be accurately modeled. Using such a high power in the series expansion is necessary to capture the most dominant harmonics, as evidenced when examining the power spectral density of the response. An investigation of how nonlinearities enter into the response is also performed. By analyzing both the actuation current and tip velocity, results show that both the voltage to current and current to velocity stages influence the nonlinear response, but the voltage to current stage is more dominantly nonlinear.
Statistical energy analysis of nonlinear vibrating systems.
Spelman, G M; Langley, R S
2015-09-28
Nonlinearities in practical systems can arise in contacts between components, possibly from friction or impacts. However, it is also known that quadratic and cubic nonlinearity can occur in the stiffness of structural elements undergoing large amplitude vibration, without the need for local contacts. Nonlinearity due purely to large amplitude vibration can then result in significant energy being found in frequency bands other than those being driven by external forces. To analyse this phenomenon, a method is developed here in which the response of the structure in the frequency domain is divided into frequency bands, and the energy flow between the frequency bands is calculated. The frequency bands are assigned an energy variable to describe the mean response and the nonlinear coupling between bands is described in terms of weighted summations of the convolutions of linear modal transfer functions. This represents a nonlinear extension to an established linear theory known as statistical energy analysis (SEA). The nonlinear extension to SEA theory is presented for the case of a plate structure with quadratic and cubic nonlinearity. PMID:26303923
Multivariate permutation entropy and its application for complexity analysis of chaotic systems
NASA Astrophysics Data System (ADS)
He, Shaobo; Sun, Kehui; Wang, Huihai
2016-11-01
To measure the complexity of multivariate systems, the multivariate permutation entropy (MvPE) algorithm is proposed. It is employed to measure complexity of multivariate system in the phase space. As an application, MvPE is applied to analyze the complexity of chaotic systems, including hyperchaotic Hénon map, fractional-order simplified Lorenz system and financial chaotic system. Results show that MvPE algorithm is effective for analyzing the complexity of the multivariate systems. It also shows that fractional-order system does not become more complex with derivative order varying. Compared with PE, MvPE has better robustness for noise and sampling interval, and the results are not affected by different normalization methods.
Damage detection in initially nonlinear systems
Bornn, Luke; Farrar, Charles; Park, Gyuhae
2009-01-01
The primary goal of Structural Health Monitoring (SHM) is to detect structural anomalies before they reach a critical level. Because of the potential life-safety and economic benefits, SHM has been widely studied over the past decade. In recent years there has been an effort to provide solid mathematical and physical underpinnings for these methods; however, most focus on systems that behave linearly in their undamaged state - a condition that often does not hold in complex 'real world' systems and systems for which monitoring begins mid-lifecycle. In this work, we highlight the inadequacy of linear-based methodology in handling initially nonlinear systems. We then show how the recently developed autoregressive support vector machine (AR-SVM) approach to time series modeling can be used for detecting damage in a system that exhibits initially nonlinear response. This process is applied to data acquired from a structure with induced nonlinearity tested in a laboratory environment.
Discrete time learning control in nonlinear systems
NASA Technical Reports Server (NTRS)
Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh
1992-01-01
In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.
Nonlinear Control of Delay and PDE Systems
NASA Astrophysics Data System (ADS)
Bekiaris-Liberis, Nikolaos
In this dissertation we develop systematic procedures for the control and analysis of general nonlinear systems with delays and of nonlinear PDE systems. We design predictor feedback laws (i.e., feedback laws that use the future, rather than the current state of the system) for the compensation of delays (i.e., after the control signal reaches the system for the first time, the system behaves as there were no delay at all) that can be time-varying or state-dependent, on the input and on the state of nonlinear systems. We also provide designs of predic- tor feedback laws for linear systems with constant distributed delays and known or unknown plant parameters, and for linear systems with simultaneous known or unknown constant delays on the input and the state. Moreover, we intro- duce infinite-dimensional backstepping transformations for each particular prob-lem, which enables us to construct Lyapunov-Krasovskii functionals. With the available Lyapunov-Krasovskii functionals we study stability, as well as, robust- ness of our control laws to plant uncertainties. We deal with coupled PDE-ODE systems. We consider nonlinear systems with wave actuator dynamics, for which we design a predictor inspired feedback law. We study stability of the closed-loop system either by constructing Lyapunov functionals, or using arguments of explicit solutions. We also consider linear sys- tems with distributed actuator and sensor dynamics governed by diffusion or wave PDEs, for which we design stabilizing feedback laws. We study stability of the closed-loop systems using Lyapunov functionals that we construct with the intro- duction of infinite-dimensional transformations of forwarding type. Finally, we develop a control design methodology for coupled nonlinear first-order hyperbolic PDEs through an application to automotive catalysts.
System interaction with linear and nonlinear characteristics
Lin, C.W. ); Tseng, W.S. )
1991-01-01
This book is covered under some of the following topics: seismic margins in piping systems, vibrational power flow in a cylindrical shell, inelastic pipework dynamics and aseismic design, an efficient method for dynamic analysis of a linearly elastic piping system with nonlinear supports.
Nonlinear coupling in the human motor system
Chen, C.C.; Kilner, J.M.; Friston, K.J.; Kiebel, S. J.; Jolly, R.K.; Ward, N. S.
2010-01-01
The synchronous discharge of neuronal assemblies is thought to facilitate communication between areas within distributed networks in the human brain. This oscillatory activity is especially interesting, given the pathological modulation of specific frequencies in diseases affecting the motor system. Many studies investigating oscillatory activity have focussed on same frequency, or linear, coupling between areas of a network. In this study, our aim was to establish a functional architecture in the human motor system responsible for induced responses as measured in normal subjects with magnetoencephalography. Specifically, we looked for evidence for additional nonlinear (between-frequency) coupling among neuronal sources and, in particular, whether nonlinearities were found predominantly in connections within areas (intrinsic), between areas (extrinsic) or both. We modelled the event-related modulation of spectral responses during a simple hand-grip using dynamic casual modelling. We compared models with and without nonlinear connections under conditions of symmetric and asymmetric interhemispheric connectivity. Bayesian model comparison suggested that the task-dependent motor network was asymmetric during right hand movements. Furthermore, it revealed very strong evidence for nonlinear coupling between sources in this distributed network, but interactions among frequencies within a source appeared linear in nature. Our results provide empirical evidence for nonlinear coupling among distributed neuronal sources in the motor system and that these play an important role in modulating spectral responses under normal conditions. PMID:20573886
System characterization in nonlinear random vibration
Paez, T.L.; Gregory, D.L.
1986-01-01
Linear structural models are frequently used for structural system characterization and analysis. In most situations they can provide satisfactory results, but under some circumstances they are insufficient for system definition. The present investigation proposes a model for nonlinear structure characterization, and demonstrates how the functions describing the model can be identified using a random vibration experiment. Further, it is shown that the model is sufficient to completely characterize the stationary random vibration response of a structure that has a harmonic frequency generating form of nonlinearity. An analytical example is presented to demonstrate the plausibility of the model.
State Identification in Nonlinear Systems
Holloway, James Paul
2005-02-06
A state estimation method based on finding a system state that causes a model to match a set of system measurements is regularized by requiring that sudden changes in system state be avoided. The required optimization is accomplished by a pattern search algorithm. The method does not require derivative information or linearization of the model. Is has been applied to a 10 dimensional model of a fast reactor system.
Optimized spectral estimation for nonlinear synchronizing systems
NASA Astrophysics Data System (ADS)
Sommerlade, Linda; Mader, Malenka; Mader, Wolfgang; Timmer, Jens; Thiel, Marco; Grebogi, Celso; Schelter, Björn
2014-03-01
In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.
Indirect learning control for nonlinear dynamical systems
NASA Technical Reports Server (NTRS)
Ryu, Yeong Soon; Longman, Richard W.
1993-01-01
In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.
Spectral decomposition of nonlinear systems with memory
NASA Astrophysics Data System (ADS)
Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.
2016-02-01
We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.
Spectral decomposition of nonlinear systems with memory.
Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J
2016-02-01
We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.
NASA Astrophysics Data System (ADS)
Zhang, Xiaoyu; Li, Qingbo; Zhang, Guangjun
2013-11-01
In this paper, a modified single-index signal regression (mSISR) method is proposed to construct a nonlinear and practical model with high-accuracy. The mSISR method defines the optimal penalty tuning parameter in P-spline signal regression (PSR) as initial tuning parameter and chooses the number of cycles based on minimizing root mean squared error of cross-validation (RMSECV). mSISR is superior to single-index signal regression (SISR) in terms of accuracy, computation time and convergency. And it can provide the character of the non-linearity between spectra and responses in a more precise manner than SISR. Two spectra data sets from basic research experiments, including plant chlorophyll nondestructive measurement and human blood glucose noninvasive measurement, are employed to illustrate the advantages of mSISR. The results indicate that the mSISR method (i) obtains the smooth and helpful regression coefficient vector, (ii) explicitly exhibits the type and amount of the non-linearity, (iii) can take advantage of nonlinear features of the signals to improve prediction performance and (iv) has distinct adaptability for the complex spectra model by comparing with other calibration methods. It is validated that mSISR is a promising nonlinear modeling strategy for multivariate calibration.
NASA Technical Reports Server (NTRS)
Hague, D. S.; Vanderberg, J. D.; Woodbury, N. W.
1974-01-01
A method for rapidly examining the probable applicability of weight estimating formulae to a specific aerospace vehicle design is presented. The Multivariate Analysis Retrieval and Storage System (MARS) is comprised of three computer programs which sequentially operate on the weight and geometry characteristics of past aerospace vehicles designs. Weight and geometric characteristics are stored in a set of data bases which are fully computerized. Additional data bases are readily added to the MARS system and/or the existing data bases may be easily expanded to include additional vehicles or vehicle characteristics.
Connectance and stability of nonlinear symplectic systems
NASA Astrophysics Data System (ADS)
Laveder, D.; Cosentino, M.; Lega, Elena; Froeschlé, C.
2008-09-01
We have revisited the problem of the transition from ordered to chaotic motion for increasing number of degrees of freedom in nonlinear symplectic maps. Following the pioneer work of Froeschlé (Phys. Rev. A 18, 277 281, 1978) we investigate such systems as a function of the number of couplings among the equations of motion, i.e. as a function of a parameter called connectance since the seminal paper of Gardner and Ashby (Nature 228, 784, 1970) about linear systems. We compare two different models showing that in the nonlinear case the connectance has to be intended as the fraction of explicit dynamical couplings among degrees of freedom, rather than the fraction of non-zero elements in a given matrix. The chaoticity increases then with the connectance until the system is fully coupled.
Accidental degeneracies in nonlinear quantum deformed systems
NASA Astrophysics Data System (ADS)
Aleixo, A. N. F.; Balantekin, A. B.
2011-09-01
We construct a multi-parameter nonlinear deformed algebra for quantum confined systems that includes many other deformed models as particular cases. We demonstrate that such systems exhibit the property of accidental pairwise energy level degeneracies. We also study, as a special case of our multi-parameter deformation formalism, the extension of the Tamm-Dancoff cutoff deformed oscillator and the occurrence of accidental pairwise degeneracy in the energy levels of the deformed system. As an application, we discuss the case of a trigonometric Rosen-Morse potential, which is successfully used in models for quantum confined systems, ranging from electrons in quantum dots to quarks in hadrons.
Nonlinear dynamic macromodeling techniques for audio systems
NASA Astrophysics Data System (ADS)
Ogrodzki, Jan; Bieńkowski, Piotr
2015-09-01
This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.
Finite-time consensus of time-varying nonlinear multi-agent systems
NASA Astrophysics Data System (ADS)
Liu, Qingrong; Liang, Zhishan
2016-08-01
This paper investigates the problem of leader-follower finite-time consensus for a class of time-varying nonlinear multi-agent systems. The dynamics of each agent is assumed to be represented by a strict feedback nonlinear system, where nonlinearities satisfy Lipschitz growth conditions with time-varying gains. The main design procedure is outlined as follows. First, it is shown that the leader-follower consensus problem is equivalent to a conventional control problem of multi-variable high-dimension systems. Second, by introducing a state transformation, the control problem is converted into the construction problem of two dynamic equations. Third, based on the Lyapunov stability theorem, the global finite-time stability of the closed-loop control system is proved, and the finite-time consensus of the concerned multi-agent systems is thus guaranteed. An example is given to verify the effectiveness of the proposed consensus protocol algorithm.
Model reduction of systems with localized nonlinearities.
Segalman, Daniel Joseph
2006-03-01
An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.
Low level monitoring and control of nonlinear systems
Cover, A.; Reneke, J.; Lenhart, S.; Protopopescu, V.
1994-12-31
In this paper, we propose a nonparametric method for monitoring and controlling nonlinear systems whose dynamics is, in general, unknown or only partially known. Our nonparametric method is based on the stochastic linearization of the underlying (unknown) nonlinear system.
An error bound for a discrete reduced order model of a linear multivariable system
NASA Technical Reports Server (NTRS)
Al-Saggaf, Ubaid M.; Franklin, Gene F.
1987-01-01
The design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction. In order for the design based on the order reduction to include a guarantee of stability, it is sufficient to have a bound on the model error. Previous work has provided such a bound for continuous-time systems for algorithms based on balancing. In this note an L-infinity bound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing.
NASA Astrophysics Data System (ADS)
Pai, P. Frank
2011-10-01
Presented here is a new time-frequency signal processing methodology based on Hilbert-Huang transform (HHT) and a new conjugate-pair decomposition (CPD) method for characterization of nonlinear normal modes and parametric identification of nonlinear multiple-degree-of-freedom dynamical systems. Different from short-time Fourier transform and wavelet transform, HHT uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift components of different time scales. Because HHT does not use pre-determined basis functions and function orthogonality for component extraction, it provides more accurate time-varying amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. CPD uses adaptive local harmonics and function orthogonality to extract and track time-localized nonlinearity-distorted harmonics without the end effect that destroys the accuracy of HHT at the two data ends. For parametric identification, the method only needs to process one steady-state response (a free undamped modal vibration or a steady-state response to a harmonic excitation) and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. A nonlinear two-degree-of-freedom system is used to illustrate the concepts and characterization of nonlinear normal modes, vibration localization, and nonlinear modal coupling. Numerical simulations show that the proposed method can provide accurate time-frequency characterization of nonlinear normal modes and parametric identification of nonlinear dynamical systems. Moreover, results show that nonlinear modal coupling makes it impossible to decompose a general nonlinear response of a highly nonlinear system into nonlinear normal modes even if nonlinear normal modes exist in the system.
NASA Technical Reports Server (NTRS)
Lefkowitz, C. P.; Tekawy, J. A.; Pujara, P. K.; Safonov, M. G.
1989-01-01
AUTOCON is an automated computer-aided design tool for the synthesis and optimization of linear multivariable control systems based upon user-defined control parameter optimization. Violations in stability and performance requirements are computed from constraints on Single Input/Single Output (SISO) open- and closed-loop transfer function frequency responses, and from constraints on the singular-value frequency responses of Multiple Input/Multiple Output (MIMO) transfer functions, for all critical plant variations. Optimum nonlinear programming algorithms are used in the search for local constrained solutions in which violations in stability and performance are caused either to vanish or be minimized for a proper selection of the control parameters. Classical control system stability and performance design can, in this way, be combined with modern multivariable robustness methods to offer general frequency response loop-shaping via a computer-aided design tool. Complete Nichols, Nyquist, Bode, singular-value Bode magnitude and transient response plots are produced, including user-defined boundary responses. AUTOCON is used to synthesize and optimize the lateral/directional flight control system for a typical high-performance aircraft.
A summary of spectral synthesis procedures for multivariable systems
NASA Technical Reports Server (NTRS)
Liberty, S. R.; Mielke, R. R.; Maynard, R. A.
1979-01-01
A new approach to the eigensystem assignment problem is presented. The approach utilizes a null-space formulation of the eigenvalue/eigenvector assignment problem to simultaneously realize arbitrary eigenvalue specifications, approximate desired modal behavior, and achieve low eigensystem sensitivity with respect to plant parameter variations. The methods are applied to the design of regulator and integral plus proportional servo control systems.
Nonlinear Network Dynamics on Earthquake Fault Systems
Rundle, Paul B.; Rundle, John B.; Tiampo, Kristy F.; Sa Martins, Jorge S.; McGinnis, Seth; Klein, W.
2001-10-01
Earthquake faults occur in interacting networks having emergent space-time modes of behavior not displayed by isolated faults. Using simulations of the major faults in southern California, we find that the physics depends on the elastic interactions among the faults defined by network topology, as well as on the nonlinear physics of stress dissipation arising from friction on the faults. Our results have broad applications to other leaky threshold systems such as integrate-and-fire neural networks.
NASA Astrophysics Data System (ADS)
Vörös, Jozef
2016-07-01
The paper deals with the parameter identification of cascade nonlinear dynamic systems with noninvertible piecewise linear input nonlinearities and backlash output nonlinearities. Application of the key term separation principle provides special expressions for the corresponding nonlinear model description that are linear in parameters. A least squares based iterative technique allows estimation of all the model parameters based on measured input/output data. Simulation studies illustrate the feasibility of proposed identification method.
Practical robustness measures in multivariable control system analysis. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Lehtomaki, N. A.
1981-01-01
The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.
Approximations of nonlinear systems having outputs
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Su, R.
1985-01-01
For a nonlinear system with output derivative x = f(x) and y = h(x), two types of linearizations about a point x(0) in state space are considered. One is the usual Taylor series approximation, and the other is defined by linearizing the appropriate Lie derivatives of the output with respect to f about x(0). The latter is called the obvservation model and appears to be quite natural for observation. It is noted that there is a coordinate system in which these two kinds of linearizations agree. In this coordinate system, a technique to construct an observer is introduced.
Rasouli, Zolaikha; Ghavami, Raouf
2016-08-01
Vanillin (VA), vanillic acid (VAI) and syringaldehyde (SIA) are important food additives as flavor enhancers. The current study for the first time is devote to the application of partial least square (PLS-1), partial robust M-regression (PRM) and feed forward neural networks (FFNNs) as linear and nonlinear chemometric methods for the simultaneous detection of binary and ternary mixtures of VA, VAI and SIA using data extracted directly from UV-spectra with overlapped peaks of individual analytes. Under the optimum experimental conditions, for each compound a linear calibration was obtained in the concentration range of 0.61-20.99 [LOD=0.12], 0.67-23.19 [LOD=0.13] and 0.73-25.12 [LOD=0.15] μgmL(-1) for VA, VAI and SIA, respectively. Four calibration sets of standard samples were designed by combination of a full and fractional factorial designs with the use of the seven and three levels for each factor for binary and ternary mixtures, respectively. The results of this study reveal that both the methods of PLS-1 and PRM are similar in terms of predict ability each binary mixtures. The resolution of ternary mixture has been accomplished by FFNNs. Multivariate curve resolution-alternating least squares (MCR-ALS) was applied for the description of spectra from the acid-base titration systems each individual compound, i.e. the resolution of the complex overlapping spectra as well as to interpret the extracted spectral and concentration profiles of any pure chemical species identified. Evolving factor analysis (EFA) and singular value decomposition (SVD) were used to distinguish the number of chemical species. Subsequently, their corresponding dissociation constants were derived. Finally, FFNNs has been used to detection active compounds in real and spiked water samples. PMID:27176001
NASA Astrophysics Data System (ADS)
Rasouli, Zolaikha; Ghavami, Raouf
2016-08-01
Vanillin (VA), vanillic acid (VAI) and syringaldehyde (SIA) are important food additives as flavor enhancers. The current study for the first time is devote to the application of partial least square (PLS-1), partial robust M-regression (PRM) and feed forward neural networks (FFNNs) as linear and nonlinear chemometric methods for the simultaneous detection of binary and ternary mixtures of VA, VAI and SIA using data extracted directly from UV-spectra with overlapped peaks of individual analytes. Under the optimum experimental conditions, for each compound a linear calibration was obtained in the concentration range of 0.61-20.99 [LOD = 0.12], 0.67-23.19 [LOD = 0.13] and 0.73-25.12 [LOD = 0.15] μg mL- 1 for VA, VAI and SIA, respectively. Four calibration sets of standard samples were designed by combination of a full and fractional factorial designs with the use of the seven and three levels for each factor for binary and ternary mixtures, respectively. The results of this study reveal that both the methods of PLS-1 and PRM are similar in terms of predict ability each binary mixtures. The resolution of ternary mixture has been accomplished by FFNNs. Multivariate curve resolution-alternating least squares (MCR-ALS) was applied for the description of spectra from the acid-base titration systems each individual compound, i.e. the resolution of the complex overlapping spectra as well as to interpret the extracted spectral and concentration profiles of any pure chemical species identified. Evolving factor analysis (EFA) and singular value decomposition (SVD) were used to distinguish the number of chemical species. Subsequently, their corresponding dissociation constants were derived. Finally, FFNNs has been used to detection active compounds in real and spiked water samples.
NASA Technical Reports Server (NTRS)
Sanchez Pena, Ricardo S.; Sideris, Athanasios
1988-01-01
A computer program implementing an algorithm for computing the multivariable stability margin to check the robust stability of feedback systems with real parametric uncertainty is proposed. The authors present in some detail important aspects of the program. An example is presented using lateral directional control system.
Detection of decoupled input/output pairs in multivariable systems.
Potts, Alain Segundo; Massaro, Leandro Cuenca; Garcia, Claudio
2015-03-01
A method is proposed to detect if there is no coupling between an input and an output in systems operating in open-loop, that is, without a supervisory controller. The proposed technique is applicable to multiple input multiple output (MIMO) systems, whose intent is to detect no-model input/output (IO) combinations in a transfer matrix. Traditional approaches for selecting IO pairs are usually performed after the plant model is identified. The presented approach is applied during the pre-identification stage and is based on IO cross-correlation, signal filtering and fuzzy logic analysis. A case study involving the identification of a 7×6 simulated Fluid Catalytic Cracking (FCC) is discussed, as well as an influence analysis of detecting no-model IO pairs in the identification process and in the performance index of a Model Predictive Controller (MPC) applied to a 2×2 simulated distillation column. Finally, the method is tested with a real dataset obtained from an FCC unit of a petrol refinery.
NASA Technical Reports Server (NTRS)
Kriegler, F. J.; Christenson, D.; Gordon, M.; Kistler, R.; Lampert, S.; Marshall, R.; Mclaughlin, R.
1974-01-01
The MIDAS System is a third-generation, fast, multispectral recognition system able to keep pace with the large quantity and high rates of data acquisition from present and projected sensors. A principal objective of the MIDAS Program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turn-around time and significant gains in throughout. The hardware and software generated in Phase I of the over-all program are described. The system contains a mini-computer to control the various high-speed processing elements in the data path and a classifier which implements an all-digital prototype multivariate-Gaussian maximum likelihood decision algorithm operating 2 x 105 pixels/sec. Sufficient hardware was developed to perform signature extraction from computer-compatible tapes, compute classifier coefficients, control the classifier operation, and diagnose operation. Diagnostic programs used to test MIDAS' operations are presented.
NASA Technical Reports Server (NTRS)
Kriegler, F. J.
1974-01-01
The MIDAS System is described as a third-generation fast multispectral recognition system able to keep pace with the large quantity and high rates of data acquisition from present and projected sensors. A principal objective of the MIDAS program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turnaround time and significant gains in throughput. The hardware and software are described. The system contains a mini-computer to control the various high-speed processing elements in the data path, and a classifier which implements an all-digital prototype multivariate-Gaussian maximum likelihood decision algorithm operating at 200,000 pixels/sec. Sufficient hardware was developed to perform signature extraction from computer-compatible tapes, compute classifier coefficients, control the classifier operation, and diagnose operation.
FREQ: A computational package for multivariable system loop-shaping procedures
NASA Technical Reports Server (NTRS)
Giesy, Daniel P.; Armstrong, Ernest S.
1989-01-01
Many approaches in the field of linear, multivariable time-invariant systems analysis and controller synthesis employ loop-sharing procedures wherein design parameters are chosen to shape frequency-response singular value plots of selected transfer matrices. A software package, FREQ, is documented for computing within on unified framework many of the most used multivariable transfer matrices for both continuous and discrete systems. The matrices are evaluated at user-selected frequency-response values, and singular values against frequency. Example computations are presented to demonstrate the use of the FREQ code.
Theoretical constraints in the design of multivariable control systems
NASA Technical Reports Server (NTRS)
Rynaski, E. G.; Mook, D. Joseph; Depena, Juan
1991-01-01
The research being performed under NASA Grant NAG1-1361 involves a more clear understanding and definition of the constraints involved in the pole-zero placement or assignment process for multiple input, multiple output systems. Complete state feedback to more than a single controller under conditions of complete controllability and observability is redundant if pole placement alone is the design objective. The additional feedback gains, above and beyond those required for pole placement can be used for eignevalue assignment or zero placement of individual closed loop transfer functions. Because both poles and zeros of individual closed loop transfer functions strongly affect the dynamic response to a pilot command input, the pole-zero placement problem is important. When fewer controllers than degrees of freedom of motion are available, complete design freedom is not possible, the transmission zeros constrain the regions of possible pole-zero placement. The effect of transmission zero constraints on the design possibilities, selection of transmission zeros and the avoidance of producing non-minimum phase transfer functions is the subject of the research being performed under this grant.
Molnár, B; Szentirmay, Z; Bodó, M; Sugár, J; Fehér, J
1992-10-18
The methods of the multivariate mathematics have been applied in several studies to increase the diagnostic reliability of medical decision support system. In the recent years some new algorithms for decision support (fuzzy logic) and for pattern recognition (neural nets), both specified by nonlinearity, were developed. This paper provides results for the application of this methods in the area of quantitative cytology and the comparison with the traditional classifiers. 21 normal, 15 dysplastic, 23 malignant, Feulgen stained gastric imprint smears were analysed on a Leitz Miamed DNA equipment. The determination of mean DNA content, the 2c deviation index (2cDI), 5c Exceeding rate (RcER), G1,S,G2 phase fraction ratios, cell nucleus area, form factor was performed. The discriminant analysis classified correctly the 95.6% of malignant cases, 86.7% of dysplasias, and 80.7% normal cases. Our diagnostic system using fuzzy logic made the diagnostic borders fine tuneable, and reliable. The back propagation neural net could classify all three diagnostic groups above 95% correctly. The application of nonlinear computational methods made the diagnostic system more reliable. The application of these algorithms are encouraged.
Linear homotopy solution of nonlinear systems of equations in geodesy
NASA Astrophysics Data System (ADS)
Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.
2010-01-01
A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.
NONLINEAR TIDES IN CLOSE BINARY SYSTEMS
Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh
2012-06-01
We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' {approx}> 10-100 M{sub Circled-Plus} at orbital periods P Almost-Equal-To 1-10 days. The nearly static 'equilibrium' tidal distortion is, however, stable to parametric resonance except for solar binaries with P {approx}< 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes short length scale waves to grow so rapidly that they must be treated as traveling waves, rather than standing waves. (3) We show that the global three-wave treatment of parametric instability typically used in the astrophysics literature does not yield the fastest-growing daughter modes or instability threshold in many cases. We find a form of parametric instability in which a single parent wave excites a very large number of daughter waves (N Almost-Equal-To 10{sup 3}[P/10 days] for a solar-type star) and drives them as a single coherent unit with
Nonlinear control for dual quaternion systems
NASA Astrophysics Data System (ADS)
Price, William D.
The motion of rigid bodies includes three degrees of freedom (DOF) for rotation, generally referred to as roll, pitch and yaw, and 3 DOF for translation, generally described as motion along the x, y and z axis, for a total of 6 DOF. Many complex mechanical systems exhibit this type of motion, with constraints, such as complex humanoid robotic systems, multiple ground vehicles, unmanned aerial vehicles (UAVs), multiple spacecraft vehicles, and even quantum mechanical systems. These motions historically have been analyzed independently, with separate control algorithms being developed for rotation and translation. The goal of this research is to study the full 6 DOF of rigid body motion together, developing control algorithms that will affect both rotation and translation simultaneously. This will prove especially beneficial in complex systems in the aerospace and robotics area where translational motion and rotational motion are highly coupled, such as when spacecraft have body fixed thrusters. A novel mathematical system known as dual quaternions provide an efficient method for mathematically modeling rigid body transformations, expressing both rotation and translation. Dual quaternions can be viewed as a representation of the special Euclidean group SE(3). An eight dimensional representation of screw theory (combining dual numbers with traditional quaternions), dual quaternions allow for the development of control techniques for 6 DOF motion simultaneously. In this work variable structure nonlinear control methods are developed for dual quaternion systems. These techniques include use of sliding mode control. In particular, sliding mode methods are developed for use in dual quaternion systems with unknown control direction. This method, referred to as self-reconfigurable control, is based on the creation of multiple equilibrium surfaces for the system in the extended state space. Also in this work, the control problem for a class of driftless nonlinear systems is
Lall, Upmanu; Devineni, Naresh; Kaheil, Yasir
2016-01-01
Multivariate simulations of a set of random variables are often needed for risk analysis. Given a historical data set, the goal is to develop simulations that reproduce the dependence structure in that data set so that the risk of potentially correlated factors can be evaluated. A nonparametric, copula-based simulation approach is developed and exemplified. It can be applied to multiple variables or to spatial fields with arbitrary dependence structures and marginal densities. The nonparametric simulator uses logspline density estimation in the univariate setting, together with a sampling strategy to reproduce dependence across variables or spatial instances, through a nonparametric numerical approximation of the underlying copula function. The multivariate data vectors are assumed to be independent and identically distributed. A synthetic example is provided to illustrate the method, followed by an application to the risk of livestock losses in Mongolia. PMID:26177987
The geometric phase in nonlinear dissipative systems
Ning, C.Z.; Haken, H. )
1992-10-30
In this paper, the authors review the recent progress made in generalizing the concept of the geometric phase to nonlinear dissipative systems. The authors first illustrate the usual form of the parallel transport law with an elementary example of the parallel shift of a line on the complex plane. Important results about the non-adiabatical geometric (Aharonov and Anandan or AA) phase [sup 18] for the Schrodinger equations are reviewed in order to make a comparison with results for dissipative systems. The authors show that a geometric phase can be defined for dissipative systems with the cyclic attractors. Systems undergoing the Hopf bifurcation with a continuous symmetry are shown to possess such cyclic attractors. Examples from laser physics are discussed to exhibit the applicability of our formalism and the widespread existence of the geometric phase in dissipative systems.
Luan, Xiaoli; Chen, Qiang; Liu, Fei
2014-09-01
This article presents a new scheme to design full matrix controller for high dimensional multivariable processes based on equivalent transfer function (ETF). Differing from existing ETF method, the proposed ETF is derived directly by exploiting the relationship between the equivalent closed-loop transfer function and the inverse of open-loop transfer function. Based on the obtained ETF, the full matrix controller is designed utilizing the existing PI tuning rules. The new proposed ETF model can more accurately represent the original processes. Furthermore, the full matrix centralized controller design method proposed in this paper is applicable to high dimensional multivariable systems with satisfactory performance. Comparison with other multivariable controllers shows that the designed ETF based controller is superior with respect to design-complexity and obtained performance.
Observers for discrete-time nonlinear systems
NASA Astrophysics Data System (ADS)
Grossman, Walter D.
Observer synthesis for discrete-time nonlinear systems with special applications to parameter estimation is analyzed. Two new types of observers are developed. The first new observer is an adaptation of the Friedland continuous-time parameter estimator to discrete-time systems. The second observer is an adaptation of the continuous-time Gauthier observer to discrete-time systems. By adapting these observers to discrete-time continuous-time parameter estimation problems which were formerly intractable become tractable. In addition to the two newly developed observers, two observers already described in the literature are analyzed and deficiencies with respect to noise rejection are demonstrated. Improved versions of these observers are proposed and their performance demonstrated. The issues of discrete-time observability, discrete-time system inversion, and optimal probing are also addressed.
Approximate controllability of nonlinear impulsive differential systems
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Mahmudov, N. I.; Kim, J. H.
2007-08-01
Many practical systems in physical and biological sciences have impulsive dynamical be- haviours during the evolution process which can be modeled by impulsive differential equations. This paper studies the approximate controllability issue for nonlinear impulsive differential and neutral functional differential equations in Hilbert spaces. Based on the semigroup theory and fixed point approach, sufficient conditions for approximate controllability of impulsive differential and neutral functional differential equations are established. Finally, two examples are presented to illustrate the utility of the proposed result. The results improve some recent results.
Particle systems and nonlinear Landau damping
Villani, Cédric
2014-03-15
Some works dealing with the long-time behavior of interacting particle systems are reviewed and put into perspective, with focus on the classical Kolmogorov–Arnold–Moser theory and recent results of Landau damping in the nonlinear perturbative regime, obtained in collaboration with Clément Mouhot. Analogies are discussed, as well as new qualitative insights in the theory. Finally, the connection with a more recent work on the inviscid Landau damping near the Couette shear flow, by Bedrossian and Masmoudi, is briefly discussed.
Design of suboptimal regulators for nonlinear systems
NASA Technical Reports Server (NTRS)
Balaram, J.; Saridis, G. N.
1985-01-01
An optimal feedback control law is preferred for the regulation of a deterministic nonlinear system. In this paper, a practical, iterative design method leading to a sequence of suboptimal control laws with successively improved performance is presented. The design method requires the determination of an upper bound to the performance of each successive control law. This is obtained by solving a partial differential inequality by means of a linear programming technique. Robustness properties and the application of the design method to the control of a robot manipulator arm are also presented.
Arbitrary eigenvalue assignments for linear time-varying multivariable control systems
NASA Technical Reports Server (NTRS)
Nguyen, Charles C.
1987-01-01
The problem of eigenvalue assignments for a class of linear time-varying multivariable systems is considered. Using matrix operators and canonical transformations, it is shown that a time-varying system that is 'lexicography-fixedly controllable' can be made via state feedback to be equivalent to a time-invariant system whose eigenvalues are arbitrarily assignable. A simple algorithm for the design of the state feedback is provided.
NASA Astrophysics Data System (ADS)
Wu, Fen; Hays, Scott
2013-09-01
This paper investigates nonlinear gain-scheduling control approaches for a class of polynomial nonlinear systems, containing an output-dependent vector field with input saturation. Using the polytopic differential inclusion and norm-bounded differential inclusion (NDI) of saturation and dead-zone functions, the nonlinear plants are transformed into systems with measurable parameters. For the polytopic differential inclusion description, a quasi-linear parameter varying (quasi-LPV) output-feedback controller will be sought for saturation control. On the other hand, the NDI model leads to a nonlinear fractional transformation (NFT) output-feedback controller for saturated nonlinear systems. The quasi-LPV and NFT output-feedback control synthesis conditions are derived in the forms of output-dependent matrix inequalities. They can be reformulated as sum-of-squares (SOS) optimisations and solved efficiently using SOS programming. The proposed nonlinear gain-scheduling saturation control approaches will be demonstrated using the Van der Pol equation.
Shahnazi, Reza
2015-01-01
An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations.
Shahnazi, Reza
2015-01-01
An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations. PMID:25104646
Parameter identification for nonlinear aerodynamic systems
NASA Technical Reports Server (NTRS)
Pearson, Allan E.
1990-01-01
Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.
Impulse position control algorithms for nonlinear systems
Sesekin, A. N.; Nepp, A. N.
2015-11-30
The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.
Boosted X Waves in Nonlinear Optical Systems
Arevalo, Edward
2010-01-15
X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed.
Boosted X waves in nonlinear optical systems.
Arévalo, Edward
2010-01-15
X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed.
Nonlinear Mixing in Optical Multicarrier Systems
NASA Astrophysics Data System (ADS)
Hameed, Mahmood Abdul
Although optical fiber has a vast spectral bandwidth, efficient use of this bandwidth is still important in order to meet the ever increased capacity demand of optical networks. In addition to wavelength division multiplexing, it is possible to partition multiple low-rate subcarriers into each high speed wavelength channel. Multicarrier systems not only ensure efficient use of optical and electrical components, but also tolerate transmission impairments. The purpose of this research is to understand the impact of mixing among subcarriers in Radio-Over-Fiber (RoF) and high speed optical transmission systems, and experimentally demonstrate techniques to minimize this impact. We also analyze impact of clipping and quantization on multicarrier signals and compare bandwidth efficiency of two popular multiplexing techniques, namely, orthogonal frequency division multiplexing (OFDM) and Nyquist modulation. For an OFDM-RoF system, we present a novel technique that minimizes the RF domain signal-signal beat interference (SSBI), relaxes the phase noise limit on the RF carrier, realizes the full potential of optical heterodyne-based RF carrier generation, and increases the performance-to-cost ratio of RoF systems. We demonstrate a RoF network that shares the same RF carrier for both downlink and uplink, avoiding the need of an additional RF oscillator in the customer unit. For multi-carrier optical transmission, we first experimentally compare performance degradations of coherent optical OFDM and single-carrier Nyquist pulse modulated systems in a nonlinear environment. We then experimentally evaluate SSBI compensation techniques in the presence of semiconductor optical amplifier (SOA) induced nonlinearities for a multicarrier optical system with direct detection. We show that SSBI contamination can be significantly reduced from the data signal when the carrier-to-signal power ratio is sufficiently low.
Double nonlinear resonance in ferromagnets and other dynamic systems
NASA Astrophysics Data System (ADS)
Bakai, A. S.
2010-08-01
The phenomenon of double nonlinear resonances in nonlinear oscillators of general type is described. The results are used to describe a double nonlinear ferromagnetic resonance in a uniaxial ferromagnet. The possibility of a similar resonance in the system of brain biocurrents is considered.
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm. PMID:25277626
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm.
Quantum dynamics of nonlinear cavity systems
NASA Astrophysics Data System (ADS)
Nation, Paul David
In this work we investigate the quantum dynamics of three different configurations of nonlinear cavity systems. We begin by carrying out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprising a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing an external flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal and noise response where it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state. Next, we consider the use of a superconducting transmission line formed from an array of dc-SQUIDs for investigating analogue Hawking radiation. We will show that biasing the array with a space-time varying flux modifies the propagation velocity of the transmission line, leading to an effective metric with a horizon. As a fundamentally quantum mechanical device, this setup allows for investigations of quantum effects such as backreaction and analogue space-time fluctuations on the Hawking process. Finally, we investigate a quantum parametric amplifier with dynamical pump mode, viewed as a zero-dimensional model of Hawking radiation from an evaporating black hole. The conditions are derived under which the spectrum of particles generated from vacuum fluctuations deviates from the thermal spectrum predicted for the conventional parametric amplifier. We find that significant deviation occurs once the pump mode (black hole) has released nearly half of its initial energy in the signal (Hawking radiation) and idler (in-falling particle) modes. As a model of black hole dynamics, this finding lends support to the view that late-time Hawking radiation contains information about the quantum state of the black hole and is entangled with the black hole's quantum
NASA Astrophysics Data System (ADS)
Li, Yang; Qin, Le; Zou, Shipeng; Long, Shijun
2014-04-01
A lots of problems may occur frequently when controlling the temperature of the enamelling machine oven in the real industrial process, such as multi-variable coupled problem. an experimental rig with triple inputs and triple outputs was devised and a simulation modeling was established accordingly in this study,. the temperature control system based on the feedforward compensation algorithm was proposed. Experimental results have shown that the system is of high efficiency, good stability and promising application.
Design of reduced-order state estimators for linear time-varying multivariable systems
NASA Technical Reports Server (NTRS)
Nguyen, Charles C.
1987-01-01
The design of reduced-order state estimators for linear time-varying multivariable systems is considered. Employing the concepts of matrix operators and the method of canonical transformations, this paper shows that there exists a reduced-order state estimator for linear time-varying systems that are 'lexicography-fixedly observable'. In addition, the eigenvalues of the estimator can be arbitrarily assigned. A simple algorithm is proposed for the design of the state estimator.
Li, Yang; Qin, Le; Zou, Shipeng; Long, Shijun
2014-04-11
A lots of problems may occur frequently when controlling the temperature of the enamelling machine oven in the real industrial process, such as multi-variable coupled problem. an experimental rig with triple inputs and triple outputs was devised and a simulation modeling was established accordingly in this study,. the temperature control system based on the feedforward compensation algorithm was proposed. Experimental results have shown that the system is of high efficiency, good stability and promising application.
Passive dynamic controllers for nonlinear mechanical systems
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.
1991-01-01
A methodology for model-independant controller design for controlling large angular motion of multi-body dynamic systems is outlined. The controlled system may consist of rigid and flexible components that undergo large rigid body motion and small elastic deformations. Control forces/torques are applied to drive the system and at the same time suppress the vibration due to flexibility of the components. The proposed controller consists of passive second-order systems which may be designed with little knowledge of the system parameter, even if the controlled system is nonlinear. Under rather general assumptions, the passive design assures that the closed loop system has guaranteed stability properties. Unlike positive real controller design, stabilization can be accomplished without direct velocity feedback. In addition, the second-order passive design allows dynamic feedback controllers with considerable freedom to tune for desired system response, and to avoid actuator saturation. After developing the basic mathematical formulation of the design methodology, simulation results are presented to illustrate the proposed approach to a flexible six-degree-of-freedom manipulator.
Nonlinear dynamic analysis of flexible multibody systems
NASA Technical Reports Server (NTRS)
Bauchau, Olivier A.; Kang, Nam Kook
1991-01-01
Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.
Gain-scheduling multivariable LPV control of an irrigation canal system.
Bolea, Yolanda; Puig, Vicenç
2016-07-01
The purpose of this paper is to present a multivariable linear parameter varying (LPV) controller with a gain scheduling Smith Predictor (SP) scheme applicable to open-flow canal systems. This LPV controller based on SP is designed taking into account the uncertainty in the estimation of delay and the variation of plant parameters according to the operating point. This new methodology can be applied to a class of delay systems that can be represented by a set of models that can be factorized into a rational multivariable model in series with left/right diagonal (multiple) delays, such as, the case of irrigation canals. A multiple pool canal system is used to test and validate the proposed control approach. PMID:27184416
Gain-scheduling multivariable LPV control of an irrigation canal system.
Bolea, Yolanda; Puig, Vicenç
2016-07-01
The purpose of this paper is to present a multivariable linear parameter varying (LPV) controller with a gain scheduling Smith Predictor (SP) scheme applicable to open-flow canal systems. This LPV controller based on SP is designed taking into account the uncertainty in the estimation of delay and the variation of plant parameters according to the operating point. This new methodology can be applied to a class of delay systems that can be represented by a set of models that can be factorized into a rational multivariable model in series with left/right diagonal (multiple) delays, such as, the case of irrigation canals. A multiple pool canal system is used to test and validate the proposed control approach.
Application of nonlinear time series models to driven systems
Hunter, N.F. Jr.
1990-01-01
In our laboratory we have been engaged in an effort to model nonlinear systems using time series methods. Our objectives have been, first, to understand how the time series response of a nonlinear system unfolds as a function of the underlying state variables, second, to model the evolution of the state variables, and finally, to predict nonlinear system responses. We hope to address the relationship between model parameters and system parameters in the near future. Control of nonlinear systems based on experimentally derived parameters is also a planned topic of future research. 28 refs., 15 figs., 2 tabs.
On state representations of nonlinear implicit systems
NASA Astrophysics Data System (ADS)
Pereira da Silva, Paulo Sergio; Batista, Simone
2010-03-01
This work considers a semi-implicit system Δ, that is, a pair (S, y), where S is an explicit system described by a state representation ? , where x(t) ∈ ℝ n and u(t) ∈ ℝ m , which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) ∈ ℝ l . An input candidate is a set of functions v = (v 1, …, v s ), which may depend on time t, on x, and on u and its derivatives up to a finite order. The problem of finding a (local) proper state representation ż = g(t, z, v) with input v for the implicit system Δ is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Δ. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Lévine, Martin, and Rouchon (1999) ('A Lie-Bäcklund Approach to Equivalence and Flatness of Nonlinear Systems', IEEE Transactions on Automatic Control, 44(5), (922-937)).
Bifurcations and Patterns in Nonlinear Dissipative Systems
Guenter Ahlers
2005-05-27
This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.
Exploring lipids with nonlinear optical microscopy in multiple biological systems
NASA Astrophysics Data System (ADS)
Alfonso-Garcia, Alba
Lipids are crucial biomolecules for the well being of humans. Altered lipid metabolism may give rise to a variety of diseases that affect organs from the cardiovascular to the central nervous system. A deeper understanding of lipid metabolic processes would spur medical research towards developing precise diagnostic tools, treatment methods, and preventive strategies for reducing the impact of lipid diseases. Lipid visualization remains a complex task because of the perturbative effect exerted by traditional biochemical assays and most fluorescence markers. Coherent Raman scattering (CRS) microscopy enables interrogation of biological samples with minimum disturbance, and is particularly well suited for label-free visualization of lipids, providing chemical specificity without compromising on spatial resolution. Hyperspectral imaging yields large datasets that benefit from tailored multivariate analysis. In this thesis, CRS microscopy was combined with Raman spectroscopy and other label-free nonlinear optical techniques to analyze lipid metabolism in multiple biological systems. We used nonlinear Raman techniques to characterize Meibum secretions in the progression of dry eye disease, where the lipid and protein contributions change in ratio and phase segregation. We employed similar tools to examine lipid droplets in mice livers aboard a spaceflight mission, which lose their retinol content contributing to the onset of nonalcoholic fatty-liver disease. We also focused on atherosclerosis, a disease that revolves around lipid-rich plaques in arterial walls. We examined the lipid content of macrophages, whose variable phenotype gives rise to contrasting healing and inflammatory activities. We also proposed new label-free markers, based on lifetime imaging, for macrophage phenotype, and to detect products of lipid oxidation. Cholesterol was also detected in hepatitis C virus infected cells, and in specific strains of age-related macular degeneration diseased cells by
A multivariate analysis approach for the Imaging Atmospheric Cerenkov Telescopes System H.E.S.S
Dubois, F.; Lamanna, G.
2008-12-24
We present a multivariate classification approach applied to the analysis of data from the H.E.S.S. Very High Energy (VHE){gamma}-ray IACT stereoscopic system. This approach combines three complementary analysis methods already successfully applied in the H.E.S.S. data analysis. The proposed approach, with the combined effective estimator X{sub eff}, is conceived to improve the signal-to-background ratio and therefore particularly relevant to the morphological studies of faint extended sources.
Dagne, Getachew; Huang, Yangxin
2012-01-01
Censored data are characteristics of many bioassays in HIV/AIDS studies where assays may not be sensitive enough to determine gradations in viral load determination among those below a detectable threshold. Not accounting for such left-censoring appropriately can lead to biased parameter estimates in most data analysis. To properly adjust for left-censoring, this paper presents an extension of the Tobit model for fitting nonlinear dynamic mixed-effects models with skew distributions. Such extensions allow one to specify the conditional distributions for viral load response to account for left-censoring, skewness and heaviness in the tails of the distributions of the response variable. A Bayesian modeling approach via Markov Chain Monte Carlo (MCMC) algorithm is used to estimate model parameters. The proposed methods are illustrated using real data from an HIV/AIDS study. PMID:22992288
NASA Technical Reports Server (NTRS)
Kriegler, F. J.; Gordon, M. F.; Mclaughlin, R. H.; Marshall, R. E.
1975-01-01
The MIDAS (Multivariate Interactive Digital Analysis System) processor is a high-speed processor designed to process multispectral scanner data (from Landsat, EOS, aircraft, etc.) quickly and cost-effectively to meet the requirements of users of remote sensor data, especially from very large areas. MIDAS consists of a fast multipipeline preprocessor and classifier, an interactive color display and color printer, and a medium scale computer system for analysis and control. The system is designed to process data having as many as 16 spectral bands per picture element at rates of 200,000 picture elements per second into as many as 17 classes using a maximum likelihood decision rule.
A Visualization System for Space-Time and Multivariate Patterns (VIS-STAMP)
Guo, Diansheng; Chen, Jin; MacEachren, Alan M.; Liao, Ke
2011-01-01
The research reported here integrates computational, visual, and cartographic methods to develop a geovisual analytic approach for exploring and understanding spatio-temporal and multivariate patterns. The developed methodology and tools can help analysts investigate complex patterns across multivariate, spatial, and temporal dimensions via clustering, sorting, and visualization. Specifically, the approach involves a self-organizing map, a parallel coordinate plot, several forms of reorderable matrices (including several ordering methods), a geographic small multiple display, and a 2-dimensional cartographic color design method. The coupling among these methods leverages their independent strengths and facilitates a visual exploration of patterns that are difficult to discover otherwise. The visualization system we developed supports overview of complex patterns and, through a variety of interactions, enables users to focus on specific patterns and examine detailed views. We demonstrate the system with an application to the IEEE InfoVis 2005 Contest data set, which contains time-varying, geographically referenced, and multivariate data for technology companies in the US. PMID:17073369
NASA Astrophysics Data System (ADS)
Evtushenko, V. F.; Myshlyaev, L. P.; Makarov, G. V.; Ivushkin, K. A.; Burkova, E. V.
2016-10-01
The structure of multi-variant physical and mathematical models of control system is offered as well as its application for adjustment of automatic control system (ACS) of production facilities on the example of coal processing plant.
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
A Simple Iterative Solution of Nonlinear Algebraic Systems
NASA Astrophysics Data System (ADS)
Gousidou, Maria; Koutitas, Christopher
2009-09-01
A simple, robust, easily programmable and efficient method for the iterative solution of nonlinear algebraic systems, commonly appearing in nonlinear mechanics, based on Newton-Raphson method (without repeatedly solving linear algebraic systems), is proposed, synoptically described and experimentally investigated. Fast convergence and easy programming are its main qualifications.
Avalappampatty Sivasamy, Aneetha; Sundan, Bose
2015-01-01
The ever expanding communication requirements in today's world demand extensive and efficient network systems with equally efficient and reliable security features integrated for safe, confident, and secured communication and data transfer. Providing effective security protocols for any network environment, therefore, assumes paramount importance. Attempts are made continuously for designing more efficient and dynamic network intrusion detection models. In this work, an approach based on Hotelling's T2 method, a multivariate statistical analysis technique, has been employed for intrusion detection, especially in network environments. Components such as preprocessing, multivariate statistical analysis, and attack detection have been incorporated in developing the multivariate Hotelling's T2 statistical model and necessary profiles have been generated based on the T-square distance metrics. With a threshold range obtained using the central limit theorem, observed traffic profiles have been classified either as normal or attack types. Performance of the model, as evaluated through validation and testing using KDD Cup'99 dataset, has shown very high detection rates for all classes with low false alarm rates. Accuracy of the model presented in this work, in comparison with the existing models, has been found to be much better. PMID:26357668
A PID de-tuned method for multivariable systems, applied for HVAC plant
NASA Astrophysics Data System (ADS)
Ghazali, A. B.
2015-09-01
A simple yet effective de-tuning of PID parameters for multivariable applications has been described. Although the method is felt to have wider application it is simulated in a 3-input/ 2-output building energy management system (BEMS) with known plant dynamics. The controller performances such as the sum output squared error and total energy consumption when the system is at steady state conditions are studied. This tuning methodology can also be extended to reduce the number of PID controllers as well as the control inputs for specified output references that are necessary for effective results, i.e. with good regulation performances being maintained.
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Tools for Nonlinear Control Systems Design
NASA Technical Reports Server (NTRS)
Sastry, S. S.
1997-01-01
This is a brief statement of the research progress made on Grant NAG2-243 titled "Tools for Nonlinear Control Systems Design", which ran from 1983 till December 1996. The initial set of PIs on the grant were C. A. Desoer, E. L. Polak and myself (for 1983). From 1984 till 1991 Desoer and I were the Pls and finally I was the sole PI from 1991 till the end of 1996. The project has been an unusually longstanding and extremely fruitful partnership, with many technical exchanges, visits, workshops and new avenues of investigation begun on this grant. There were student visits, long term.visitors on the grant and many interesting joint projects. In this final report I will only give a cursory description of the technical work done on the grant, since there was a tradition of annual progress reports and a proposal for the succeeding year. These progress reports cum proposals are attached as Appendix A to this report. Appendix B consists of papers by me and my students as co-authors sorted chronologically. When there are multiple related versions of a paper, such as a conference version and journal version they are listed together. Appendix C consists of papers by Desoer and his students as well as 'solo' publications by other researchers supported on this grant similarly chronologically sorted.
Robust nonlinear variable selective control for networked systems
NASA Astrophysics Data System (ADS)
Rahmani, Behrooz
2016-10-01
This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi-Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H2 performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.
State analysis of nonlinear systems using local canonical variate analysis
Hunter, N.F.
1997-01-01
There are many instances in which time series measurements are used to derive an empirical model of a dynamical system. State space reconstruction from time series measurement has applications in many scientific and engineering disciplines including structural engineering, biology, chemistry, climatology, control theory, and physics. Prediction of future time series values from empirical models was attempted as early as 1927 by Yule, who applied linear prediction methods to the sunspot values. More recently, efforts in this area have centered on two related aspects of time series analysis, namely prediction and modeling. In prediction future time series values are estimated from past values, in modeling, fundamental characteristics of the state model underlying the measurements are estimated, such as dimension and eigenvalues. In either approach a measured time series, [{bold y}(t{sub i})], i= 1,... N is assumed to derive from the action of a smooth dynamical system, s(t+{bold {tau}})=a(s(t)), where the bold notation indicates the (potentially ) multivariate nature of the time series. The time series is assumed to derive from the state evolution via a measurement function c. {bold y}(t)=c(s(t)) In general the states s(t), the state evolution function a and the measurement function c are In unknown, and must be inferred from the time series measurements. We approach this problem from the standpoint of time series analysis. We review the principles of state space reconstruction. The specific model formulation used in the local canonical variate analysis algorithm and a detailed description of the state space reconstruction algorithm are included. The application of the algorithm to a single-degree-of- freedom Duffing-like Oscillator and the difficulties involved in reconstruction of an unmeasured degree of freedom in a four degree of freedom nonlinear oscillator are presented. The advantages and current limitations of state space reconstruction are summarized.
Nonlinear Control of Dynamical Systems from Time Series
NASA Astrophysics Data System (ADS)
Petrov, Valery; Showalter, Kenneth
1996-04-01
Feedback control of multidimensional, nonlinear single-input single-output systems is formulated in terms of an invariant hypersurface in the delayed state space of a system observable and a control parameter. The surface is created directly from the response of the system to random perturbations, providing a model-independent nonlinear control algorithm. The algorithm can be used to stabilize unstable states or to drive a system to any particular objective state in a minimum number of steps.
NASA Technical Reports Server (NTRS)
Sankaran, V.
1974-01-01
An iterative procedure for determining the constant gain matrix that will stabilize a linear constant multivariable system using output feedback is described. The use of this procedure avoids the transformation of variables which is required in other procedures. For the case in which the product of the output and input vector dimensions is greater than the number of states of the plant, general solution is given. In the case in which the states exceed the product of input and output vector dimensions, a least square solution which may not be stable in all cases is presented. The results are illustrated with examples.
Breather compactons in nonlinear Klein-Gordon systems.
Dinda, P T; Remoissenet, M
1999-11-01
We demonstrate the existence of a localized breathing mode with a compact support, i.e., a stationary breather compacton, in a nonlinear Klein-Gordon system. This breather compacton results from a delicate balance between the harmonicity of the substrate potential and the total nonlinearity induced by the substrate potential and the coupling forces between adjacent lattice sites.
Efficient solution procedures for systems with local non-linearities
NASA Astrophysics Data System (ADS)
Ibrahimbegovic, Adnan; Wilson, Edward L.
1992-06-01
This paper presents several methods for enhancing computational efficiency in both static and dynamic analysis of structural systems with localized nonlinear behavior. A significant reduction of computational effort with respect to brute-force nonlinear analysis is achieved in all cases at the insignificant (or no) loss of accuracy. The presented methodologies are easily incorporated into a standard computer program for linear analysis.
A Method for Exploiting Redundancy to Accommodate Actuator Limits in Multivariable Systems
NASA Technical Reports Server (NTRS)
Litt, Jonathan; Roulette, Greg
1995-01-01
This paper introduces a new method for accommodating actuator saturation in a multivariable system with actuator redundancy. Actuator saturation can cause significant deterioration in control system performance because unmet demand may result in sluggish transients and oscillations in response to setpoint changes. To help compensate for this problem, a technique has been developed which takes advantage of redundancy in multivariable systems to redistribute the unmet control demand over the remaining useful effectors. This method is not a redesign procedure, rather it modifies commands to the unlimited effectors to compensate for those which are limited, thereby exploiting the built-in redundancy. The original commands are modified by the increments due to unmet demand, but when a saturated effector comes off its limit, the incremental commands disappear and the original unmodified controller remains intact. This scheme provides a smooth transition between saturated and unsaturated modes as it divides up the unmet requirement over any available actuators. This way, if there is sufficiently redundant control authority, performance can be maintained.
On the benefit of DMT modulation in nonlinear VLC systems.
Qian, Hua; Cai, Sunzeng; Yao, Saijie; Zhou, Ting; Yang, Yang; Wang, Xudong
2015-02-01
In a visible light communication (VLC) system, the nonlinear characteristic of the light emitting diode (LED) in transmitter is a limiting factor of system performance. Modern modulation signals with large peak-to-power-ratio (PAPR) suffers uneven distortion. The nonlinear response directly impacts the intensity modulation and direct detection VLC system with pulse-amplitude modulation (PAM). The amplitude of the PAM signal is distorted unevenly and large signal is vulnerable to noise. Orthogonal linear transformations, such as discrete multi-tone (DMT) modulation, can spread the nonlinear effects evenly to each data symbol, thus perform better than PAM signals. In this paper, we provide theoretical analysis on the benefit of DMT modulation in nonlinear VLC system. We show that the DMT modulation is a better choice than the PAM modulation for the VLC system as the DMT modulation is more robust against nonlinearity. We also show that the post-distortion nonlinear elimination method, which is applied at the receiver, can be a reliable solution to the nonlinear VLC system. Simulation results show that the post-distortion greatly improves the system performance for the DMT modulation.
Gad, R S; Parab, J S; Naik, G M
2010-11-01
Multivariate system spectroscopic model plays important role in understanding chemometrics of ensemble under study. Here in this manuscript we discuss various approaches of modeling of spectroscopic system and demonstrate how Lorentz oscillator can be used to model any general spectroscopic system. Chemometric studies require customized templates design for the corresponding variants participating in ensemble, which generates the characteristic matrix of the ensemble under study. The typical biological system that resembles human blood tissue consisting of five major constituents i.e., alanine, urea, lactate, glucose, ascorbate; has been tested on the model. The model was validated using three approaches, namely, root mean square error (RMSE) analysis in the range of ±5% confidence interval, clerk gird error plot, and RMSE versus percent noise level study. Also the model was tested across various template sizes (consisting of samples ranging from 10 up to 1000) to ascertain the validity of partial least squares regression. The model has potential in understanding the chemometrics of proteomics pathways.
NASA Astrophysics Data System (ADS)
Gad, R. S.; Parab, J. S.; Naik, G. M.
2010-11-01
Multivariate system spectroscopic model plays important role in understanding chemometrics of ensemble under study. Here in this manuscript we discuss various approaches of modeling of spectroscopic system and demonstrate how Lorentz oscillator can be used to model any general spectroscopic system. Chemometric studies require customized templates design for the corresponding variants participating in ensemble, which generates the characteristic matrix of the ensemble under study. The typical biological system that resembles human blood tissue consisting of five major constituents i.e., alanine, urea, lactate, glucose, ascorbate; has been tested on the model. The model was validated using three approaches, namely, root mean square error (RMSE) analysis in the range of ±5% confidence interval, clerk gird error plot, and RMSE versus percent noise level study. Also the model was tested across various template sizes (consisting of samples ranging from 10 up to 1000) to ascertain the validity of partial least squares regression. The model has potential in understanding the chemometrics of proteomics pathways.
A mathematical theory of learning control for linear discrete multivariable systems
NASA Technical Reports Server (NTRS)
Phan, Minh; Longman, Richard W.
1988-01-01
When tracking control systems are used in repetitive operations such as robots in various manufacturing processes, the controller will make the same errors repeatedly. Here consideration is given to learning controllers that look at the tracking errors in each repetition of the process and adjust the control to decrease these errors in the next repetition. A general formalism is developed for learning control of discrete-time (time-varying or time-invariant) linear multivariable systems. Methods of specifying a desired trajectory (such that the trajectory can actually be performed by the discrete system) are discussed, and learning controllers are developed. Stability criteria are obtained which are relatively easy to use to insure convergence of the learning process, and proper gain settings are discussed in light of measurement noise and system uncertainties.
NASA Technical Reports Server (NTRS)
Kriegler, F. J.; Christenson, D.; Gordon, M.; Kistler, R.; Lampert, S.; Marshall, R.; Mclaughlin, R.
1974-01-01
The Midas System is a third-generation, fast, multispectral recognition system able to keep pace with the large quantity and high rates of data acquisition from present and projected sensors. A principal objective of the MIDAS Program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turn-around time and significant gains in throughput. The hardware and software generated in Phase I of the overall program are described. The system contains a mini-computer to control the various high-speed processing elements in the data path and a classifier which implements an all-digital prototype multivariate-Gaussian maximum likelihood decision algorithm operating at 2 x 100,000 pixels/sec. Sufficient hardware was developed to perform signature extraction from computer-compatible tapes, compute classifier coefficients, control the classifier operation, and diagnose operation. The MIDAS construction and wiring diagrams are given.
Control design for a class of nonlinear parameter varying systems
NASA Astrophysics Data System (ADS)
Cai, Xiushan; Liu, Yang; Zhang, Wei
2015-07-01
Stabilisation for a class of one-sided Lipschitz nonlinear parameter varying systems is dealt with in this paper. First, the nonlinear parameter varying system is represented as a subsystem of a differential inclusion. Sufficient conditions for exponential stabilisation for the differential inclusion are given by solving linear matrix inequalities. Then a continuous control law is designed to stabilise the differential inclusion. It leads to stabilising the nonlinear parameter varying system. Finally, a simulation example is presented to show the validity and advantages of the proposed method.
Analysis and design of robust decentralized controllers for nonlinear systems
Schoenwald, D.A.
1993-07-01
Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.
An experimental study of nonlinear dynamic system identification
NASA Astrophysics Data System (ADS)
Stry, Greselda I.; Mook, D. Joseph
1990-12-01
A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.
NASA Astrophysics Data System (ADS)
Alfonso, Lester; Zamora, Jose; Cruz, Pedro
2015-04-01
The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.
Eigenvalue assignment by minimal state-feedback gain in LTI multivariable systems
NASA Astrophysics Data System (ADS)
Ataei, Mohammad; Enshaee, Ali
2011-12-01
In this article, an improved method for eigenvalue assignment via state feedback in the linear time-invariant multivariable systems is proposed. This method is based on elementary similarity operations, and involves mainly utilisation of vector companion forms, and thus is very simple and easy to implement on a digital computer. In addition to the controllable systems, the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs. Moreover, two types of state-feedback gain matrices can be achieved by this method: (1) the numerical one, which is unique, and (2) the parametric one, in which its parameters are determined in order to achieve a gain matrix with minimum Frobenius norm. The numerical examples are presented to demonstrate the advantages of the proposed method.
Dong, Jiuxiang; Wang, Youyi; Yang, Guang-Hong
2010-12-01
This paper considers the output feedback control problem for nonlinear discrete-time systems, which are represented by a type of fuzzy systems with local nonlinear models. By using the estimations of the states and nonlinear functions in local models, sufficient conditions for designing observer-based controllers are given for discrete-time nonlinear systems. First, a separation property, i.e., the controller and the observer can be independently designed, is proved for the class of fuzzy systems. Second, a two-step procedure with cone complementarity linearization algorithms is also developed for solving the H( ∞) dynamic output feedback (DOF) control problem. Moreover, for the case where the nonlinear functions in local submodels are measurable, a convex condition for designing H(∞) controllers is given by a new DOF control scheme. In contrast to the existing methods, the new methods can design output feedback controllers with fewer fuzzy rules as well as less computational burden, which is helpful for controller designs and implementations. Lastly, numerical examples are given to illustrate the effectiveness of the proposed methods.
Optimal second order sliding mode control for nonlinear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-07-01
In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.
Multivariate model of female black bear habitat use for a Geographic Information System
Clark, Joseph D.; Dunn, James E.; Smith, Kimberly G.
1993-01-01
Simple univariate statistical techniques may not adequately assess the multidimensional nature of habitats used by wildlife. Thus, we developed a multivariate method to model habitat-use potential using a set of female black bear (Ursus americanus) radio locations and habitat data consisting of forest cover type, elevation, slope, aspect, distance to roads, distance to streams, and forest cover type diversity score in the Ozark Mountains of Arkansas. The model is based on the Mahalanobis distance statistic coupled with Geographic Information System (GIS) technology. That statistic is a measure of dissimilarity and represents a standardized squared distance between a set of sample variates and an ideal based on the mean of variates associated with animal observations. Calculations were made with the GIS to produce a map containing Mahalanobis distance values within each cell on a 60- × 60-m grid. The model identified areas of high habitat use potential that could not otherwise be identified by independent perusal of any single map layer. This technique avoids many pitfalls that commonly affect typical multivariate analyses of habitat use and is a useful tool for habitat manipulation or mitigation to favor terrestrial vertebrates that use habitats on a landscape scale.
Smith predictor with inverted decoupling for square multivariable time delay systems
NASA Astrophysics Data System (ADS)
Garrido, Juan; Vázquez, Francisco; Morilla, Fernando; Normey-Rico, Julio E.
2016-01-01
This paper presents a new methodology to design multivariable Smith predictor for n×n processes with multiple time delays based on the centralised inverted decoupling structure. The controller elements are calculated in order to achieve good reference tracking and decoupling response. Independent of the system size, very simple general expressions for the controller elements are obtained. The realisability conditions are provided and the particular case of processes with all of its elements as first-order plus time delay systems is discussed in more detail. A diagonal filter is added to the proposed control structure in order to improve the disturbance rejection without modifying the nominal set-point response and to obtain a stable output prediction in unstable plants. The effectiveness of the method is illustrated through different simulation examples in comparison with other works.
NASA Technical Reports Server (NTRS)
Waszak, Martin R.
1992-01-01
The application of a sector-based stability theory approach to the formulation of useful uncertainty descriptions for linear, time-invariant, multivariable systems is explored. A review of basic sector properties and sector-based approach are presented first. The sector-based approach is then applied to several general forms of parameter uncertainty to investigate its advantages and limitations. The results indicate that the sector uncertainty bound can be used effectively to evaluate the impact of parameter uncertainties on the frequency response of the design model. Inherent conservatism is a potential limitation of the sector-based approach, especially for highly dependent uncertain parameters. In addition, the representation of the system dynamics can affect the amount of conservatism reflected in the sector bound. Careful application of the model can help to reduce this conservatism, however, and the solution approach has some degrees of freedom that may be further exploited to reduce the conservatism.
New stability conditions for nonlinear time varying delay systems
NASA Astrophysics Data System (ADS)
Elmadssia, S.; Saadaoui, K.; Benrejeb, M.
2016-07-01
In this paper, new practical stability conditions for a class of nonlinear time varying delay systems are proposed. The study is based on the use of a specific state space description, known as the Benrejeb characteristic arrow form matrix, and aggregation techniques to obtain delay-dependent stability conditions. Application of this method to delayed Lurie-Postnikov nonlinear systems is given. Illustrative examples are presented to show the effectiveness of the proposed approach.
NASA Astrophysics Data System (ADS)
Ravindranath, A.; Devineni, N.
2015-12-01
While India has a long history of prediction of the All India Monsoon, work on spatially specific attributes of the monsoon, as well as monsoon break periods has only recently emerged. However, from a risk management context, prognostic information of a single variable such as total precipitation or average temperature will be of less utility especially for specific operational purposes. An integrated regional climate-weather forecast system covering precipitation, temperature and humidity etc. over the year will benefit the farmers in the context of a specific decision time table for irrigation scheduling as well as for pre-season crop choices. Hence, contrary to the existing forecasting methods that develop multi time scale information of a single variable at a time, in this paper, we introduce an integrated regional multivariate climate-weather forecasting system that directly relates to agricultural decision making and risk mitigation. These multi-scale risk attributes include mutually dependent, spatially disaggregated statistics such as total rainfall, average temperature, growing degree days, relative humidity, total number of rainfall days/dry spell length, and cumulative water deficits that inform the potential irrigation water requirements for crops. Given that these attributes exhibit mutual dependence across space and time, we propose to explore common ocean-atmospheric conditions from the observations and the state of the art Global Circulation Models (GCMs) that can be utilized as the predictor variables for the forecasting system. Hierarchical Bayesian methods are be used to develop the integrated forecast system. The developed multivariate forecasts will be adapted and disseminated as decision tools for the farmers under the extension projects in Punjab region of India.
Multivariate Multi-Data Assimilation System in Regional Model With High Resolution
NASA Astrophysics Data System (ADS)
Benkiran, M.; Chanut, J.; Greiner, E.; Giraud St Albin, S.; Drillet, Y.
2008-12-01
Mercator Ocean has developed a regional North East Shelf forecasting system over the North East Atlantic, taking advantage of the recent developments in NEMO (1/12). This regional forecasting system uses boundary conditions from the operational real-time Mercator Ocean North Atlantic high resolution system (1/12). The assimilation component of the Mercator Ocean system, is based on a reduced-order Kalman filter (the SEEK or Singular Extended Evolutive Kalman filter). The error statistics are represented in a sub-space spanned by a small number of dominant 3D error directions. The data assimilation system allows to constrain the model in a multivariate way with Sea Surface Temperature (RTG-SST), together with all available satellite Sea Level Anomalies, and with in situ observations from the CORIOLIS database, including ARGO floats temperature and salinity measurements.At last, we used PALM coupler which provides a general structure for a modular implementation of a data assimilation system, and makes easier the changes in the analysis algorithm. We will confront the results obtained with the regional forecast system (1/12) with IAU (Incremental Analysis Updates) to the ones obtained with Mercator Ocean North Atlantic high resolution system (1/12).
Multivariate Multi-data Assimilation System in Regional Model with High Resolution
NASA Astrophysics Data System (ADS)
Benkiran, M.; Bourdalle-Badie, R.; Drillet, Y.; Greiner, E.; Chanut, J.
2009-12-01
Mercator Ocean has developed a regional North East Shelf forecasting system over the North East Atlantic, taking advantage of the recent developments in NEMO (1/12°). This regional forecasting system uses boundary conditions from the operational real-time Mercator Ocean North Atlantic high resolution system (1/12°). The assimilation component of the Mercator Ocean system, is based on a reduced-order Kalman filter (the SEEK or Singular Extended Evolutive Kalman filter). The error statistics are represented in a sub-space spanned by a small number of dominant 3D error directions. The data assimilation system allows to constrain the model in a multivariate way with Sea Surface Temperature (RTG-SST), together with all available satellite Sea Level Anomalies, and with in situ observations from the CORIOLIS database, including ARGO floats temperature and salinity measurements.At last, we used PALM coupler which provides a general structure for a modular implementation of a data assimilation system, and makes easier the changes in the analysis algorithm. We will confront the results obtained with the regional forecast system (1/12°) with IAU (Incremental Analysis Updates) to the ones obtained with Mercator Ocean North Atlantic high resolution system (1/12°).
Multivariate Multi-data Assimilation System in Regional Model with High Resolution
NASA Astrophysics Data System (ADS)
Benkiran, M.; Chanut, J.; Giraud St Albin, S.; Drillet, Y.
2010-12-01
Mercator Ocean has developed a regional North East Shelf forecasting system over the North East Atlantic, taking advantage of the recent developments in NEMO (1/12°). This regional forecasting system uses boundary conditions from the operational real-time Mercator Ocean North Atlantic high resolution system (1/12°). The assimilation component of the Mercator Ocean system, is based on a reduced-order Kalman filter (the SEEK or Singular Extended Evolutive Kalman filter). The error statistics are represented in a sub-space spanned by a small number of dominant 3D error directions. The data assimilation system allows to constrain the model in a multivariate way with Sea Surface Temperature (RTG-SST), together with all available satellite Sea Level Anomalies, and with in situ observations from the CORIOLIS database, including ARGO floats temperature and salinity measurements.At last, we used PALM coupler which provides a general structure for a modular implementation of a data assimilation system, and makes easier the changes in the analysis algorithm. We will confront the results obtained with the regional forecast system (1/12°) with IAU (Incremental Analysis Updates) to the ones obtained with Mercator Ocean North Atlantic high resolution system (1/12°).
3-D Mesh Generation Nonlinear Systems
Christon, M. A.; Dovey, D.; Stillman, D. W.; Hallquist, J. O.; Rainsberger, R. B
1994-04-07
INGRID is a general-purpose, three-dimensional mesh generator developed for use with finite element, nonlinear, structural dynamics codes. INGRID generates the large and complex input data files for DYNA3D, NIKE3D, FACET, and TOPAZ3D. One of the greatest advantages of INGRID is that virtually any shape can be described without resorting to wedge elements, tetrahedrons, triangular elements or highly distorted quadrilateral or hexahedral elements. Other capabilities available are in the areas of geometry and graphics. Exact surface equations and surface intersections considerably improve the ability to deal with accurate models, and a hidden line graphics algorithm is included which is efficient on the most complicated meshes. The primary new capability is associated with the boundary conditions, loads, and material properties required by nonlinear mechanics programs. Commands have been designed for each case to minimize user effort. This is particularly important since special processing is almost always required for each load or boundary condition.
Self-characterization of linear and nonlinear adaptive optics systems.
Hampton, Peter J; Conan, Rodolphe; Keskin, Onur; Bradley, Colin; Agathoklis, Pan
2008-01-10
We present methods used to determine the linear or nonlinear static response and the linear dynamic response of an adaptive optics (AO) system. This AO system consists of a nonlinear microelectromechanical systems deformable mirror (DM), a linear tip-tilt mirror (TTM), a control computer, and a Shack-Hartmann wavefront sensor. The system is modeled using a single-input-single-output structure to determine the one-dimensional transfer function of the dynamic response of the chain of system hardware. An AO system has been shown to be able to characterize its own response without additional instrumentation. Experimentally determined models are given for a TTM and a DM. PMID:18188192
Applications of nonlinear systems theory to control design
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Villarreal, Ramiro
1988-01-01
For most applications in the control area, the standard practice is to approximate a nonlinear mathematical model by a linear system. Since the feedback linearizable systems contain linear systems as a subclass, the procedure of approximating a nonlinear system by a feedback linearizable one is examined. Because many physical plants (e.g., aircraft at the NASA Ames Research Center) have mathematical models which are close to feedback linearizable systems, such approximations are certainly justified. Results and techniques are introduced for measuring the gap between the model and its truncated linearizable part. The topic of pure feedback systems is important to the study.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system. PMID:24808035
Flight investigation of a multivariable model-following control system for rotorcraft
NASA Technical Reports Server (NTRS)
Hilbert, K. B.; Lebacqz, J. V.; Hindson, W. S.
1986-01-01
A high-bandwidth, multivariable, explicit model-following control system for advanced rotorcraft has been developed and evaluated on the NASA Ames CH-47B fly-by-wire helicopter. This control system has expanded the in-flight simulation capabilities of the CH-47B to support research efforts directed at the next generation of superaugmented helicopters. A detailed, analytical model of the augmented CH-47B has also been developed to support the flight tests. Analysis using this theoretical model was used to expose fundamental limitations caused by the basic vehicle characteristics and original control system implementation that had affected the performance of the model-following control system. Improvements were made to the nominal control system design to compensate for large time delays created by the higher-orderd dynamics of the aircraft and its control system. With these improvements, high bandwidth control and excellent model-following performance were achieved. Both analytical and flight-test results for the lateral axis are presented and compared. In addition, frequency-domain techniques are employed for documenting the system performance.
Parameter and Structure Inference for Nonlinear Dynamical Systems
NASA Technical Reports Server (NTRS)
Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark
2006-01-01
A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.
Nonlinear signal processing using neural networks: Prediction and system modelling
Lapedes, A.; Farber, R.
1987-06-01
The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.
Multivariable output feedback robust adaptive tracking control design for a class of delayed systems
NASA Astrophysics Data System (ADS)
Mirkin, Boris; Gutman, Per-Olof
2015-02-01
In this paper, we develop a model reference adaptive control scheme for a class of multi-input multi-output nonlinearly perturbed dynamic systems with unknown time-varying state delays which is also robust with respect to an external disturbance with unknown bounds. The output feedback adaptive control scheme uses feedback actions only, and thus does not require a direct measurement of the command or disturbance signals. A suitable Lyapunov-Krasovskii type functional is introduced to design the adaptation algorithms and to prove stability.
Nonlinear time reversal in a wave chaotic system.
Frazier, Matthew; Taddese, Biniyam; Antonsen, Thomas; Anlage, Steven M
2013-02-01
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the time-reversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication and point out other applications.
Code System for Solving Nonlinear Systems of Equations via the Gauss-Newton Method.
1981-08-31
Version 00 REGN solves nonlinear systems of numerical equations in difficult cases: high nonlinearity, poor initial approximations, a large number of unknowns, ill condition or degeneracy of a problem.
Put, R; Van Gyseghem, E; Coomans, D; Vander Heyden, Y
2005-11-25
In order to select chromatographic starting conditions to be optimized during further method development of the separation of a given mixture, so-called generic orthogonal chromatographic systems could be explored in parallel. In this paper the use of univariate and multivariate regression trees (MRT) was studied to define the most orthogonal subset from a given set of chromatographic systems. Two data sets were considered, which contain the retention data of 68 structurally diversive drugs on sets of 32 and 38 chromatographic systems, respectively. For both the univariate and multivariate approaches no other data but the measured retention factors are needed to build the decision trees. Since multivariate regression trees are used in an unsupervised way, they are called auto-associative multivariate regression trees (AAMRT). For all decision trees used, a variable importance list of the predictor variables can be derived. It was concluded that based on these ranked lists, both for univariate and multivariate regression trees, a selection of the most orthogonal systems from a given set of systems can be obtained in a user-friendly and fast way.
Development of a nonlinear optical measurement-4 coherent imaging system
NASA Astrophysics Data System (ADS)
Chen, Xiaojun; Song, Yinglin; Gu, Jihua; Yang, Junyi; Shui, Min; Hou, Dengke; Zhu, Zongjie
2009-07-01
After the nonlinear optical phenomena were discovered, people began to research the techniques to detect the optical nonlinearities of materials. In this paper, a new optical nonlinear measurement technique-4f coherent imaging system is recommended. The system has many advantages: single shot real-time measurement, simple experimental apparatus, high sensitivity, being able to detect the magnitude and sign of both nonlinear absorption and refraction at the same time, low requirement of beam spatial distribution, and so on. This paper introduces the theory of the 4f system and makes a detailed review and expounds development and application of the 4f coherent image system. The nerve of the experiment is improving the phase diaphragm. The shape of the diaphragm from the double-slits to the small rectangular object, and transition to a circular aperture, finally forming a circular phase diaphragm, which is a circular aperture in the center add a phase object. Following these diaphragm changes, the sensitivity of the system is greatly improved. The latest developments of the system are series-wound double 4f coherent imaging technique and the time-resolved pump-probe system based on NIT-PO. The time-resolved pump-probe system based on NIT-PO can be used to measure the dynamic characteristics of excited states nonlinear absorption and refraction.
Adaptive control of nonlinear systems with actuator failures and uncertainties
NASA Astrophysics Data System (ADS)
Tang, Xidong
2005-11-01
Actuator failures have damaging effect on the performance of control systems, leading to undesired system behavior or even instability. Actuator failures are unknown in terms of failure time instants, failure patterns, and failure parameters. For system safety and reliability, the compensation of actuator failures is of both theoretical and practical significance. This dissertation is to further the study of adaptive designs for actuator failure compensation to nonlinear systems. In this dissertation a theoretical framework for adaptive control of nonlinear systems with actuator failures and system uncertainties is established. The contributions are the development of new adaptive nonlinear control schemes to handle unknown actuator failures for convergent tracking performance, the specification of conditions as a guideline for applications and system designs, and the extension of the adaptive nonlinear control theory. In the dissertation, adaptive actuator failure compensation is studied for several classes of nonlinear systems. In particular, adaptive state feedback schemes are developed for feedback linearizable systems and parametric strict-feedback systems. Adaptive output feedback schemes are deigned for output-feedback systems and a class of systems with unknown state-dependent nonlinearities. Furthermore, adaptive designs are addressed for MIMO systems with actuator failures, based on two grouping techniques: fixed grouping and virtual grouping. Theoretical issues such as controller structures, actuation schemes, zero dynamics, observation, grouping conditions, closed-loop stability, and tracking performance are extensively investigated. For each scheme, design conditions are clarified, and detailed stability and performance analysis is presented. A variety of applications including a wing-rock model, twin otter aircraft, hypersonic aircraft, and cooperative multiple manipulators are addressed with simulation results showing the effectiveness of the
Identification of nonlinear optical systems using adaptive kernel methods
NASA Astrophysics Data System (ADS)
Wang, Xiaodong; Zhang, Changjiang; Zhang, Haoran; Feng, Genliang; Xu, Xiuling
2005-12-01
An identification approach of nonlinear optical dynamic systems, based on adaptive kernel methods which are modified version of least squares support vector machine (LS-SVM), is presented in order to obtain the reference dynamic model for solving real time applications such as adaptive signal processing of the optical systems. The feasibility of this approach is demonstrated with the computer simulation through identifying a Bragg acoustic-optical bistable system. Unlike artificial neural networks, the adaptive kernel methods possess prominent advantages: over fitting is unlikely to occur by employing structural risk minimization criterion, the global optimal solution can be uniquely obtained owing to that its training is performed through the solution of a set of linear equations. Also, the adaptive kernel methods are still effective for the nonlinear optical systems with a variation of the system parameter. This method is robust with respect to noise, and it constitutes another powerful tool for the identification of nonlinear optical systems.
Non-linear system identification in flow-induced vibration
Spanos, P.D.; Zeldin, B.A.; Lu, R.
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
Relations between static and dynamic exponents in nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Badii, R.; Broggi, G.
1990-01-01
The rules governing the evolution of nonlinear dynamical systems are systematically detected by constructing a hierarchical tree of symbol sequences. Relations between local partial dimensions and Lyapunov exponents are obtained from equations for the probabilities of symbol sequences on the logic tree. These relations are nonlinear and involve an open hierarchy of equations, which shows that the dimension spectrum f(α) cannot be obtained in closed form from the sole knowledge of the local Lyapunov exponents.
Diagnosis of nonlinear systems using time series analysis
Hunter, N.F. Jr.
1991-01-01
Diagnosis and analysis techniques for linear systems have been developed and refined to a high degree of precision. In contrast, techniques for the analysis of data from nonlinear systems are in the early stages of development. This paper describes a time series technique for the analysis of data from nonlinear systems. The input and response time series resulting from excitation of the nonlinear system are embedded in a state space. The form of the embedding is optimized using local canonical variate analysis and singular value decomposition techniques. From the state space model, future system responses are estimated. The expected degree of predictability of the system is investigated using the state transition matrix. The degree of nonlinearity present is quantified using the geometry of the transfer function poles in the z plane. Examples of application to a linear single-degree-of-freedom system, a single-degree-of-freedom Duffing Oscillator, and linear and nonlinear three degree of freedom oscillators are presented. 11 refs., 9 figs.
3-D Mesh Generation Nonlinear Systems
1994-04-07
INGRID is a general-purpose, three-dimensional mesh generator developed for use with finite element, nonlinear, structural dynamics codes. INGRID generates the large and complex input data files for DYNA3D, NIKE3D, FACET, and TOPAZ3D. One of the greatest advantages of INGRID is that virtually any shape can be described without resorting to wedge elements, tetrahedrons, triangular elements or highly distorted quadrilateral or hexahedral elements. Other capabilities available are in the areas of geometry and graphics. Exact surfacemore » equations and surface intersections considerably improve the ability to deal with accurate models, and a hidden line graphics algorithm is included which is efficient on the most complicated meshes. The primary new capability is associated with the boundary conditions, loads, and material properties required by nonlinear mechanics programs. Commands have been designed for each case to minimize user effort. This is particularly important since special processing is almost always required for each load or boundary condition.« less
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time. PMID:26986334
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
Variational principle for nonlinear wave propagation in dissipative systems
NASA Astrophysics Data System (ADS)
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
Modeling a Nonlinear Liquid Level System by Cellular Neural Networks
NASA Astrophysics Data System (ADS)
Hernandez-Romero, Norberto; Seck-Tuoh-Mora, Juan Carlos; Gonzalez-Hernandez, Manuel; Medina-Marin, Joselito; Flores-Romero, Juan Jose
This paper presents the analogue simulation of a nonlinear liquid level system composed by two tanks; the system is controlled using the methodology of exact linearization via state feedback by cellular neural networks (CNNs). The relevance of this manuscript is to show how a block diagram representing the analogue modeling and control of a nonlinear dynamical system, can be implemented and regulated by CNNs, whose cells may contain numerical values or arithmetic and control operations. In this way the dynamical system is modeled by a set of local-interacting elements without need of a central supervisor.
NASA Technical Reports Server (NTRS)
Valavani, Lena
1995-01-01
The main motivation for the work under the present grant was to use nonlinear feedback linearization methods to further enhance performance capabilities of the aircraft, and robustify its response throughout its operating envelope. The idea was to use these methods in lieu of standard Taylor series linearization, in order to obtain a well behaved linearized plant, in its entire operational regime. Thus, feedback linearization was going to constitute an 'inner loop', which would then define a 'design plant model' to be compensated for robustness and guaranteed performance in an 'outer loop' application of modern linear control methods. The motivation for this was twofold; first, earlier work had shown that by appropriately conditioning the plant through conventional, simple feedback in an 'inner loop', the resulting overall compensated plant design enjoyed considerable enhancement of performance robustness in the presence of parametric uncertainty. Second, the nonlinear techniques did not have any proven robustness properties in the presence of unstructured uncertainty; a definition of robustness (and performance) is very difficult to achieve outside the frequency domain; to date, none is available for the purposes of control system design. Thus, by proper design of the outer loop, such properties could still be 'injected' in the overall system.
Experimental nonlinear laser systems: Bigger data for better science?
Kane, D. M.; Toomey, J. P.; McMahon, C.; Noblet, Y.; Argyris, A.; Syvridis, D.
2014-10-06
Bigger data is supporting knowledge discovery in nonlinear laser systems as will be demonstrated with examples from three semiconductor laser based systems – one with optical feedback, a photonic integrated circuit (PIC) chaotic laser and a frequency shifted feedback laser system.
Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems.
Zhang, Yanjun; Tao, Gang; Chen, Mou
2016-09-01
This paper presents a new study on the adaptive neural network-based control of a class of noncanonical nonlinear systems with large parametric uncertainties. Unlike commonly studied canonical form nonlinear systems whose neural network approximation system models have explicit relative degree structures, which can directly be used to derive parameterized controllers for adaptation, noncanonical form nonlinear systems usually do not have explicit relative degrees, and thus their approximation system models are also in noncanonical forms. It is well-known that the adaptive control of noncanonical form nonlinear systems involves the parameterization of system dynamics. As demonstrated in this paper, it is also the case for noncanonical neural network approximation system models. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparameterize such neural network system models for adaptive control design, and that such reparameterization can be realized using a relative degree formulation, a concept yet to be studied for general neural network system models. This paper then derives the parameterized controllers that guarantee closed-loop stability and asymptotic output tracking for noncanonical form neural network system models. An illustrative example is presented with the simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method.
Wallace, Jack; Champagne, Pascale; Monnier, Anne-Charlotte
2015-01-01
A pilot-scale hybrid-passive treatment system operated at the Merrick Landfill in North Bay, Ontario, Canada, treats municipal landfill leachate and provides for subsequent natural attenuation. Collected leachate is directed to a hybrid-passive treatment system, followed by controlled release to a natural attenuation zone before entering the nearby Little Sturgeon River. The study presents a comprehensive evaluation of the performance of the system using multivariate statistical techniques to determine the interactions between parameters, major pollutants in the leachate, and the biological and chemical processes occurring in the system. Five parameters (ammonia, alkalinity, chemical oxygen demand (COD), "heavy" metals of interest, with atomic weights above calcium, and iron) were set as criteria for the evaluation of system performance based on their toxicity to aquatic ecosystems and importance in treatment with respect to discharge regulations. System data for a full range of water quality parameters over a 21-month period were analyzed using principal components analysis (PCA), as well as principal components (PC) and partial least squares (PLS) regressions. PCA indicated a high degree of association for most parameters with the first PC, which explained a high percentage (>40%) of the variation in the data, suggesting strong statistical relationships among most of the parameters in the system. Regression analyses identified 8 parameters (set as independent variables) that were most frequently retained for modeling the five criteria parameters (set as dependent variables), on a statistically significant level: conductivity, dissolved oxygen (DO), nitrite (NO2(-)), organic nitrogen (N), oxidation reduction potential (ORP), pH, sulfate and total volatile solids (TVS). The criteria parameters and the significant explanatory parameters were most important in modeling the dynamics of the passive treatment system during the study period. Such techniques and
Wallace, Jack; Champagne, Pascale; Monnier, Anne-Charlotte
2015-01-01
A pilot-scale hybrid-passive treatment system operated at the Merrick Landfill in North Bay, Ontario, Canada, treats municipal landfill leachate and provides for subsequent natural attenuation. Collected leachate is directed to a hybrid-passive treatment system, followed by controlled release to a natural attenuation zone before entering the nearby Little Sturgeon River. The study presents a comprehensive evaluation of the performance of the system using multivariate statistical techniques to determine the interactions between parameters, major pollutants in the leachate, and the biological and chemical processes occurring in the system. Five parameters (ammonia, alkalinity, chemical oxygen demand (COD), "heavy" metals of interest, with atomic weights above calcium, and iron) were set as criteria for the evaluation of system performance based on their toxicity to aquatic ecosystems and importance in treatment with respect to discharge regulations. System data for a full range of water quality parameters over a 21-month period were analyzed using principal components analysis (PCA), as well as principal components (PC) and partial least squares (PLS) regressions. PCA indicated a high degree of association for most parameters with the first PC, which explained a high percentage (>40%) of the variation in the data, suggesting strong statistical relationships among most of the parameters in the system. Regression analyses identified 8 parameters (set as independent variables) that were most frequently retained for modeling the five criteria parameters (set as dependent variables), on a statistically significant level: conductivity, dissolved oxygen (DO), nitrite (NO2(-)), organic nitrogen (N), oxidation reduction potential (ORP), pH, sulfate and total volatile solids (TVS). The criteria parameters and the significant explanatory parameters were most important in modeling the dynamics of the passive treatment system during the study period. Such techniques and
Analysis techniques for multivariate root loci. [a tool in linear control systems
NASA Technical Reports Server (NTRS)
Thompson, P. M.; Stein, G.; Laub, A. J.
1980-01-01
Analysis and techniques are developed for the multivariable root locus and the multivariable optimal root locus. The generalized eigenvalue problem is used to compute angles and sensitivities for both types of loci, and an algorithm is presented that determines the asymptotic properties of the optimal root locus.
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
NASA Astrophysics Data System (ADS)
Fan, Wei; Liu, Jin-Yang
2013-10-01
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.
Convex aggregative modelling of infinite memory nonlinear systems
NASA Astrophysics Data System (ADS)
Wachel, Paweł
2016-08-01
The convex aggregation technique is applied for modelling general class of nonlinear systems with unknown structure and infinite memory. The finite sample size properties of the algorithm are formally established and compared to the standard least-squares counterpart of the method. The proposed algorithm demonstrates its advantages when the a-priori knowledge and the measurement data are both scarce, that is, when the information about the actual system structure is unknown or uncertain and the measurement set is small and disturbed by a noise. Numerical experiments illustrate application and practical benefits of the method for various nonlinear systems.
Performance evaluation of nonlinear weighted T-system
NASA Astrophysics Data System (ADS)
Benfekir, A.; Hamaci, S.; Boimond, J.-L.; Labadi, K.
2013-10-01
This article deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGMs). These graphs are an extension of weighted T-systems studied in the Petri net literature. These models do not admit a linear representation in (min, +) algebra. This nonlinearity is due to the presence of weights on arcs. To mitigate this problem of nonlinearity and to apply some basic results used to analyse the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min, +) linear model.
Robust Nonlinear Feedback Control of Aircraft Propulsion Systems
NASA Technical Reports Server (NTRS)
Garrard, William L.; Balas, Gary J.; Litt, Jonathan (Technical Monitor)
2001-01-01
This is the final report on the research performed under NASA Glen grant NASA/NAG-3-1975 concerning feedback control of the Pratt & Whitney (PW) STF 952, a twin spool, mixed flow, after burning turbofan engine. The research focussed on the design of linear and gain-scheduled, multivariable inner-loop controllers for the PW turbofan engine using H-infinity and linear, parameter-varying (LPV) control techniques. The nonlinear turbofan engine simulation was provided by PW within the NASA Rocket Engine Transient Simulator (ROCETS) simulation software environment. ROCETS was used to generate linearized models of the turbofan engine for control design and analysis as well as the simulation environment to evaluate the performance and robustness of the controllers. Comparison between the H-infinity, and LPV controllers are made with the baseline multivariable controller and developed by Pratt & Whitney engineers included in the ROCETS simulation. Simulation results indicate that H-infinity and LPV techniques effectively achieve desired response characteristics with minimal cross coupling between commanded values and are very robust to unmodeled dynamics and sensor noise.
Schenone, Agustina V; Culzoni, María J; Marsili, Nilda R; Goicoechea, Héctor C
2013-06-01
The performance of MCR-ALS was studied in the modeling of non-linear kinetic-spectrophotometric data acquired by a stopped-flow system for the quantitation of tartrazine in the presence of brilliant blue and sunset yellow FCF as possible interferents. In the present work, MCR-ALS and U-PCA/RBL were firstly applied to remove the contribution of unexpected components not included in the calibration set. Secondly, a polynomial function was used to model the non-linear data obtained by the implementation of the algorithms. MCR-ALS was the only strategy that allowed the determination of tartrazine in test samples accurately. Therefore, it was applied for the analysis of tartrazine in beverage samples with minimum sample preparation and short analysis time. The proposed method was validated by comparison with a chromatographic procedure published in the literature. Mean recovery values between 98% and 100% and relative errors of prediction values between 4% and 9% were indicative of the good performance of the method.
NASA Astrophysics Data System (ADS)
Smolders, K.; Volckaert, M.; Swevers, J.
2008-11-01
This paper presents a nonlinear model-based iterative learning control procedure to achieve accurate tracking control for nonlinear lumped mechanical continuous-time systems. The model structure used in this iterative learning control procedure is new and combines a linear state space model and a nonlinear feature space transformation. An intuitive two-step iterative algorithm to identify the model parameters is presented. It alternates between the estimation of the linear and the nonlinear model part. It is assumed that besides the input and output signals also the full state vector of the system is available for identification. A measurement and signal processing procedure to estimate these signals for lumped mechanical systems is presented. The iterative learning control procedure relies on the calculation of the input that generates a given model output, so-called offline model inversion. A new offline nonlinear model inversion method for continuous-time, nonlinear time-invariant, state space models based on Newton's method is presented and applied to the new model structure. This model inversion method is not restricted to minimum phase models. It requires only calculation of the first order derivatives of the state space model and is applicable to multivariable models. For periodic reference signals the method yields a compact implementation in the frequency domain. Moreover it is shown that a bandwidth can be specified up to which learning is allowed when using this inversion method in the iterative learning control procedure. Experimental results for a nonlinear single-input-single-output system corresponding to a quarter car on a hydraulic test rig are presented. It is shown that the new nonlinear approach outperforms the linear iterative learning control approach which is currently used in the automotive industry on durability test rigs.
Numerical studies of identification in nonlinear distributed parameter systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.
1989-01-01
An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.
NASA Astrophysics Data System (ADS)
Kurt, Mehmet; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.
2014-03-01
We consider a linear cantilever beam attached to ground through a strongly nonlinear stiffness at its free boundary, and study its dynamics computationally by the assumed-modes method. The nonlinear stiffness of this system has no linear component, so it is essentially nonlinear and nonlinearizable. We find that the strong nonlinearity mostly affects the lower-frequency bending modes and gives rise to strongly nonlinear beat phenomena. Analysis of these beats proves that they are caused by internal resonance interactions of nonlinear normal modes (NNMs) of the system. These internal resonances are not of the classical type since they occur between bending modes whose linearized natural frequencies are not necessarily related by rational ratios; rather, they are due to the strong energy-dependence of the frequency of oscillation of the corresponding NNMs of the beam (arising from the strong local stiffness nonlinearity) and occur at energy ranges where the frequencies of these NNMs are rationally related. Nonlinear effects start at a different energy level for each mode. Lower modes are influenced at lower energies due to larger modal displacements than higher modes and thus, at certain energy levels, the NNMs become rationally related, which results in internal resonance. The internal resonances of NNMs are studied using a reduced order model of the beam system. Then, a nonlinear system identification method is developed, capable of identifying this type of strongly nonlinear modal interactions. It is based on an adaptive step-by-step application of empirical mode decomposition (EMD) to the measured time series, which makes it valid for multi-frequency beating signals. Our work extends an earlier nonlinear system identification approach developed for nearly mono-frequency (monochromatic) signals. The extended system identification method is applied to the identification of the strongly nonlinear dynamics of the considered cantilever beam with the local strong
Wallace, Jack; Champagne, Pascale; Monnier, Anne-Charlotte
2015-01-15
Highlights: • Performance of a hybrid passive landfill leachate treatment system was evaluated. • 33 Water chemistry parameters were sampled for 21 months and statistically analyzed. • Parameters were strongly linked and explained most (>40%) of the variation in data. • Alkalinity, ammonia, COD, heavy metals, and iron were criteria for performance. • Eight other parameters were key in modeling system dynamics and criteria. - Abstract: A pilot-scale hybrid-passive treatment system operated at the Merrick Landfill in North Bay, Ontario, Canada, treats municipal landfill leachate and provides for subsequent natural attenuation. Collected leachate is directed to a hybrid-passive treatment system, followed by controlled release to a natural attenuation zone before entering the nearby Little Sturgeon River. The study presents a comprehensive evaluation of the performance of the system using multivariate statistical techniques to determine the interactions between parameters, major pollutants in the leachate, and the biological and chemical processes occurring in the system. Five parameters (ammonia, alkalinity, chemical oxygen demand (COD), “heavy” metals of interest, with atomic weights above calcium, and iron) were set as criteria for the evaluation of system performance based on their toxicity to aquatic ecosystems and importance in treatment with respect to discharge regulations. System data for a full range of water quality parameters over a 21-month period were analyzed using principal components analysis (PCA), as well as principal components (PC) and partial least squares (PLS) regressions. PCA indicated a high degree of association for most parameters with the first PC, which explained a high percentage (>40%) of the variation in the data, suggesting strong statistical relationships among most of the parameters in the system. Regression analyses identified 8 parameters (set as independent variables) that were most frequently retained for modeling
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity.
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-12
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic XY spin chains from the Toda equations are studied in detail.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
NASA Astrophysics Data System (ADS)
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-01
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.
Nonlinear system guidance in the presence of transmission zero dynamics
NASA Technical Reports Server (NTRS)
Meyer, G.; Hunt, L. R.; Su, R.
1995-01-01
An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.
H∞ filtering for piecewise homogeneous Markovian jump nonlinear systems
NASA Astrophysics Data System (ADS)
Zhao, Feng; Zhang, Qingling; Wang, Guoliang
2016-10-01
This paper concerns the problem of H∞ filtering for piecewise homogeneous Markovian jump nonlinear systems. Different from the existing studies in the literatures, the existence of variations in transition rates for Markovian jump nonlinear systems is considered. The purpose of the paper is to design mode-dependent and mode-independent filters, such that the dynamics of the filtering errors are stochastic integral input-to-state stable with H∞ performance index. Using the linear matrix inequality method and the Lyapunov functional method, sufficient conditions for the solution to the H∞ filtering problem are derived. Finally, three examples are proposed to illustrate the effectiveness of the given theoretical results.
Baez-Cazull, S. E.; McGuire, J.T.; Cozzarelli, I.M.; Voytek, M.A.
2008-01-01
Determining the processes governing aqueous biogeochemistry in a wetland hydrologically linked to an underlying contaminated aquifer is challenging due to the complex exchange between the systems and their distinct responses to changes in precipitation, recharge, and biological activities. To evaluate temporal and spatial processes in the wetland-aquifer system, water samples were collected using cm-scale multichambered passive diffusion samplers (peepers) to span the wetland-aquifer interface over a period of 3 yr. Samples were analyzed for major cations and anions, methane, and a suite of organic acids resulting in a large dataset of over 8000 points, which was evaluated using multivariate statistics. Principal component analysis (PCA) was chosen with the purpose of exploring the sources of variation in the dataset to expose related variables and provide insight into the biogeochemical processes that control the water chemistry of the system. Factor scores computed from PCA were mapped by date and depth. Patterns observed suggest that (i) fermentation is the process controlling the greatest variability in the dataset and it peaks in May; (ii) iron and sulfate reduction were the dominant terminal electron-accepting processes in the system and were associated with fermentation but had more complex seasonal variability than fermentation; (iii) methanogenesis was also important and associated with bacterial utilization of minerals as a source of electron acceptors (e.g., barite BaSO4); and (iv) seasonal hydrological patterns (wet and dry periods) control the availability of electron acceptors through the reoxidation of reduced iron-sulfur species enhancing iron and sulfate reduction. Copyright ?? 2008 by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America. All rights reserved.
Accelerator-Feasible N-Body Nonlinear Integrable System
Danilov, V.; Nagaitsev, S.
2014-12-23
Nonlinear N-body integrable Hamiltonian systems, where N is an arbitrary number, attract the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This paper presents a new integrable system, which can be realized in facilities such as particle accelerators. This feature makes it more attractive than many of the previous such systems with singular or unphysical forces.
Geometrically Induced Nonlinearity in Materials and Structural Systems
NASA Astrophysics Data System (ADS)
Ebrahimi, Hamid
For structural analysis there are three sources of nonlinear behavior. The corresponding nonlinear effects are identified by material, geometry and boundary condition nonlinearities. Here in the present work we focused on nonlinear behavior of structural systems that arises from geometry and specifically tackled three problems: nonlinearity in shell structures, nonlinearity in scale-substrate systems and nonlinearity is cellular solids. Firstly, we present a new instability that is observed in the indentation of a highly ellipsoidal shell by a horizontal plate. Above a critical indentation depth, the plate loses contact with the shell in a series of well-defined `blisters' along the long axis of the ellipsoid. We characterize the onset of this instability and explain it using scaling arguments, numerical simulations and experiments. We also characterize the properties of the blistering pattern by showing how the number of blisters and their size depend on both the geometrical properties of the shell and the indentation but not on the shell's elastic modulus. This blistering instability may be used to determine the thickness of highly ellipsoidal shells simply by squashing them between two plates. For the second problem, we investigate the nonlinear mechanical effects of biomimetic scale like attachments on the behavior of an elastic substrate brought about by the contact interaction of scales in pure bending using qualitative experiments, analytical models and detailed finite element analysis. Our results reveal the existence of three distinct kinematic phases of operation spanning linear, nonlinear and rigid behavior driven by kinematic interactions of scales. The response of the modified elastic beam strongly depends on the size and spatial overlap of rigid scales. The nonlinearity is perceptible even in relatively small strain regime and without invoking material level complexities of either the scales or the substrate. And lastly, we develop a new class of two
Nasser Saadatzi, Mohammad; Poshtan, Javad; Sadegh Saadatzi, Mohammad; Tafazzoli, Faezeh
2013-01-01
Electric wheelchair (EW) is subject to diverse types of terrains and slopes, but also to occupants of various weights, which causes the EW to suffer from highly perturbed dynamics. A precise multivariable dynamics of the EW is obtained using Lagrange equations of motion which models effects of slopes as output-additive disturbances. A static pre-compensator is analytically devised which considerably decouples the EW's dynamics and also brings about a more accurate identification of the EW. The controller is designed with a disturbance-observer (DOB) two-degree-of-freedom architecture, which reduces sensitivity to the model uncertainties while enhancing rejection of the disturbances. Upon disturbance rejection, noise reduction, and robust stability of the control system, three fitness functions are presented by which the DOB is tuned using a multi-objective optimization (MOO) approach namely non-dominated sorting genetic algorithm-II (NSGA-II). Finally, experimental results show desirable performance and robust stability of the proposed algorithm. PMID:22959528
Huang, Shuangbing; Liu, Changrong; Wang, Yanxin; Zhan, Hongbin
2014-01-01
The effects of various geochemical processes on arsenic enrichment in a high-arsenic aquifer at Jianghan Plain in Central China were investigated using multivariate models developed from combined adaptive neuro-fuzzy inference system (ANFIS) and multiple linear regression (MLR). The results indicated that the optimum variable group for the AFNIS model consisted of bicarbonate, ammonium, phosphorus, iron, manganese, fluorescence index, pH, and siderite saturation. These data suggest that reductive dissolution of iron/manganese oxides, phosphate-competitive adsorption, pH-dependent desorption, and siderite precipitation could integrally affect arsenic concentration. Analysis of the MLR models indicated that reductive dissolution of iron(III) was primarily responsible for arsenic mobilization in groundwaters with low arsenic concentration. By contrast, for groundwaters with high arsenic concentration (i.e., > 170 μg/L), reductive dissolution of iron oxides approached a dynamic equilibrium. The desorption effects from phosphate-competitive adsorption and the increase in pH exhibited arsenic enrichment superior to that caused by iron(III) reductive dissolution as the groundwater chemistry evolved. The inhibition effect of siderite precipitation on arsenic mobilization was expected to exist in groundwater that was highly saturated with siderite. The results suggest an evolutionary dominance of specific geochemical process over other factors controlling arsenic concentration, which presented a heterogeneous distribution in aquifers. Supplemental materials are available for this article. Go to the publisher's online edition of the Journal of Environmental Science and Health, Part A, to view the supplemental file. PMID:24345245
A Regularized Linear Dynamical System Framework for Multivariate Time Series Analysis
Liu, Zitao; Hauskrecht, Milos
2015-01-01
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning Multivariate Time Series (MTS). However, in general, it is difficult to set the dimension of an LDS’s hidden state space. A small number of hidden states may not be able to model the complexities of a MTS, while a large number of hidden states can lead to overfitting. In this paper, we study learning methods that impose various regularization penalties on the transition matrix of the LDS model and propose a regularized LDS learning framework (rLDS) which aims to (1) automatically shut down LDSs’ spurious and unnecessary dimensions, and consequently, address the problem of choosing the optimal number of hidden states; (2) prevent the overfitting problem given a small amount of MTS data; and (3) support accurate MTS forecasting. To learn the regularized LDS from data we incorporate a second order cone program and a generalized gradient descent method into the Maximum a Posteriori framework and use Expectation Maximization to obtain a low-rank transition matrix of the LDS model. We propose two priors for modeling the matrix which lead to two instances of our rLDS. We show that our rLDS is able to recover well the intrinsic dimensionality of the time series dynamics and it improves the predictive performance when compared to baselines on both synthetic and real-world MTS datasets. PMID:25905027
Federated nonlinear predictive filtering for the gyroless attitude determination system
NASA Astrophysics Data System (ADS)
Zhang, Lijun; Qian, Shan; Zhang, Shifeng; Cai, Hong
2016-11-01
This paper presents a federated nonlinear predictive filter (NPF) for the gyroless attitude determination system with star sensor and Global Positioning System (GPS) sensor. This approach combines the good qualities of both the NPF and federated filter. In order to combine them, the equivalence relationship between the NPF and classical Kalman filter (KF) is demonstrated from algorithm structure and estimation criterion. The main features of this approach include a nonlinear predictive filtering algorithm to estimate uncertain model errors and determine the spacecraft attitude by using attitude kinematics and dynamics, and a federated filtering algorithm to process measurement data from multiple attitude sensors. Moreover, a fault detection and isolation algorithm is applied to the proposed federated NPF to improve the estimation accuracy even when one sensor fails. Numerical examples are given to verify the navigation performance and fault-tolerant performance of the proposed federated nonlinear predictive attitude determination algorithm.
A simple approach to nonlinear estimation of physical systems
Christakos, G.
1988-01-01
Recursive algorithms for estimating the states of nonlinear physical systems are developed. This requires some key hypotheses regarding the structure of the underlying processes. Members of this class of random processes have several desirable properties for the nonlinear estimation of random signals. An assumption is made about the form of the estimator, which may then take account of a wide range of applications. Under the above assumption, the estimation algorithm is mathematically suboptimal but effective and computationally attractive. It may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. To link theory with practice, some numerical results for a simulated system are presented, in which the responses from the proposed and the extended Kalman algorithms are compared. ?? 1988.
Multivariate Strategies in Functional Magnetic Resonance Imaging
ERIC Educational Resources Information Center
Hansen, Lars Kai
2007-01-01
We discuss aspects of multivariate fMRI modeling, including the statistical evaluation of multivariate models and means for dimensional reduction. In a case study we analyze linear and non-linear dimensional reduction tools in the context of a "mind reading" predictive multivariate fMRI model.
Frequency bands of strongly nonlinear homogeneous granular systems.
Lydon, Joseph; Jayaprakash, K R; Ngo, Duc; Starosvetsky, Yuli; Vakakis, Alexander F; Daraio, Chiara
2013-07-01
Recent numerical studies on an infinite number of identical spherical beads in Hertzian contact showed the presence of frequency bands [Jayaprakash, Starosvetsky, Vakakis, Peeters, and Kerschen, Nonlinear Dyn. 63, 359 (2011)]. These bands, denoted here as propagation and attenuation bands (PBs and ABs), are typically present in linear or weakly nonlinear periodic media; however, their counterparts are not intuitive in essentially nonlinear periodic media where there is a complete lack of classical linear acoustics, i.e., in "sonic vacua." Here, we study the effects of PBs and ABs on the forced dynamics of ordered, uncompressed granular systems. Through numerical and experimental techniques, we find that the dynamics of these systems depends critically on the frequency and amplitude of the applied harmonic excitation. For fixed forcing amplitude, at lower frequencies, the oscillations are large in amplitude and governed by strongly nonlinear and nonsmooth dynamics, indicating PB behavior. At higher frequencies the dynamics is weakly nonlinear and smooth, in the form of compressed low-amplitude oscillations, indicating AB behavior. At the boundary between the PB and the AB large-amplitude oscillations due to resonance occur, giving rise to collisions between beads and chaotic dynamics; this renders the forced dynamics sensitive to initial and forcing conditions, and hence unpredictable. Finally, we study asymptotically the near field standing wave dynamics occurring for high frequencies, well inside the AB. PMID:23944453
Parameter identification for nonlinear aerodynamic systems
NASA Technical Reports Server (NTRS)
Pearson, Allan E.
1991-01-01
Work continues on frequency analysis for transfer function identification, both with respect to the continued development of the underlying algorithms and in the identification study of two physical systems. Some new results of a theoretical nature were recently obtained that lend further insight into the frequency domain interpretation of the research. Progress in each of those areas is summarized. Although not related to the system identification problem, some new results were obtained on the feedback stabilization of linear time lag systems.
The coupled nonlinear dynamics of a lift system
NASA Astrophysics Data System (ADS)
Crespo, Rafael Sánchez; Kaczmarczyk, Stefan; Picton, Phil; Su, Huijuan
2014-12-01
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
The coupled nonlinear dynamics of a lift system
Crespo, Rafael Sánchez E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Picton, Phil E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk
2014-12-10
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
Non-linear dynamic analysis of geared systems, part 2
NASA Technical Reports Server (NTRS)
Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet
1990-01-01
A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.
Applications of Linear Systems Theory to Spectroscopic Instrumentation and Multivariate Analysis
NASA Astrophysics Data System (ADS)
Erickson, Chris L.
This research employs linear systems theory to design novel spectroscopic instruments, explain their operation, and provide insight into methods of data analysis. The first study examines the relationship between digital filtering, a technique based on linear systems theory, and multivariate regression, a statistical method. The study focuses on quantitative property estimation for one -sided, repetitive, linear, shift-invariant systems, and compares matched filtering, Kalman innovation filtering, classical least-squares regression, and principal components regression. Kalman innovation filters, which are derived by making signals independent of interferences via orthogonalization, are similar to the respective columns of the pseudo-inverse of the pure signal matrix in classical least-squares regression, and to the regression vectors of principal components least -squares regression, which are derived via calibration. Inverse regression methods, such as principal components regression, are advantageous in that if the experiment is carefully designed, interferences need not be explicitly defined and properties that depend on multiple components can be estimated. In the second study, an absorption spectrophotometer based on a novel stationary interferometer is described. A major advantage of the interferometer is that it requires few optical components: minimally a slit, a collimator, a planar mirror, a magnification lens, and a photodiode array detector. The interferometer images a linear spatial interferogram on a photodiode array. Fourier transformation of the detected interferogram yields the desired spectrum. Equations describing interferometer operation are derived using electromagnetic wave theory and linear systems theory. Systems theory is also used to model and correct systematic errors. The interferometer's baseline noise, resolution, dynamic range and precision are assessed and compared to those of a modern grating-based photodiode-array spectrograph
Simple nonlinear systems and navigating catastrophes
NASA Astrophysics Data System (ADS)
Harré, Michael S.; Atkinson, Simon R.; Hossain, Liaquat
2013-06-01
Tipping points are a common occurrence in complex adaptive systems. In such systems feedback dynamics strongly influence equilibrium points and they are one of the principal concerns of research in this area. Tipping points occur as small changes in system parameters result in disproportionately large changes in the global properties of the system. In order to show how tipping points might be managed we use the Maximum Entropy (MaxEnt) method developed by Jaynes to find the fixed points of an economic system in two different ways. In the first, economic agents optimise their choices based solely on their personal benefits. In the second they optimise the total benefits of the system, taking into account the effects of all agent's actions. The effect is to move the game from a recently introduced dual localised Lagrangian problem to that of a single global Lagrangian. This leads to two distinctly different but related solutions where localised optimisation provides more flexibility than global optimisation. This added flexibility allows an economic system to be managed by adjusting the relationship between macro parameters, in this sense such manipulations provide for the possibility of "steering" an economy around potential disasters.
Turing instability in reaction-diffusion systems with nonlinear diffusion
NASA Astrophysics Data System (ADS)
Zemskov, E. P.
2013-10-01
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Turing instability in reaction-diffusion systems with nonlinear diffusion
Zemskov, E. P.
2013-10-15
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Nonlinear optical systems based on fullerene-containing media
NASA Astrophysics Data System (ADS)
Belousova, Inna M.; Belousov, Vlidilen P.; Bespalov, Victor G.; Grigorev, V. A.; Danilov, Oleg B.; Zevlakov, A. P.; Zgonnick, V. N.; Kalintsev, Alexander G.; Kris'ko, A. V.; Mironova, N. G.; Sosnov, Eugene N.; Ponomarev, Alexander N.
2000-03-01
We present the results of theoretical and experimental studies on creation of nonlinear optical systems on a base of fullerene-containing media: power radiation limiters, photorefractive media for dynamic hologram recording, and devices for controlling spatial and temporal parameters of radiation.
Passive dynamic controllers for non-linear mechanical systems
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.
1992-01-01
The objective is to develop active model-independent controllers for slewing and vibration control of nonlinear multibody flexible systems, including flexible robots. The topics are presented in viewgraph form and include: passive stabilization; work-energy rate principle; Liapunov theory; displacement feedback; dynamic controller; displacement and acceleration feedback; velocity feedback; displacement feedback; physical interaction; a 6-DOF robot; and simulation results.
Non-linear Systems and Educational Development in Europe.
ERIC Educational Resources Information Center
Reilly, David H.
1999-01-01
European educational systems are under immense pressure to change, develop, improve, and satisfy many conflicting demands. Educational development and improvement in these countries is unlikely to progress in a neat, orderly, and linear fashion. Applying nonlinear (chaos) theory to development theory may aid understanding of educational…
Identifying approximate linear models for simple nonlinear systems
NASA Technical Reports Server (NTRS)
Horta, L. G.; Juang, J.-N.
1985-01-01
This paper addresses the identification (realization) of approximate linear models from response data for certain nonlinear dynamic systems. Response characteristics for several typical nonlinear joints are analyzed mathematically and represented by series expansions. The parameters of the series expansion are then compared with the modal parameters of a linear model identified by the Eigensystem Realization Algorithm. The agreement of the identified model and the analytically derived representation is excellent for the cases studied. Also laboratory data from a model which exhibited stiffening behavior was analyzed using the Eigensystem Realization algorithm and Fast Fourier Transform. The laboratory experiment demonstrated the ability of the technique to recover the model characteristics using real data.
Arithmetic coding as a non-linear dynamical system
NASA Astrophysics Data System (ADS)
Nagaraj, Nithin; Vaidya, Prabhakar G.; Bhat, Kishor G.
2009-04-01
In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, non-linear dynamical system known as Generalized Luröth Series (GLS). GLS achieves Shannon's entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.
Multivariate analysis of groundwater quality and modeling impact of ground heat pump system
NASA Astrophysics Data System (ADS)
Thuyet, D. Q.; Saito, H.; Muto, H.; Saito, T.; Hamamoto, S.; Komatsu, T.
2013-12-01
The ground source heat pump system (GSHP) has recently become a popular building heating or cooling method, especially in North America, Western Europe, and Asia, due to advantages in reducing energy consumption and greenhouse gas emission. Because of the stability of the ground temperature, GSHP can effectively exchange the excess or demand heat of the building to the ground during the building air conditioning in the different seasons. The extensive use of GSHP can potentially disturb subsurface soil temperature and thus the groundwater quality. Therefore the assessment of subsurface thermal and environmental impacts from the GSHP operations is necessary to ensure sustainable use of GSHP system as well as the safe use of groundwater resources. This study aims to monitor groundwater quality during GSHP operation and to develop a numerical model to assess changes in subsurface soil temperature and in groundwater quality as affected by GSHP operation. A GSHP system was installed in Fuchu city, Tokyo, and consists of two closed double U-tubes (50-m length) buried vertically in the ground with a distance of 7.3 m from each U-tube located outside a building. An anti-freezing solution was circulated inside the U-tube for exchanging the heat between the building and the ground. The temperature at every 5-m depth and the groundwater quality including concentrations of 16 trace elements, pH, EC, Eh and DO in the shallow aquifer (32-m depth) and the deep aquifer (44-m depth) were monitored monthly since 2012, in an observation well installed 3 m from the center of the two U-tubes.Temporal variations of each element were evaluated using multivariate analysis and geostatistics. A three-dimensional heat exchange model was developed in COMSOL Multiphysics4.3b to simulate the heat exchange processes in subsurface soils. Results showed the difference in groundwater quality between the shallow and deep aquifers to be significant for some element concentrations and DO, but
Tracer experiment design for unique identification of nonlinear physiological systems.
DiStefano, J J
1976-02-01
The design of tracer kinetic experiments, the purpose of which is to elucidate uniquely the internal couplings of a nonlinear dynamic system, is considered for a practical class of models of physiological systems. The extent of information about the real system contained in tracer kinetic data is a central issue. Criteria for determining whether nonlinear model parameters can be estimated from small-signal, "linearizing" tracer experiments are developed and illustrated by examples. The concept of "structural identifiability" is employed in this analysis to determine which model parameters can be and which cannot be determined "uniquely" from given input-output data; a step-by-step procedure based on an extension of this concept is presented for adapting the overall approach to the experimental design problem. Estimation of unmeasurable endogenous inputs and system state variables, problems that are intimately related to parameter estimation for physiological systems, are also considered. PMID:1259027
Nonlinear dynamics and quantum entanglement in optomechanical systems.
Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2014-03-21
To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.
Nonlinear dynamics of fluid-structure systems. Annual technical report
Moon, F.C.; Muntean, G.
1994-01-01
We are investigating the nonlinear dynamics of a row of cylindrical tubes excited by the cross flow of fluid. Both experimental and analytical/numerical studies have been conducted. The goal of this research is to look for low dimensional dynamic models in flow- induced vibrations using modern methods of dynamical systems and chaos theory. The experimental study uses a 25 cm {times} 25 cm wind tunnel with flow velocity in the range of 15 m/sec. The use of a wind tunnel to explore dynamic phenomenon compliments the work of Chen at Argonne National Laboratory who also is conducting experiments with a water tunnel. The principal nonlinearities studies are impact constraints due to gaps in the cylinder supports and nonlinear fluid forces.
Nonlinear Dynamics, Chaotic and Complex Systems
NASA Astrophysics Data System (ADS)
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
Hamiltonian formalism of weakly nonlinear hydrodynamic systems
Pavlov, M.V.
1988-05-01
A study is made of systems of quasilinear equations that are diagonalizable and Hamiltonian and have the condition /delta//sub i/v/sub i/ /triple bond/ 0, where u/sub t//sup i/ /equal/ v/sup i/(u)u/sub x//sup i/, i = 1, ..., N. The conservation laws of such systems are found, together with the metric and Poisson bracket. For definite examples it is shown how solutions are found. The conditions for the existence of solutions and continuity of commuting flows are found.
On discrete control of nonlinear systems with applications to robotics
NASA Technical Reports Server (NTRS)
Eslami, Mansour
1989-01-01
Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.
Response of MDOF strongly nonlinear systems to fractional Gaussian noises.
Deng, Mao-Lin; Zhu, Wei-Qiu
2016-08-01
In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems. PMID:27586630
Nonlinear system vibration---The appearance of chaos
Hunter, N.F. Jr.
1990-01-01
This paper begins with an examination of the differential equation for a single degree of freedom force excited oscillator and considers the state space behavior of linear, nonlinear, and chaotic single degree of freedom systems. The fundamental characteristics of classical chaos are reviewed: sensitivity to initial conditions, positive Lyapunov exponents, complex Poincare maps, fractal properties of motion in the state space, and broadening of the power spectrum of the system response. Illustrated examples of chaotic behavior include motion in a two well potential -- the chaos beam described in Moon and a hardening base excited Duffing system. Chaos-like phenomenon which occur with nonperiodic forcing are examined in the context of the two well potential and hardening Duffing systems. The paper concludes with some suggestions for detecting and modelling nonlinear or chaotic behavior. 19 refs., 19 figs.
Stable Inversion for Nonlinear Nonminimum-Phase Time Varying Systems
NASA Technical Reports Server (NTRS)
Devasia, S.; Paden, B.
1998-01-01
In this paper, we extend stable inversion to nonlinear time-varying systems and study computational issues; the technique is applicable to minimum-phase as well as nonminimum-phase systems. The inversion technique is new, even in the linear time-varying case, and relies on partitioning (the dichotomic split of) the linearized system dynamics into time-varying, stable, and unstable, submanifolds. This dichotomic split is used to build time-varying filters which are, in turn, the basis of a contraction used to find a bounded inverse input-state trajectory. Finding the inverse input-state trajectory allows the development or exact-output tracking controllers. The method is local to the time-varying trajectory and requires that the internal dynamics vary slowly; however, the method represents a significant advance relative to presently available tracking controllers. Present techniques are restricted to time-invariant nonlinear systems and, in the general case, track only asymptotically.
Robust nonlinear system identification using neural-network models.
Lu, S; Basar, T
1998-01-01
We study the problem of identification for nonlinear systems in the presence of unknown driving noise, using both feedforward multilayer neural network and radial basis function network models. Our objective is to resolve the difficulty associated with the persistency of excitation condition inherent to the standard schemes in the neural identification literature. This difficulty is circumvented here by a novel formulation and by using a new class of identification algorithms recently obtained by Didinsky et al. We show how these algorithms can be exploited to successfully identify the nonlinearity in the system using neural-network models. By embedding the original problem in one with noise-perturbed state measurements, we present a class of identifiers (under L1 and L2 cost criteria) which secure a good approximant for the system nonlinearity provided that some global optimization technique is used. In this respect, many available learning algorithms in the current neural-network literature, e.g., the backpropagation scheme and the genetic algorithms-based scheme, with slight modifications, can ensure the identification of the system nonlinearity. Subsequently, we address the same problem under a third, worst case L(infinity) criterion for an RBF modeling. We present a neural-network version of an H(infinity)-based identification algorithm from Didinsky et al and show how, along with an appropriate choice of control input to enhance excitation, under both full-state-derivative information (FSDI) and noise-perturbed full-state-information (NPFSI), it leads to satisfaction of a relevant persistency of excitation condition, and thereby to robust identification of the nonlinearity. Results from several simulation studies have been included to demonstrate the effectiveness of these algorithms.
Robust Stabilization of a Class of passive Nonlinear Systems
NASA Technical Reports Server (NTRS)
Joshi, Suresh M.; Kelkar, Atul G.
1996-01-01
The problem of feedback stabilization is considered for a class of nonlinear, finite dimensional, time invariant passive systems that are affine in control. Using extensions of the Kalman-Yakubovch lemma, it is shown that such systems can be stabilized by a class of finite demensional, linear, time-invariant controllers which are strictly positive real in the weak or marginal sense. The stability holds regardless of model uncertainties, and is therefore, robust.
Diffusive limits of nonlinear hyperbolic systems with variable coefficients
NASA Astrophysics Data System (ADS)
Miyoshi, Hironari; Tsutsumi, Masayoshi
2016-09-01
We consider the initial-boundary value problem for a 2-speed system of first-order nonhomogeneous semilinear hyperbolic equations whose leading terms have a small positive parameter. Using energy estimates and a compactness lemma, we show that the diffusion limit of the sum of the solutions of the hyperbolic system, as the parameter tends to zero, verifies the nonlinear parabolic equation of the p-Laplacian type.
Multivariate time series modeling of short-term system scale irrigation demand
NASA Astrophysics Data System (ADS)
Perera, Kushan C.; Western, Andrew W.; George, Biju; Nawarathna, Bandara
2015-12-01
Travel time limits the ability of irrigation system operators to react to short-term irrigation demand fluctuations that result from variations in weather, including very hot periods and rainfall events, as well as the various other pressures and opportunities that farmers face. Short-term system-wide irrigation demand forecasts can assist in system operation. Here we developed a multivariate time series (ARMAX) model to forecast irrigation demands with respect to aggregated service points flows (IDCGi, ASP) and off take regulator flows (IDCGi, OTR) based across 5 command areas, which included area covered under four irrigation channels and the study area. These command area specific ARMAX models forecast 1-5 days ahead daily IDCGi, ASP and IDCGi, OTR using the real time flow data recorded at the service points and the uppermost regulators and observed meteorological data collected from automatic weather stations. The model efficiency and the predictive performance were quantified using the root mean squared error (RMSE), Nash-Sutcliffe model efficiency coefficient (NSE), anomaly correlation coefficient (ACC) and mean square skill score (MSSS). During the evaluation period, NSE for IDCGi, ASP and IDCGi, OTR across 5 command areas were ranged 0.98-0.78. These models were capable of generating skillful forecasts (MSSS ⩾ 0.5 and ACC ⩾ 0.6) of IDCGi, ASP and IDCGi, OTR for all 5 lead days and IDCGi, ASP and IDCGi, OTR forecasts were better than using the long term monthly mean irrigation demand. Overall these predictive performance from the ARMAX time series models were higher than almost all the previous studies we are aware. Further, IDCGi, ASP and IDCGi, OTR forecasts have improved the operators' ability to react for near future irrigation demand fluctuations as the developed ARMAX time series models were self-adaptive to reflect the short-term changes in the irrigation demand with respect to various pressures and opportunities that farmers' face, such as
Reduced-size kernel models for nonlinear hybrid system identification.
Le, Van Luong; Bloch, Grard; Lauer, Fabien
2011-12-01
This brief paper focuses on the identification of nonlinear hybrid dynamical systems, i.e., systems switching between multiple nonlinear dynamical behaviors. Thus the aim is to learn an ensemble of submodels from a single set of input-output data in a regression setting with no prior knowledge on the grouping of the data points into similar behaviors. To be able to approximate arbitrary nonlinearities, kernel submodels are considered. However, in order to maintain efficiency when applying the method to large data sets, a preprocessing step is required in order to fix the submodel sizes and limit the number of optimization variables. This brief paper proposes four approaches, respectively inspired by the fixed-size least-squares support vector machines, the feature vector selection method, the kernel principal component regression and a modification of the latter, in order to deal with this issue and build sparse kernel submodels. These are compared in numerical experiments, which show that the proposed approach achieves the simultaneous classification of data points and approximation of the nonlinear behaviors in an efficient and accurate manner.
Nonlinear stability of discrete shocks for systems of conservation laws
NASA Astrophysics Data System (ADS)
Liu, Jian-Guo; Xin, Zhouping
1993-09-01
In this paper we study the asymptotic nonlinear stability of discrete shocks for the Lax-Friedrichs scheme for approximating general m×m systems of nonlinear hyperbolic conservation laws. It is shown that weak single discrete shocks for such a scheme are nonlinearly stable in the L p-norm for all p ≧ 1, provided that the sums of the initial perturbations equal zero. These results should shed light on the convergence of the numerical solution constructed by the Lax-Friedrichs scheme for the single-shock solution of system of hyperbolic conservation laws. If the Riemann solution corresponding to the given far-field states is a superposition of m single shocks from each characteristic family, we show that the corresponding multiple discrete shocks are nonlinearly stable in L p (P ≧ 2). These results are proved by using both a weighted estimate and a characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the Lax-Friedrichs scheme.
Nonlinear Network Dynamics on Earthquake Fault Systems
NASA Astrophysics Data System (ADS)
Rundle, P. B.; Rundle, J. B.; Tiampo, K. F.
2001-12-01
Understanding the physics of earthquakes is essential if large events are ever to be forecast. Real faults occur in topologically complex networks that exhibit cooperative, emergent space-time behavior that includes precursory quiescence or activation, and clustering of events. The purpose of this work is to investigate the sensitivity of emergent behavior of fault networks to changes in the physics on the scale of single faults or smaller. In order to investigate the effect of changes at small scales on the behavior of the network, we need to construct models of earthquake fault systems that contain the essential physics. A network topology is therefore defined in an elastic medium, the stress Green's functions (i.e. the stress transfer coefficients) are computed, frictional properties are defined and the system is driven via the slip deficit as defined below. The long-range elastic interactions produce mean-field dynamics in the simulations. We focus in this work on the major strike-slip faults in Southern California that produce the most frequent and largest magnitude events. To determine the topology and properties of the network, we used the tabulation of fault properties published in the literature. We have found that the statistical distribution of large earthquakes on a model of a topologically complex, strongly correlated real fault network is highly sensitive to the precise nature of the stress dissipation properties of the friction laws associated with individual faults. These emergent, self-organizing space-time modes of behavior are properties of the network as a whole, rather than of the individual fault segments of which the network is comprised (ref: PBR et al., Physical Review Letters, in press, 2001).
Downing, D.J.; Fedorov, V.; Lawkins, W.F.; Morris, M.D.; Ostrouchov, G.
1996-05-01
Large data series with more than several million multivariate observations, representing tens of megabytes or even gigabytes of data, are difficult or impossible to analyze with traditional software. The shear amount of data quickly overwhelms both the available computing resources and the ability of the investigator to confidently identify meaningful patterns and trends which may be present. The purpose of this research is to give meaningful definition to `large data set analysis` and to describe and illustrate a technique for identifying unusual events in large data series. The technique presented here is based on the theory of nonlinear dynamical systems.
Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems
NASA Astrophysics Data System (ADS)
Williams, Rube B.
2004-02-01
Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.
Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems
Williams, Rube B.
2004-02-04
Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.
Digital self-triggered robust control of nonlinear systems
NASA Astrophysics Data System (ADS)
Di Benedetto, M. D.; Di Gennaro, S.; D'Innocenzo, A.
2013-09-01
In this paper, we develop novel results on self-triggered control of nonlinear systems, subject to perturbations, and sensing/computation/actuation delays. First, considering an unperturbed nonlinear system with bounded delays, we provide conditions that guarantee the existence of a self-triggered control strategy stabilizing the closed-loop system. Then, considering parameter uncertainties, disturbances and bounded delays, we provide conditions guaranteeing the existence of a self-triggered strategy that keeps the state arbitrarily close to the equilibrium point. In both cases, we provide a methodology for the computation of the next execution time. We show on an example the relevant benefits obtained with this approach in terms of energy consumption with respect to control algorithms based on a constant sampling with a sensible reduction of the average sampling time.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Digital simulation and modeling of nonlinear stochastic systems
Richardson, J M; Rowland, J R
1981-04-01
Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.
Observer-based controller for nonlinear analytical systems
NASA Astrophysics Data System (ADS)
Elloumi, S.; Belhouane, M. M.; Benhadj Braiek, N.
2016-06-01
In this paper, we propose to design a polynomial observer-based control for nonlinear systems and to determine sufficient linear matrix inequality (LMI) global stabilisation conditions of the polynomial controlled system augmented by its observer. The design of the observer-based control leverages some notations from the Kronecker product and the power of matrices properties for the state space description of polynomial systems. The stability study of the polynomial controlled system augmented by its observer is based on the Lyapunov stability direct method. Intensive simulations are performed to illustrate the validity and the effectiveness of the polynomial approach used to design the control.
Spatial nonlinearities: Cascading effects in the earth system
Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, S.; Havstad, K. M.
2006-01-01
Nonlinear interactions and feedbacks associated with thresholds through time and across space are common features of biological, physical and materials systems. These spatial nonlinearities generate surprising behavior where dynamics at one scale cannot be easily predicted based on information obtained at finer or broader scales. These cascading effects often result in severe consequences for the environment and human welfare (i.e., catastrophes) that are expected to be particularly important under conditions of changes in climate and land use. In this chapter, we illustrate the usefulness of a general conceptual and mathematical framework for understanding and forecasting spatially nonlinear responses to global change. This framework includes cross-scale interactions, threshold behavior and feedback mechanisms. We focus on spatial nonlinearities produced by fine-scale processes that cascade through time and across space to influence broad spatial extents. Here we describe the spread of catastrophic events in the context of our cross-disciplinary framework using examples from biology (wildfires, desertification, infectious diseases) and engineering (structural failures) and discuss the consequences of applying these ideas to forecasting future dynamics under a changing global environment.
Non-linear HRV indices under autonomic nervous system blockade.
Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel
2014-01-01
Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.
On the orthogonalised reverse path method for nonlinear system identification
NASA Astrophysics Data System (ADS)
Muhamad, P.; Sims, N. D.; Worden, K.
2012-09-01
The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673-708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach - the orthogonalised reverse path (ORP) method - is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.
Blow-up of the solution of a nonlinear system of equations with positive energy
NASA Astrophysics Data System (ADS)
Korpusov, M. O.
2012-06-01
We consider the Dirichlet problem for a nonlinear system of equations, continuing our study of nonlinear hyperbolic equations and systems of equations with an arbitrarily large positive energy. We use a modified Levine method to prove the blow-up.
Adaptive control of Hammerstein-Wiener nonlinear systems
NASA Astrophysics Data System (ADS)
Zhang, Bi; Hong, Hyokchan; Mao, Zhizhong
2016-07-01
The Hammerstein-Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein-Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.
Modeling and identification of parallel and feedback nonlinear systems
Chen, Hai-Wen
1994-10-01
Structural classification and parameter estimation (SCPE) methods have been used for studying single-input single. output (SISO) parallel and feedback nonlinear system models from input-output (I-O) measurements. The uniqueness of the I-O mappings of different models and parameter uniqueness of the I-O mapping of a given structural model are evaluated. The former aids in defining the conditions under which different model structures may be differentiated from one another. The latter defines the conditions under which a given model parameter can be uniquely estimated from I-O measurements. SCPE methods presented in this paper can be further developed to study more complicated multi-input multi-output (MIMO) block-structured models which will provide useful techniques for modeling and identifying highly complex nonlinear systems.
Nonlinear formulation for flexible multibody system with large deformation
NASA Astrophysics Data System (ADS)
Liu, Jinyang; Hong, Jiazhen
2007-02-01
In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation.
Diagnosis of nonlinear systems using kernel principal component analysis
NASA Astrophysics Data System (ADS)
Kallas, M.; Mourot, G.; Maquin, D.; Ragot, J.
2014-12-01
Technological advances in the process industries during the past decade have resulted in increasingly complicated processes, systems and products. Therefore, recent researches consider the challenges in their design and management for successful operation. While principal component analysis (PCA) technique is widely used for diagnosis, its structure cannot describe nonlinear related variables. Thus, an extension to the case of nonlinear systems is presented in a feature space for process monitoring. Working in a high-dimensional feature space, it is necessary to get back to the original space. Hence, an iterative pre-image technique is derived to provide a solution for fault diagnosis. The relevance of the proposed technique is illustrated on artificial and real dataset.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity.
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-12
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic XY spin chains from the Toda equations are studied in detail. PMID:27563938
On-line estimation of nonlinear physical systems
Christakos, G.
1988-01-01
Recursive algorithms for estimating states of nonlinear physical systems are presented. Orthogonality properties are rediscovered and the associated polynomials are used to linearize state and observation models of the underlying random processes. This requires some key hypotheses regarding the structure of these processes, which may then take account of a wide range of applications. The latter include streamflow forecasting, flood estimation, environmental protection, earthquake engineering, and mine planning. The proposed estimation algorithm may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. Moreover, the method has several advantages over nonrecursive estimators like disjunctive kriging. To link theory with practice, some numerical results for a simulated system are presented, in which responses from the proposed and extended Kalman algorithms are compared. ?? 1988 International Association for Mathematical Geology.
NASA Astrophysics Data System (ADS)
Salman, A.; Shufan, E.; Lapidot, I.; Tsror, L.; Zeiri, L.; Sahu, R. K.; Moreh, R.; Mordechai, S.; Huleihel, M.
2015-12-01
Fourier Transform Infrared (FTIR) and Raman spectroscopies have emerged as powerful tools for chemical analysis. This is due to their ability to provide detailed information about the spatial distribution of chemical composition at the molecular level. A biological sample, i.e. bacteria or fungi, has a typical spectrum. This spectral fingerprint, characterizes the sample and can therefore be used for differentiating between biology samples which belong to different groups, i.e., several different isolates of a given fungi. When the spectral differences between the groups are minute, multivariate analysis should be used to provide a good differentiation. We hereby review several results which demonstrate the differentiation success obtained by combining spectroscopy measurements and multivariate analysis.
On the Davey-Stewartson system with competing nonlinearities
NASA Astrophysics Data System (ADS)
Zhu, Shihui
2016-03-01
This paper is concerned with the blow-up solutions for the Davey-Stewartson system with competing nonlinearities, which results in the loss of scaling invariance. The best constant of a new gG-N type inequality is given to find the sharp threshold mass of blow-up and global existence. Moreover, under the sharp threshold mass, the dynamical behavior of blow-up solutions is investigated, including L2-concentration, L2 weak limits, and limiting profile.
An iterative method for systems of nonlinear hyperbolic equations
NASA Technical Reports Server (NTRS)
Scroggs, Jeffrey S.
1989-01-01
An iterative algorithm for the efficient solution of systems of nonlinear hyperbolic equations is presented. Parallelism is evident at several levels. In the formation of the iteration, the equations are decoupled, thereby providing large grain parallelism. Parallelism may also be exploited within the solves for each equation. Convergence of the interation is established via a bounding function argument. Experimental results in two-dimensions are presented.
NASA Astrophysics Data System (ADS)
Donges, Jonathan; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik; Marwan, Norbert; Dijkstra, Henk; Kurths, Jürgen
2016-04-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology. pyunicorn is available online at https://github.com/pik-copan/pyunicorn. Reference: J.F. Donges, J. Heitzig, B. Beronov, M. Wiedermann, J. Runge, Q.-Y. Feng, L. Tupikina, V. Stolbova, R.V. Donner, N. Marwan, H.A. Dijkstra, and J. Kurths, Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package, Chaos 25, 113101 (2015), DOI: 10.1063/1.4934554, Preprint: arxiv.org:1507.01571 [physics.data-an].
Nonlinear closed-loop control system for intracranial pressure regulation.
Coté, G L; Durai, R; Zoghi, B
1995-01-01
A nonlinear closed-loop control system with flat pressure-versus-flow characteristics that is aimed at regulating intracranial pressure (ICP) by adjusting the volume of cerebral spinal fluid (CSF) was designed, built, and tested. The control system design allows both the pressure setpoint and hysteresis to be adjusted to overcome the difficulties inherent in differential pressure-activated, fixed resistance, open-loop shunts. A dynamic six-compartment bench-top fluid system, which mimics the cerebral spinal fluid system, was designed, built, and tested. A computer simulation was developed which included the nonlinear on-off controller with hysteresis and a sixth-order, linear, multicompartmental model of the CSF system. The computer model and in vitro system results showed the ability of the system to track and compensate for pressure variations above and below normal as well as for spurious outputs that mimic such in vivo problems as blood pressure changes, sneezing, or coughing. There was one discrepancy between the simulated and in vitro results. The in vitro system had a higher rate of increase in pressure due to the more rigid compliance of the materials used, whereas the computer model compliance, based on the basal in vivo compliance of the CSF system, was less rigid. Based on these findings, the controller was modified to account for short-duration, extremely elevated pressures. PMID:8572426
Donges, Jonathan F; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik V; Marwan, Norbert; Dijkstra, Henk A; Kurths, Jürgen
2015-11-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology. PMID:26627561
NASA Astrophysics Data System (ADS)
Donges, Jonathan F.; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik V.; Marwan, Norbert; Dijkstra, Henk A.; Kurths, Jürgen
2015-11-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.
Bandlimited computerized improvements in characterization of nonlinear systems with memory
NASA Astrophysics Data System (ADS)
Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.
2016-05-01
The present article discusses some inroads in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] over many years of developmental research. The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms on the system are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order in order to combat and reasonably alleviate the curse of dimensionality.
Method of Conjugate Radii for Solving Linear and Nonlinear Systems
NASA Technical Reports Server (NTRS)
Nachtsheim, Philip R.
1999-01-01
This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.
Noise and nonlinearities in digital magnetic recording systems
NASA Astrophysics Data System (ADS)
Xing, Xinzhi
1998-11-01
Various types of noise and nonlinearities in digital magnetic recording systems are investigated in this dissertation. Measurement techniques and analyzing methods are developed to understand each phenomenon. The nonlinearities due to the replay process using MR sensors are studied in Chapter 4. The nonlinearities are determined by comparing the measured signal with that obtained from a linear analysis. A characterization method of transition noise is developed in Chapter 5. Approximating transition noise by several leading 'modes' allows the noise parameters to be determined experimentally. Chapter 6 covers the investigation of disk substrate texture induced noise. The noise mechanism and characteristics are systematically studied. An analytical noise correlation function that directly relates the noise with the fluctuations of the textured disk surface is also developed in this chapter. An error rate model including colored and nonstationary noise is developed to further understand the impact of noise on system performance in Chapter 7. Noise with different characteristics is shown to influence the system performance differently. In addition, the influence of texture noise is examined in term of each noise parameter based upon the noise model developed in Chapter 6. Finally, in Chapter 8, the effect of finite write field rise time on recording performance is studied. Recording performance predicted by a simplified analytical model is compared with the measurements. It is shown that a slow flux rise time causes a degraded field gradient during writing, which results in a broader written transition, a larger NLTS, and noisier transition boundaries.
NASA Technical Reports Server (NTRS)
Christenson, D.; Gordon, M.; Kistler, R.; Kriegler, F.; Lampert, S.; Marshall, R.; Mclaughlin, R.
1977-01-01
A third-generation, fast, low cost, multispectral recognition system (MIDAS) able to keep pace with the large quantity and high rates of data acquisition from large regions with present and projected sensots is described. The program can process a complete ERTS frame in forty seconds and provide a color map of sixteen constituent categories in a few minutes. A principle objective of the MIDAS program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turn-around time and significant gains in throughput. The hardware and software generated in the overall program is described. The system contains a midi-computer to control the various high speed processing elements in the data path, a preprocessor to condition data, and a classifier which implements an all digital prototype multivariate Gaussian maximum likelihood or a Bayesian decision algorithm. Sufficient software was developed to perform signature extraction, control the preprocessor, compute classifier coefficients, control the classifier operation, operate the color display and printer, and diagnose operation.
Multicomponent Nonlinear Systems of Bose-Fermi Fields: Exact Solutions
Kostov, Nikolay A.; Gerdjikov, Vladimir S.; Valchev, Tihomir I.
2011-04-07
We present families of stationary solutions for a multicomponent nonlinear system of two boson and N{sub f} fermion fields in terms of elliptic functions of modulus k. This system is an extention of models, describing Bose-Fermi mixtures in the mean field approximation. We also single out the particular cases when the quasiperiodic solutions become periodic ones. In the limit of sinusoidal external potential (k{yields}0) our solutions model periodic waves trapped in an optical lattice. The other limit k{yields}1 provides solutions expressed by hyperbolic functions (vector solitons). Thus we demonstrate that our system describes quasi-periodic and periodic waves, as well as solitons.
NASA Technical Reports Server (NTRS)
Gettman, Chang-Ching LO
1993-01-01
This thesis develops and demonstrates an approach to nonlinear control system design using linearization by state feedback. The design provides improved transient response behavior allowing faster maneuvering of payloads by the SRMS. Modeling uncertainty is accounted for by using a second feedback loop designed around the feedback linearized dynamics. A classical feedback loop is developed to provide the easy implementation required for the relatively small on board computers. Feedback linearization also allows the use of higher bandwidth model based compensation in the outer loop, since it helps maintain stability in the presence of the nonlinearities typically neglected in model based designs.
Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.
Nagarale, Ravindrakumar M; Patre, B M
2014-05-01
This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller.
Reinforcement learning to adaptive control of nonlinear systems.
Hwang, Kao-Shing; Tan, S W; Tsai, Min-Cheng
2003-01-01
Based on the feedback linearization theory, this paper presents how a reinforcement learning scheme that is adopted to construct artificial neural networks (ANNs) can linearize a nonlinear system effectively. The proposed reinforcement linearization learning system (RLLS) consists of two sub-systems: The evaluation predictor (EP) is a long-term policy selector, and the other is a short-term action selector composed of linearizing control (LC) and reinforce predictor (RP) elements. In addition, a reference model plays the role of the environment, which provides the reinforcement signal to the linearizing process. The RLLS thus receives reinforcement signals to accomplish the linearizing behavior to control a nonlinear system such that it can behave similarly to the reference model. Eventually, the RLLS performs identification and linearization concurrently. Simulation results demonstrate that the proposed learning scheme, which is applied to linearizing a pendulum system, provides better control reliability and robustness than conventional ANN schemes. Furthermore, a PI controller is used to control the linearized plant where the affine system behaves like a linear system.
Autonomous Navigation System Using a Fuzzy Adaptive Nonlinear H∞ Filter
Outamazirt, Fariz; Li, Fu; Yan, Lin; Nemra, Abdelkrim
2014-01-01
Although nonlinear H∞ (NH∞) filters offer good performance without requiring assumptions concerning the characteristics of process and/or measurement noises, they still require additional tuning parameters that remain fixed and that need to be determined through trial and error. To address issues associated with NH∞ filters, a new SINS/GPS sensor fusion scheme known as the Fuzzy Adaptive Nonlinear H∞ (FANH∞) filter is proposed for the Unmanned Aerial Vehicle (UAV) localization problem. Based on a real-time Fuzzy Inference System (FIS), the FANH∞ filter continually adjusts the higher order of the Taylor development thorough adaptive bounds (δi) and adaptive disturbance attenuation (γ), which significantly increases the UAV localization performance. The results obtained using the FANH∞ navigation filter are compared to the NH∞ navigation filter results and are validated using a 3D UAV flight scenario. The comparison proves the efficiency and robustness of the UAV localization process using the FANH∞ filter. PMID:25244587
Autonomous navigation system using a fuzzy adaptive nonlinear H∞ filter.
Outamazirt, Fariz; Li, Fu; Yan, Lin; Nemra, Abdelkrim
2014-09-19
Although nonlinear H∞ (NH∞) filters offer good performance without requiring assumptions concerning the characteristics of process and/or measurement noises, they still require additional tuning parameters that remain fixed and that need to be determined through trial and error. To address issues associated with NH∞ filters, a new SINS/GPS sensor fusion scheme known as the Fuzzy Adaptive Nonlinear H∞ (FANH∞) filter is proposed for the Unmanned Aerial Vehicle (UAV) localization problem. Based on a real-time Fuzzy Inference System (FIS), the FANH∞ filter continually adjusts the higher order of the Taylor development thorough adaptive bounds and adaptive disturbance attenuation , which significantly increases the UAV localization performance. The results obtained using the FANH∞ navigation filter are compared to the NH∞ navigation filter results and are validated using a 3D UAV flight scenario. The comparison proves the efficiency and robustness of the UAV localization process using the FANH∞ filter.
Swarming behaviors in multi-agent systems with nonlinear dynamics
Yu, Wenwu; Chen, Guanrong; Cao, Ming; Lü, Jinhu; Zhang, Hai-Tao
2013-12-15
The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.
Autonomous navigation system using a fuzzy adaptive nonlinear H∞ filter.
Outamazirt, Fariz; Li, Fu; Yan, Lin; Nemra, Abdelkrim
2014-01-01
Although nonlinear H∞ (NH∞) filters offer good performance without requiring assumptions concerning the characteristics of process and/or measurement noises, they still require additional tuning parameters that remain fixed and that need to be determined through trial and error. To address issues associated with NH∞ filters, a new SINS/GPS sensor fusion scheme known as the Fuzzy Adaptive Nonlinear H∞ (FANH∞) filter is proposed for the Unmanned Aerial Vehicle (UAV) localization problem. Based on a real-time Fuzzy Inference System (FIS), the FANH∞ filter continually adjusts the higher order of the Taylor development thorough adaptive bounds and adaptive disturbance attenuation , which significantly increases the UAV localization performance. The results obtained using the FANH∞ navigation filter are compared to the NH∞ navigation filter results and are validated using a 3D UAV flight scenario. The comparison proves the efficiency and robustness of the UAV localization process using the FANH∞ filter. PMID:25244587
Digit replacement: A generic map for nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
García-Morales, Vladimir
2016-09-01
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface.
Nonlinear problems of complex natural systems: Sun and climate dynamics.
Bershadskii, A
2013-01-13
The universal role of the nonlinear one-third subharmonic resonance mechanism in generation of strong fluctuations in complex natural dynamical systems related to global climate is discussed using wavelet regression detrended data. The role of the oceanic Rossby waves in the year-scale global temperature fluctuations and the nonlinear resonance contribution to the El Niño phenomenon have been discussed in detail. The large fluctuations in the reconstructed temperature on millennial time scales (Antarctic ice core data for the past 400,000 years) are also shown to be dominated by the one-third subharmonic resonance, presumably related to the Earth's precession effect on the energy that the intertropical regions receive from the Sun. The effects of galactic turbulence on the temperature fluctuations are also discussed. PMID:23185052
Frank, T D
2002-07-01
Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived for stochastic delay differential equations. Natural, periodic, and reflective boundary conditions are discussed. Both Ito and Stratonovich calculus are used. In particular, our Fokker-Planck approach recovers the generalized delay Fokker-Planck equation proposed by Guillouzic et al. The results obtained are applied to a model for population growth: the Gompertz model with delay and multiplicative white noise.
Nonlinear dynamics of global atmospheric and earth system processes
NASA Technical Reports Server (NTRS)
Zhang, Taiping; Verbitsky, Mikhail; Saltzman, Barry; Mann, Michael E.; Park, Jeffrey; Lall, Upmanu
1995-01-01
During the grant period, the authors continued ongoing studies aimed at enhancing their understanding of the operation of the atmosphere as a complex nonlinear system interacting with the hydrosphere, biosphere, and cryosphere in response to external radiative forcing. Five papers were completed with support from the grant, representing contributions in three main areas of study: (1) theoretical studies of the interactive atmospheric response to changed biospheric boundary conditions measurable from satellites; (2) statistical-observational studies of global-scale temperature variability on interannual to century time scales; and (3) dynamics of long-term earth system changes associated with ice sheet surges.
A minimum time control algorithm for linear and nonlinear systems
NASA Technical Reports Server (NTRS)
Wen, J.; Desrochers, A. A.
1985-01-01
The minimum time control problem with bounded control has long been of interest to control engineers. Much of the theoretical study of this problem has been limited to linear systems and the results are usually problem-specific. This paper presents a new computational method for solving the minimum-time control problem when the control action is assumed to be bang-bang. A gradient-based algorithm is developed where the switching times are updated to minimize the final state missed distance. The algorithm is applicable to linear and nonlinear problems, including multi-input systems.
Discrete-time ? filtering for nonlinear polynomial systems
NASA Astrophysics Data System (ADS)
Basin, M. V.; Hernandez-Gonzalez, M.
2016-07-01
This paper presents a suboptimal ? filtering problem solution for a class of discrete-time nonlinear polynomial systems over linear observations. The solution is obtained splitting the whole problem into finding a-priori and a-posteriori equations for state estimates and gain matrices. The closed-form filtering equations for the state estimate and gain matrix are obtained in case of a third-degree polynomial system. Numerical simulations are carried out to show effectiveness of the proposed filter. The obtained filter is compared to the extended Kalman-like ? filter.
Temporal and spatial structures of nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Purwins, Hans-Georg; Klempt, Günter; Berkemeier, Jürgen
The present article contains the description of simple experiments mounted for a demonstration of temporal and spatial structures of dissipative nonlinear dynamical systems. The systematic approach possible to systems with few degrees of freedom is described on an elementary level showing experiments on a rotating nonlinear oscillator. The temporal structure elements are those contained in the stationary, periodic, quasi-periodic, and chaotic motion. Structures of systems with many degrees of freedom are demonstrated by showing experiments on real spatially extended electronic circuits and gas discharge systems both described by reaction diffusion equations. Such systems have a complexity and richness of structures far beyond what can be described systematically by current techniques. However, for special cases a quantitative understanding is possible. Also filaments of rather well defined size and shape observed in our experiments can be considered as simple elements building up a variety of spatial patterns. We also show that noise is decisive in many cases for the formation and the nonreproducibility of stationary structures. Finally, we stress some features common to reaction diffusion systems and living beings.
Develop advanced nonlinear signal analysis topographical mapping system
NASA Technical Reports Server (NTRS)
1994-01-01
The Space Shuttle Main Engine (SSME) has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature, pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system; (2) develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amount of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. High compression ratio can be achieved to allow minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities; and (3) integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of
Develop advanced nonlinear signal analysis topographical mapping system
NASA Technical Reports Server (NTRS)
Jong, Jen-Yi
1993-01-01
The SSME has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) Develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system. (2) Develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amounts of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. A high compression ratio can be achieved to allow the minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities. (3) Integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for a quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of malfunction, and indicate
Del Giudice, G; Padulano, R; Siciliano, D
2016-01-01
The lack of geometrical and hydraulic information about sewer networks often excludes the adoption of in-deep modeling tools to obtain prioritization strategies for funds management. The present paper describes a novel statistical procedure for defining the prioritization scheme for preventive maintenance strategies based on a small sample of failure data collected by the Sewer Office of the Municipality of Naples (IT). Novelty issues involve, among others, considering sewer parameters as continuous statistical variables and accounting for their interdependences. After a statistical analysis of maintenance interventions, the most important available factors affecting the process are selected and their mutual correlations identified. Then, after a Box-Cox transformation of the original variables, a methodology is provided for the evaluation of a vulnerability map of the sewer network by adopting a joint multivariate normal distribution with different parameter sets. The goodness-of-fit is eventually tested for each distribution by means of a multivariate plotting position. The developed methodology is expected to assist municipal engineers in identifying critical sewers, prioritizing sewer inspections in order to fulfill rehabilitation requirements. PMID:26901717
Hybrid fault diagnosis of nonlinear systems using neural parameter estimators.
Sobhani-Tehrani, E; Talebi, H A; Khorasani, K
2014-02-01
This paper presents a novel integrated hybrid approach for fault diagnosis (FD) of nonlinear systems taking advantage of both the system's mathematical model and the adaptive nonlinear approximation capability of computational intelligence techniques. Unlike most FD techniques, the proposed solution simultaneously accomplishes fault detection, isolation, and identification (FDII) within a unified diagnostic module. At the core of this solution is a bank of adaptive neural parameter estimators (NPEs) associated with a set of single-parameter fault models. The NPEs continuously estimate unknown fault parameters (FPs) that are indicators of faults in the system. Two NPE structures, series-parallel and parallel, are developed with their exclusive set of desirable attributes. The parallel scheme is extremely robust to measurement noise and possesses a simpler, yet more solid, fault isolation logic. In contrast, the series-parallel scheme displays short FD delays and is robust to closed-loop system transients due to changes in control commands. Finally, a fault tolerant observer (FTO) is designed to extend the capability of the two NPEs that originally assumes full state measurements for systems that have only partial state measurements. The proposed FTO is a neural state estimator that can estimate unmeasured states even in the presence of faults. The estimated and the measured states then comprise the inputs to the two proposed FDII schemes. Simulation results for FDII of reaction wheels of a three-axis stabilized satellite in the presence of disturbances and noise demonstrate the effectiveness of the proposed FDII solutions under partial state measurements.
Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems.
Wang, Chi-Hsu; Lin, Tsung-Chih; Lee, Tsu-Tian; Liu, Han-Leih
2002-01-01
A new hybrid direct/indirect adaptive fuzzy neural network (FNN) controller with a state observer and supervisory controller for a class of uncertain nonlinear dynamic systems is developed in this paper. The hybrid adaptive FNN controller, the free parameters of which can be tuned on-line by an observer-based output feedback control law and adaptive law, is a combination of direct and indirect adaptive FNN controllers. A weighting factor, which can be adjusted by the tradeoff between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive FNN controller and direct adaptive FNN controller. Furthermore, a supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be deactivated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Two nonlinear systems, namely, inverted pendulum system and Chua's (1989) chaotic circuit, are fully illustrated to track sinusoidal signals. The resulting hybrid direct/indirect FNN control systems show better performances, i.e., tracking error and control effort can be made smaller and it is more flexible during the design process.
Turing pattern formation in the Brusselator system with nonlinear diffusion.
Gambino, G; Lombardo, M C; Sammartino, M; Sciacca, V
2013-10-01
In this work we investigate the effect of density-dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in one-dimensional and two-dimensional spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supercritical and subcritical Turing patterns with multiple branches of stable solutions leading to hysteresis. Moreover, we consider traveling patterning waves: When the domain size is large, the pattern forms sequentially and traveling wave fronts are the precursors to patterning. We derive the Ginzburg-Landau equation and describe the traveling front enveloping a pattern which invades the domain. We show the emergence of radially symmetric target patterns, and, through a matching procedure, we construct the outer amplitude equation and the inner core solution. PMID:24229267
Turing pattern formation in the Brusselator system with nonlinear diffusion
NASA Astrophysics Data System (ADS)
Gambino, G.; Lombardo, M. C.; Sammartino, M.; Sciacca, V.
2013-10-01
In this work we investigate the effect of density-dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in one-dimensional and two-dimensional spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supercritical and subcritical Turing patterns with multiple branches of stable solutions leading to hysteresis. Moreover, we consider traveling patterning waves: When the domain size is large, the pattern forms sequentially and traveling wave fronts are the precursors to patterning. We derive the Ginzburg-Landau equation and describe the traveling front enveloping a pattern which invades the domain. We show the emergence of radially symmetric target patterns, and, through a matching procedure, we construct the outer amplitude equation and the inner core solution.
Nonlinear Information Processing in a Model Sensory System
Chacron, Maurice J.
2016-01-01
Understanding the mechanisms by which sensory neurons encode and decode information remains an important goal in neuroscience. We quantified the performance of optimal linear and nonlinear encoding models in a well-characterized sensory system: the electric sense of weakly electric fish. We show that linear encoding models generally perform better under spatially localized stimulation than under spatially diffuse stimulation. Through pharmacological blockade of feedback input and spatial saturation of the receptive field center, we show that there is significantly less synaptic noise under spatially diffuse stimuli as compared with spatially localized stimuli. Modeling results suggest that pyramidal cells nonlinearly encode sensory information through shunting in their dendrites and clarify the influence of synaptic noise on the performance of linear encoding models. Finally, we used information theory to quantify the performance of linear decoders. While the optimal linear decoder for spatially localized stimuli could capture 60% of the information in pyramidal cell spike trains, the optimal linear decoder for spatially diffuse stimuli could only capture 40% of the information. These results show that nonlinear decoders are necessary to fully access information in pyramidal cell spike trains, and we discuss potential mechanisms by which higher-order neurons could decode this information. PMID:16495358
General purpose nonlinear system solver based on Newton-Krylov method.
2013-12-01
KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].
Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Martin, Corless
2004-01-01
We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.
NASA Astrophysics Data System (ADS)
Gupta, Samit Kumar; Sarma, Amarendra K.
2016-07-01
In this work, we have studied the peregrine rogue wave dynamics, with a solitons on finite background (SFB) ansatz, in the recently proposed (Ablowitz and Musslimani, (2013) [31]) continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity. We have found that the continuous nonlinear Schrödinger system with PT-symmetric nonlinearity also admits Peregrine soliton solution. Motivated by the fact that Peregrine solitons are regarded as prototypical solutions of rogue waves, we have studied Peregrine rogue wave dynamics in the c-PTNLSE model. Upon numerical computation, we observe the appearance of low-intense Kuznetsov-Ma (KM) soliton trains in the absence of transverse shift (unbroken PT-symmetry) and well-localized high-intense Peregrine rogue waves in the presence of transverse shift (broken PT-symmetry) in a definite parametric regime.
Linear theory for filtering nonlinear multiscale systems with model error
Berry, Tyrus; Harlim, John
2014-01-01
In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure
On the transmissibilities of nonlinear vibration isolation system
NASA Astrophysics Data System (ADS)
Lu, Zeqi; Brennan, Michael J.; Chen, Li-Qun
2016-08-01
Transmissibility is a key parameter to quantify the effectiveness of a vibration isolation system. Under harmonic excitation, the force transmissibility of a linear vibration isolation system is defined as the ratio between the amplitude of the force transmitted to the host structure and the excitation force amplitude, and the displacement transmissibility is the ratio between the displacement amplitude of the payload and that of the base. For a nonlinear vibration isolation system, the force or the displacement responses usually have more frequency components than the excitation. For a harmonic excitation, the response may be periodic, quasi-periodic or chaotic. Therefore, the amplitude ratio cannot well define the transmissibility. The root-mean-square ratio of the response to the excitation is suggested to define the transmissibility. The significance of the modified transmissibility is highlighted in a nonlinear two-stage vibration isolation system consisting of two linear spring connected linear vibration isolators with two additional horizontal linear springs. Harmonic balance method (HBM) is applied to determine the responses with the fundamental and third harmonic. Numerical simulations reveal that chaos may occur in the responses. In both cases, the modified transmissibility works while the original definition cannot be applied to chaotic response.
Lotka-Volterra representation of general nonlinear systems.
Hernández-Bermejo, B; Fairén, V
1997-02-01
In this article we elaborate on the structure of the generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial transformations and the underlying structure of classes of equivalence. Each class possesses a unique representative under the classical quadratic Lotka-Volterra form. We show how other standard modeling forms of biological interest, such as S-systems or mass-action systems, are naturally embedded into the GLV form, which thus provides a formal framework for their comparison and for the establishment of transformation rules. We also focus on the issue of recasting of general nonlinear systems into the GLV format. We present a procedure for doing so and point at possible sources of ambiguity that could make the resulting Lotka-Volterra system dependent on the path followed. We then provide some general theorems that define the operational and algorithmic framework in which this is not the case.
Directing nonlinear dynamic systems to any desired orbit
Zonghua, L. |; Shigang, C.
1997-01-01
A method of controlling arbitrary nonlinear dynamic systems, dx/dt=F(x,t) (x{element_of}R{sup n}), is presented. It is proved that the system can be entrained to any arbitrary {open_quotes}goal{close_quotes} dynamics g(t) by use of the open-loop action and adjusting the control parameter at the same time. Examples of some entrainment {open_quotes}goals{close_quotes} are given for the Lorenz and the R{umlt o}ssler systems. The basins of entrainment are also established for the Lorenz, R{umlt o}ssler, and Duffing systems. Numerical studies show that this method works as well as the closed-loop control method [Physica D {bold 85}, 1 (1995); Phys. Lett. A {bold 213}, 148 (1996)]. {copyright} {ital 1997} {ital The American Physical Society}
FINDS: A fault inferring nonlinear detection system. User's guide
NASA Technical Reports Server (NTRS)
Lancraft, R. E.; Caglayan, A. K.
1983-01-01
The computer program FINDS is written in FORTRAN-77, and is intended for operation on a VAX 11-780 or 11-750 super minicomputer, using the VMS operating system. The program detects, isolates, and compensates for failures in navigation aid instruments and onboard flight control and navigation sensors of a Terminal Configured Vehicle aircraft in a Microwave Landing System environment. In addition, FINDS provides sensor fault tolerant estimates for the aircraft states which are then used by an automatic guidance and control system to land the aircraft along a prescribed path. FINDS monitors for failures by evaluating all sensor outputs simultaneously using the nonlinear analytic relationships between the various sensor outputs arising from the aircraft point mass equations of motion. Hence, FINDS is an integrated sensor failure detection and isolation system.
Sustained small oscillations in nonlinear control systems. [launch vehicle dynamics
NASA Technical Reports Server (NTRS)
George, J. H.; Gunderson, R. W.; Hahn, H.
1975-01-01
Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.
A universal approach to the study of nonlinear systems
NASA Astrophysics Data System (ADS)
Hwa, Rudolph C.
2004-07-01
A large variety of nonlinear systems have been treated by a common approach that emphasizes the fluctuation of spatial patterns. By using the same method of analysis it is possible to discuss the chaotic behaviors of quark jets and logistic map in the same language. Critical behaviors of quark-hadron phase transition in heavy-ion collisions and of photon production at the threshold of lasing can also be described by a common scaling behavior. The universal approach also makes possible an insight into the recently discovered phenomenon of wind reversal in cryogenic turbulence as a manifestation of self-organized criticality.
M-MRAC for Nonlinear Systems with Bounded Disturbances
NASA Technical Reports Server (NTRS)
Stepanyan, Vahram; Krishnakumar, Kalmanje
2011-01-01
This paper presents design and performance analysis of a modified reference model MRAC (M-MRAC) architecture for a class of multi-input multi-output uncertain nonlinear systems in the presence of bounded disturbances. M-MRAC incorporates an error feedback in the reference model definition, which allows for fast adaptation without generating high frequency oscillations in the control signal, which closely follows the certainty equivalent control signal. The benefits of the method are demonstrated via a simulation example of an aircraft's wing rock motion.
Alberich, Arístides; Díaz-Cruz, José Manuel; Ariño, Cristina; Esteban, Miquel
2008-01-01
A new mathematical algorithm is proposed to correct the progressive potential shift of some voltammetric signals that decrease the linearity of the data. The corrected data matrix can be further analysed by Multivariate Curve Resolution by Alternating Least Squares (MCR-ALS) and the vector including the potential shift corrections can be fitted to specific equations such as that by DeFord-Hume. A detailed discussion is given on the different cases of potential shift correction, and, in some of them, mathematical simulation is made or experimental systems [Cd(ii)-glutathione and Zn(ii)-glycine] are analysed.
Practical application of equivalent linearization approaches to nonlinear piping systems
Park, Y.J.; Hofmayer, C.H.
1995-05-01
The use of mechanical energy absorbers as an alternative to conventional hydraulic and mechanical snubbers for piping supports has attracted a wide interest among researchers and practitioners in the nuclear industry. The basic design concept of energy absorbers (EA) is to dissipate the vibration energy of piping systems through nonlinear hysteretic actions of EA!s under design seismic loads. Therefore, some type of nonlinear analysis needs to be performed in the seismic design of piping systems with EA supports. The equivalent linearization approach (ELA) can be a practical analysis tool for this purpose, particularly when the response approach (RSA) is also incorporated in the analysis formulations. In this paper, the following ELA/RSA methods are presented and compared to each other regarding their practice and numerical accuracy: Response approach using the square root of sum of squares (SRSS) approximation (denoted RS in this paper). Classical ELA based on modal combinations and linear random vibration theory (denoted CELA in this paper). Stochastic ELA based on direct solution of response covariance matrix (denoted SELA in this paper). New algorithms to convert response spectra to the equivalent power spectral density (PSD) functions are presented for both the above CELA and SELA methods. The numerical accuracy of the three EL are studied through a parametric error analysis. Finally, the practicality of the presented analysis is demonstrated in two application examples for piping systems with EA supports.
Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.
Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong
2015-11-01
The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness. PMID:26277007
Nonlinear dynamics of a simplified engine-propeller system
NASA Astrophysics Data System (ADS)
Yu, S. D.; Warwick, S. A.; Zhang, X.
2009-07-01
This paper presents a procedure for studying dynamical behaviors of a simplified engine-propeller dynamical system consisting of a number of bodies of plane motions. The equation of motion of the complex system is obtained using the Lagrange equation and solved numerically using the 4th order Runge-Kutta method. Various simulations were performed to investigate the transient and steady state behaviors of the multiple body system while taking into consideration the engine pressure pulsations, nonlinear inertia of moving bodies, and nonlinear aerodynamic load. Sub-harmonics and super harmonics in the steady state responses for different power and propeller pitch settings are obtained using the fast Fourier transform. Numerical simulations indicate that the 1.5 order is the dominant order of harmonics in the steady state oscillatory motion of the crankshaft. The findings and procedure presented in the paper are useful to the aerospace industry in certifying reciprocating engines and propellers. The crankshaft oscillatory velocities obtained from the simplified rigid body model are in good agreement with the experimental data for a SAITO-450 engine and a SOLO propeller at a 6″ pitch setting.
Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Agarwal, S.; Wettlaufer, J. S.
2014-12-01
We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.
Nonlinear natural engine: Model for thermodynamic processes in mesoscale systems
Wheatley, John; Buchanan, D. S.; Swift, G. W.; Migliori, A.; Hofler, T.
1985-01-01
To develop intuition on the possible application of concepts from thermodynamic heat engines to mesoscale systems, we have constructed and studied a model thermoacoustic heat engine. The model consists of a chain of coupled nonlinear acoustic vibrators in which the primary thermodynamic medium is argon gas, the secondary thermodynamic medium is constituted by solids bounding the gas, and frequencies are ca. 3 × 102 Hz. The nonlinear elements are the necks, made flexible by means of an oil-loaded DuPont Kapton film, of Helmholtz resonators. When the primary medium is driven uniformly by an acoustic driver at a frequency somewhat below the low-amplitude resonant frequency and at a high enough driving amplitude, stationary localized or solitary states appear irreversibly on the chain. These are characterized by a higher vibrational amplitude than that in surrounding vibrators, where the amplitude can decrease; by the appearance of deep subharmonics of the drive frequency, corresponding to driven low-frequency vibrations of the Kapton film-oil systems; and by the pumping of heat toward the localized states. Possible implications of these results for mesoscale systems consisting of chains of molecular vibrators are then discussed. Images PMID:16593625
Localized Nonlinear Waves in Systems with Time- and Space-Modulated Nonlinearities
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Konotop, Vladimir V.
2008-04-25
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schroedinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.
Stabilizing model predictive control for constrained nonlinear distributed delay systems.
Mahboobi Esfanjani, R; Nikravesh, S K Y
2011-04-01
In this paper, a model predictive control scheme with guaranteed closed-loop asymptotic stability is proposed for a class of constrained nonlinear time-delay systems with discrete and distributed delays. A suitable terminal cost functional and also an appropriate terminal region are utilized to achieve asymptotic stability. To determine the terminal cost, a locally asymptotically stabilizing controller is designed and an appropriate Lyapunov-Krasoskii functional of the locally stabilized system is employed as the terminal cost. Furthermore, an invariant set for locally stabilized system which is established by using the Razumikhin Theorem is used as the terminal region. Simple conditions are derived to obtain terminal cost and terminal region in terms of Bilinear Matrix Inequalities. The method is illustrated by a numerical example.
THz impulse radar for biomedical sensing: nonlinear system behavior
NASA Astrophysics Data System (ADS)
Brown, E. R.; Sung, Shijun; Grundfest, W. S.; Taylor, Z. D.
2014-03-01
The THz impulse radar is an "RF-inspired" sensor system that has performed remarkably well since its initial development nearly six years ago. It was developed for ex vivo skin-burn imaging, and has since shown great promise in the sensitive detection of hydration levels in soft tissues of several types, such as in vivo corneal and burn samples. An intriguing aspect of the impulse radar is its hybrid architecture which combines the high-peak-power of photoconductive switches with the high-responsivity and -bandwidth (RF and video) of Schottky-diode rectifiers. The result is a very sensitive sensor system in which the post-detection signal-to-noise ratio depends super-linearly on average signal power up to a point where the diode is "turned on" in the forward direction, and then behaves quasi-linearly beyond that point. This paper reports the first nonlinear systems analysis done on the impulse radar using MATLAB.
Dynamics of large constrained nonlinear systems -- A taxonomy theory
Venkatasubramanian, V.; Schaettler, H.; Zaborszky, J.
1995-11-01
This paper provides an overview of the taxonomy theory which has been proposed as a fundamental platform for solving practical stability related problems in large constrained nonlinear systems such as the electric power system. The theory reveals a two-level intertwined cellular nature of the constrained system dynamics which serves as a unifying structure, a taxonomy, for analyzing nonlinear phenomena in large system models. These broadly divide into the state space aspects (related to dynamic stability issues among others) and the parameter space aspects (connected with bifurcation phenomena among others). In the state-space formulation, the boundary of the region of attraction for the operating point is shown (under certain Morse-Smale like assumptions) to be composed of stable manifolds of certain anchors and portions of the singularity surface. Such boundary characterization provides the foundation for rigorous Lyapunov theoretic transient stability methods. In the parameter space analysis, the feasibility region which is bounded by the feasibility boundary provides a safe operating region for guaranteeing local stability at the equilibrium under slow parametric variations. The feasibility boundary where the operating point undergoes loss of local stability is characterized in the form of three principal bifurcations including a new bifurcation called the singularity induced bifurcation. An overview of the recent results which prove that the two-level structure exists even in nonsmooth models that incorporate the effects of system hard limits is also included. Specifically hard limits induce a number of new bifurcations. This natural taxonomy of the system dynamics stands as the backbone for developing practical and rigorous computational techniques in detecting diverse instability mechanisms.
Nonlinear system modeling with random matrices: echo state networks revisited.
Zhang, Bai; Miller, David J; Wang, Yue
2012-01-01
Echo state networks (ESNs) are a novel form of recurrent neural networks (RNNs) that provide an efficient and powerful computational model approximating nonlinear dynamical systems. A unique feature of an ESN is that a large number of neurons (the "reservoir") are used, whose synaptic connections are generated randomly, with only the connections from the reservoir to the output modified by learning. Why a large randomly generated fixed RNN gives such excellent performance in approximating nonlinear systems is still not well understood. In this brief, we apply random matrix theory to examine the properties of random reservoirs in ESNs under different topologies (sparse or fully connected) and connection weights (Bernoulli or Gaussian). We quantify the asymptotic gap between the scaling factor bounds for the necessary and sufficient conditions previously proposed for the echo state property. We then show that the state transition mapping is contractive with high probability when only the necessary condition is satisfied, which corroborates and thus analytically explains the observation that in practice one obtains echo states when the spectral radius of the reservoir weight matrix is smaller than 1.
NASA Astrophysics Data System (ADS)
Zhang, Qian; Wang, Qunjing; Li, Guoli
2016-05-01
This article deals with the identification of nonlinear model and Nonlinear Predictive Functional Controller (NPFC) design based on the Hammerstein structure for the turntable servo system. As a mechanism with multi-mass rotational system, nonlinearities significantly influence the system operation, especially when the turntable is in the states of zero-crossing distortion or rapid acceleration/deceleration, etc. The field data from identification experiments are processed by Comprehensive Learning Particle Swarm Optimization (CLPSO). As a result, Hammerstein model can be derived to describe the input-output relationship globally, considering all the linear and nonlinear factors of the turntable system. Cross validation results demonstrate good correspondence between the real equipment and the identified model. In the second part of this manuscript, a nonlinear control strategy based on the genetic algorithm and predictive control is developed. The global nonlinear predictive controller is carried out by two steps: (i) build the linear predictive functional controller with state space equations for the linear subsystem of Hammerstein model, and (ii) optimize the global control variable by minimizing the cost function through genetic algorithm. On the basis of distinguish model for turntable and the effectiveness of NPFC, the good performance of tracking ability is achieved in the simulation results.
Adaptive RSOV filter using the FELMS algorithm for nonlinear active noise control systems
NASA Astrophysics Data System (ADS)
Zhao, Haiquan; Zeng, Xiangping; He, Zhengyou; Li, Tianrui
2013-01-01
This paper presents a recursive second-order Volterra (RSOV) filter to solve the problems of signal saturation and other nonlinear distortions that occur in nonlinear active noise control systems (NANC) used for actual applications. Since this nonlinear filter based on an infinite impulse response (IIR) filter structure can model higher than second-order and third-order nonlinearities for systems where the nonlinearities are harmonically related, the RSOV filter is more effective in NANC systems with either a linear secondary path (LSP) or a nonlinear secondary path (NSP). Simulation results clearly show that the RSOV adaptive filter using the multichannel structure filtered-error least mean square (FELMS) algorithm can further greatly reduce the computational burdens and is more suitable to eliminate nonlinear distortions in NANC systems than a SOV filter, a bilinear filter and a third-order Volterra (TOV) filter.
Time-optimal quantum control of nonlinear two-level systems
NASA Astrophysics Data System (ADS)
Chen, Xi; Ban, Yue; Hegerfeldt, Gerhard C.
2016-08-01
Nonlinear two-level Landau-Zener type equations for systems with relevance for Bose-Einstein condensates and nonlinear optics are considered and the minimal time Tmin to drive an initial state to a given target state is investigated. Surprisingly, the nonlinearity may be canceled by a time-optimal unconstrained driving and Tmin becomes independent of the nonlinearity. For constrained and unconstrained driving explicit expressions are derived for Tmin, the optimal driving, and the protocol.
NASA Technical Reports Server (NTRS)
Crutcher, H. L.; Falls, L. W.
1976-01-01
Sets of experimentally determined or routinely observed data provide information about the past, present and, hopefully, future sets of similarly produced data. An infinite set of statistical models exists which may be used to describe the data sets. The normal distribution is one model. If it serves at all, it serves well. If a data set, or a transformation of the set, representative of a larger population can be described by the normal distribution, then valid statistical inferences can be drawn. There are several tests which may be applied to a data set to determine whether the univariate normal model adequately describes the set. The chi-square test based on Pearson's work in the late nineteenth and early twentieth centuries is often used. Like all tests, it has some weaknesses which are discussed in elementary texts. Extension of the chi-square test to the multivariate normal model is provided. Tables and graphs permit easier application of the test in the higher dimensions. Several examples, using recorded data, illustrate the procedures. Tests of maximum absolute differences, mean sum of squares of residuals, runs and changes of sign are included in these tests. Dimensions one through five with selected sample sizes 11 to 101 are used to illustrate the statistical tests developed.
NASA Technical Reports Server (NTRS)
Phan, Minh; Juang, Jer-Nan; Longman, Richard W.
1991-01-01
A formulation is presented for identification of linear multivariable from a single set of input-output data. The identification method is formulated with the mathematical framework of learning identifications, by extension of the repetition domain concept to include shifting time intervals. This method contrasts with existing learning approaches that require data from multiple experiments. In this method, the system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded real eigenvalue assignment procedure. Through this relationship, the Markov parameters of the observer are identified. The Markov parameters of the actual system are recovered from those of the observer, and then used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and numerical examples presented to illustrate.
Nonlinear wave propagation in discrete and continuous systems
NASA Astrophysics Data System (ADS)
Rothos, V. M.
2016-09-01
In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.
One-Time Pad as a nonlinear dynamical system
NASA Astrophysics Data System (ADS)
Nagaraj, Nithin
2012-11-01
The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, DNA cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, AES are not even proven to be computationally secure). In this work, we prove that the OTP encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the GLS that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that OTP encryption is related to Randomized Arithmetic Coding - a scheme for joint compression and encryption.
A globalization procedure for solving nonlinear systems of equations
NASA Astrophysics Data System (ADS)
Shi, Yixun
1996-09-01
A new globalization procedure for solving a nonlinear system of equationsF(x)D0 is proposed based on the idea of combining Newton step and the steepest descent step WITHIN each iteration. Starting with an arbitrary initial point, the procedure converges either to a solution of the system or to a local minimizer off(x)D1/2F(x)TF(x). Each iteration is chosen to be as close to a Newton step as possible and could be the Newton step itself. Asymptotically the Newton step will be taken in each iteration and thus the convergence is quadratic. Numerical experiments yield positive results. Further generalizations of this procedure are also discussed in this paper.
Evidence for nonlinear capacitance in biomembrane channel system.
Ghosh, S; Bera, A K; Das, S
1999-10-01
The electrophysiological properties of voltage-dependent anion channels from mitochondrial membrane have been studied in a bilayer membrane system. It was observed that the probability of opening of the membrane channel depends on externally applied voltage and the plot is a bell-shaped curve symmetric around probability axis. A scheme of conformational energy levels under varying externally applied voltage was formulated. Assuming that the probability follows Boltzmann distribution, we arrive at an expression of change in energy containing a separate term identical to the energy of a capacitor. This fact indicates the possibility of existence of an added capacitance due to the channel protein. Further it was shown that the aforesaid channel capacitor could be a function of voltage leading to nonlinearity. We have offered a general method of calculating nonlinear capacitance from the experimental data on opening probability of a membrane channel. In case of voltage-dependent anion channel the voltage dependence of the capacitor has a power 0.786. The results have been interpreted in view of the structural organization of the channel protein in the membrane. Our hypothesis is that the phenomenon of capacitor behaviour is a general one for membrane channels.
An approximation theory for the identification of nonlinear distributed parameter systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.
An approximation theory for the identification of nonlinear distributed parameter systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1990-01-01
An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato appproximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.
Predictability of extremes in non-linear hierarchically organized systems
NASA Astrophysics Data System (ADS)
Kossobokov, V. G.; Soloviev, A.
2011-12-01
Understanding the complexity of non-linear dynamics of hierarchically organized systems progresses to new approaches in assessing hazard and risk of the extreme catastrophic events. In particular, a series of interrelated step-by-step studies of seismic process along with its non-stationary though self-organized behaviors, has led already to reproducible intermediate-term middle-range earthquake forecast/prediction technique that has passed control in forward real-time applications during the last two decades. The observed seismic dynamics prior to and after many mega, great, major, and strong earthquakes demonstrate common features of predictability and diverse behavior in course durable phase transitions in complex hierarchical non-linear system of blocks-and-faults of the Earth lithosphere. The confirmed fractal nature of earthquakes and their distribution in space and time implies that many traditional estimations of seismic hazard (from term-less to short-term ones) are usually based on erroneous assumptions of easy tractable analytical models, which leads to widespread practice of their deceptive application. The consequences of underestimation of seismic hazard propagate non-linearly into inflicted underestimation of risk and, eventually, into unexpected societal losses due to earthquakes and associated phenomena (i.e., collapse of buildings, landslides, tsunamis, liquefaction, etc.). The studies aimed at forecast/prediction of extreme events (interpreted as critical transitions) in geophysical and socio-economical systems include: (i) large earthquakes in geophysical systems of the lithosphere blocks-and-faults, (ii) starts and ends of economic recessions, (iii) episodes of a sharp increase in the unemployment rate, (iv) surge of the homicides in socio-economic systems. These studies are based on a heuristic search of phenomena preceding critical transitions and application of methodologies of pattern recognition of infrequent events. Any study of rare
Multivariable speed synchronisation for a parallel hybrid electric vehicle drivetrain
NASA Astrophysics Data System (ADS)
Alt, B.; Antritter, F.; Svaricek, F.; Schultalbers, M.
2013-03-01
In this article, a new drivetrain configuration of a parallel hybrid electric vehicle is considered and a novel model-based control design strategy is given. In particular, the control design covers the speed synchronisation task during a restart of the internal combustion engine. The proposed multivariable synchronisation strategy is based on feedforward and decoupled feedback controllers. The performance and the robustness properties of the closed-loop system are illustrated by nonlinear simulation results.
Optimum Damping in a Non-Linear Base Isolation System
NASA Astrophysics Data System (ADS)
Jangid, R. S.
1996-02-01
Optimum isolation damping for minimum acceleration of a base-isolated structure subjected to earthquake ground excitation is investigated. The stochastic model of the El-Centro1940 earthquake, which preserves the non-stationary evolution of amplitude and frequency content of ground motion, is used as an earthquake excitation. The base isolated structure consists of a linear flexible shear type multi-storey building supported on a base isolation system. The resilient-friction base isolator (R-FBI) is considered as an isolation system. The non-stationary stochastic response of the system is obtained by the time dependent equivalent linearization technique as the force-deformation of the R-FBI system is non-linear. The optimum damping of the R-FBI system is obtained under important parametric variations; i.e., the coefficient of friction of the R-FBI system, the period and damping of the superstructure; the effective period of base isolation. The criterion selected for optimality is the minimization of the top floor root mean square (r.m.s.) acceleration. It is shown that the above parameters have significant effects on optimum isolation damping.
Dispersion and nonlinear effects in OFDM-RoF system
NASA Astrophysics Data System (ADS)
Alhasson, Bader H.; Bloul, Albe M.; Matin, M.
2010-08-01
The radio-over-fiber (RoF) network has been a proven technology to be the best candidate for the wireless-access technology, and the orthogonal frequency division multiplexing (OFDM) technique has been established as the core technology in the physical layer of next generation wireless communication system, as a result OFDM-RoF has drawn attentions worldwide and raised many new research topics recently. At the present time, the trend of information industry is towards mobile, wireless, digital and broadband. The next generation network (NGN) has motivated researchers to study higher-speed wider-band multimedia communication to transmit (voice, data, and all sorts of media such as video) at a higher speed. The NGN would offer services that would necessitate broadband networks with bandwidth higher than 2Mbit/s per radio channel. Many new services emerged, such as Internet Protocol TV (IPTV), High Definition TV (HDTV), mobile multimedia and video stream media. Both speed and capacity have been the key objectives in transmission. In the meantime, the demand for transmission bandwidth increased at a very quick pace. The coming of 4G and 5G era will provide faster data transmission and higher bit rate and bandwidth. Taking advantages of both optical communication and wireless communication, OFDM Radio over Fiber (OFDM-RoF) system is characterized by its high speed, large capacity and high spectral efficiency. However, up to the present there are some problems to be solved, such as dispersion and nonlinearity effects. In this paper we will study the dispersion and nonlinearity effects and their elimination in OFDM-radio-over-fiber system.
Noise in Nonlinear Dynamical Systems 3 Volume Paperback Set
NASA Astrophysics Data System (ADS)
Moss, Frank; McClintock, P. V. E.
2011-11-01
Volume 1: List of contributors; Preface; Introduction to volume one; 1. Noise-activated escape from metastable states: an historical view Rolf Landauer; 2. Some Markov methods in the theory of stochastic processes in non-linear dynamical systems R. L. Stratonovich; 3. Langevin equations with coloured noise J. M. Sancho and M. San Miguel; 4. First passage time problems for non-Markovian processes Katja Lindenberg, Bruce J. West and Jaume Masoliver; 5. The projection approach to the Fokker-Planck equation: applications to phenomenological stochastic equations with coloured noises Paolo Grigolini; 6. Methods for solving Fokker-Planck equations with applications to bistable and periodic potentials H. Risken and H. D. Vollmer; 7. Macroscopic potentials, bifurcations and noise in dissipative systems Robert Graham; 8. Transition phenomena in multidimensional systems - models of evolution W. Ebeling and L. Schimansky-Geier; 9. Coloured noise in continuous dynamical systems: a functional calculus approach Peter Hanggi; Appendix. On the statistical treatment of dynamical systems L. Pontryagin, A. Andronov and A. Vitt; Index. Volume 2: List of contributors; Preface; Introduction to volume two; 1. Stochastic processes in quantum mechanical settings Ronald F. Fox; 2. Self-diffusion in non-Markovian condensed-matter systems Toyonori Munakata; 3. Escape from the underdamped potential well M. Buttiker; 4. Effect of noise on discrete dynamical systems with multiple attractors Edgar Knobloch and Jeffrey B. Weiss; 5. Discrete dynamics perturbed by weak noise Peter Talkner and Peter Hanggi; 6. Bifurcation behaviour under modulated control parameters M. Lucke; 7. Period doubling bifurcations: what good are they? Kurt Wiesenfeld; 8. Noise-induced transitions Werner Horsthemke and Rene Lefever; 9. Mechanisms for noise-induced transitions in chemical systems Raymond Kapral and Edward Celarier; 10. State selection dynamics in symmetry-breaking transitions Dilip K. Kondepudi; 11. Noise in a
Wang, Yuan-Jay
2007-10-01
A new method is proposed to compute all feasible robust stabilizing controllers for preventing the generation of limit cycle of nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity. The describing function analysis method is employed to approximate the behaviors of the nonlinearity. The Kharitonov theorem is utilized to characterize parametric uncertainties in the linear plant and nonlinearity. Necessary conditions for limit cycles are established. Boundaries for the generation of limit cycle and boundaries for asymptotic stability are portrayed exploiting the stability equation method. The region for prescribed limit cycle behavior and the region for asymptotic stability are located. An admissible specification-oriented Kharitonov region is found directly on the controller parameter plane. The region is non-conservative and constitutes all of the feasible controller gain sets to achieve robust prevention of limit cycle for the considered uncertain nonlinear control systems. The way to tune the controller gains is suggested. Finally, for comparison purpose, two illustrative examples proposed in the literature are given to show how the proposed algorithm can be effectively applied to tune a robust controller to achieve a prescribed limit cycle behavior and accomplish robust limit cycle amplitude suppression and prevention.
Multivariate moment closure techniques for stochastic kinetic models
Lakatos, Eszter Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models
NASA Astrophysics Data System (ADS)
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Method and system for non-linear motion estimation
NASA Technical Reports Server (NTRS)
Lu, Ligang (Inventor)
2011-01-01
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
Equations for Nonlinear MHD Convection in Shearless Magnetic Systems
Pastukhov, V.P.
2005-07-15
A closed set of reduced dynamic equations is derived that describe nonlinear low-frequency flute MHD convection and resulting nondiffusive transport processes in weakly dissipative plasmas with closed or open magnetic field lines. The equations obtained make it possible to self-consistently simulate transport processes and the establishment of the self-consistent plasma temperature and density profiles for a large class of axisymmetric nonparaxial shearless magnetic devices: levitated dipole configurations, mirror systems, compact tori, etc. Reduced equations that are suitable for modeling the long-term evolution of the plasma on time scales comparable to the plasma lifetime are derived by the method of the adiabatic separation of fast and slow motions.
Linear and Nonlinear Systems Analysis of the Visual System: Why does it seem so linear?
Shapley, Robert
2009-01-01
Linear and nonlinear systems analysis are tools that can be used to study communication systems like the visual system. The first step of systems analysis often is to test whether or not the system is linear. Retinal pathways are surprisingly linear, and some neurons in the visual cortex also emulate linear sensory transducers. We conclude that the retinal linearity depends on specialized ribbon synapses while cortical linearity is the result of balanced excitatory and inhibitory synaptic interactions. PMID:18940193
Nonlinear Silicon Waveguides for Integrated Fiber Laser Systems
NASA Astrophysics Data System (ADS)
Wong, Chi Yan
Silicon-on-insulator (SOI) based photonic devices have attracted great interest from photonics community because of its compatibility with state-of-the-art CMOS fabrication processes and its potential of making energy efficient and low cost photonic integrated circuits (PICs) for high bandwidth optical interconnects and integrated optical sensors. Wavelength division multiplexing (WDM) is already widely used in optical communications and is also of interest for optical sensors, providing advantages of low cost, and high speed compared with single wavelength approach. However, the cost and the bulkiness of WDM systems increase proportionally with the number of wavelengths if conventional external laser source is used. Therefore, low cost and compact laser source with stable and high line quality is of great interest for integrated sensors. In this thesis, we investigate the incorporation of silicon photonic devices as intracavity elements in fiber lasers for various applications. Therefore, the high flexibly and rich functionalities of fiber lasers can be directly used in the PIC. Also, high-speed feedback control of the cavity becomes possible. The possibility of applying nonlinear SOI waveguides to fiber lasers is investigated. We propose and demonstrate a multiwavelength erbium-doped fiber laser stabilized by four-wave mixing (FWM) in a nonlinear SOI waveguide. Such multiwavelength lasers are potentially suitable for WDM sensing. The wavelength selectivity was achieved by an intracavity Fabry-Perot comb filter. Making use of the nonlinearity of the SOI waveguide, a multiwavelength laser with six output wavelengths at 0.8 nm spacing was achieved. We study a passive mode-locked erbium-doped fiber ring laser based on a nonlinear SOI microring resonator (MRR). By using the MRR as the comb filter and the nonlinear medium, a stable mode-locked pulse train at 100 GHz was produced by filter-driven four-wave mixing. Such lasers can act as high repetition rate optical
Guidance of Nonlinear Nonminimum-Phase Dynamic Systems
NASA Technical Reports Server (NTRS)
Devasia, Santosh
1996-01-01
The research work has advanced the inversion-based guidance theory for: systems with non-hyperbolic internal dynamics; systems with parameter jumps; and systems where a redesign of the output trajectory is desired. A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics was developed. This approach integrated stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics was used (a) to remove non-hyperbolicity which is an obstruction to applying stable inversion techniques and (b) to reduce large preactuation times needed to apply stable inversion for near non-hyperbolic cases. The method was applied to an example helicopter hover control problem with near non-hyperbolic internal dynamics for illustrating the trade-off between exact tracking and reduction of preactuation time. Future work will extend these results to guidance of nonlinear non-hyperbolic systems. The exact output tracking problem for systems with parameter jumps was considered. Necessary and sufficient conditions were derived for the elimination of switching-introduced output transient. While previous works had studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches), such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is also applicable to nonminimum-phase systems and leads to bounded but possibly non-causal solutions. In addition, for the case when the reference trajectories are generated by an exosystem, we developed an exact-tracking controller which could be written in a feedback form. As in standard regulator theory, we also obtained a linear map from the states of the exosystem to the desired system state, which was defined via a matrix differential equation.
NASA Astrophysics Data System (ADS)
Bona, J. L.; Chen, M.; Saut, J.-C.
2004-05-01
In part I of this work (Bona J L, Chen M and Saut J-C 2002 Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J. Nonlinear Sci. 12 283-318), a four-parameter family of Boussinesq systems was derived to describe the propagation of surface water waves. Similar systems are expected to arise in other physical settings where the dominant aspects of propagation are a balance between the nonlinear effects of convection and the linear effects of frequency dispersion. In addition to deriving these systems, we determined in part I exactly which of them are linearly well posed in various natural function classes. It was argued that linear well-posedness is a natural necessary requirement for the possible physical relevance of the model in question. In this paper, it is shown that the first-order correct models that are linearly well posed are in fact locally nonlinearly well posed. Moreover, in certain specific cases, global well-posedness is established for physically relevant initial data. In part I, higher-order correct models were also derived. A preliminary analysis of a promising subclass of these models shows them to be well posed.
Zhang, Yajun; Chai, Tianyou; Wang, Hong
2011-11-01
This paper presents a novel nonlinear control strategy for a class of uncertain single-input and single-output discrete-time nonlinear systems with unstable zero-dynamics. The proposed method combines adaptive-network-based fuzzy inference system (ANFIS) with multiple models, where a linear robust controller, an ANFIS-based nonlinear controller and a switching mechanism are integrated using multiple models technique. It has been shown that the linear controller can ensure the boundedness of the input and output signals and the nonlinear controller can improve the dynamic performance of the closed loop system. Moreover, it has also been shown that the use of the switching mechanism can simultaneously guarantee the closed loop stability and improve its performance. As a result, the controller has the following three outstanding features compared with existing control strategies. First, this method relaxes the assumption of commonly-used uniform boundedness on the unmodeled dynamics and thus enhances its applicability. Second, since ANFIS is used to estimate and compensate the effect caused by the unmodeled dynamics, the convergence rate of neural network learning has been increased. Third, a "one-to-one mapping" technique is adapted to guarantee the universal approximation property of ANFIS. The proposed controller is applied to a numerical example and a pulverizing process of an alumina sintering system, respectively, where its effectiveness has been justified.
A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems
ERIC Educational Resources Information Center
Stavrou, D.; Duit, R.; Komorek, M.
2008-01-01
A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…
NASA Technical Reports Server (NTRS)
Fitzjerrell, D. G.
1974-01-01
A general study of the stability of nonlinear as compared to linear control systems is presented. The analysis is general and, therefore, applies to other types of nonlinear biological control systems as well as the cardiovascular control system models. Both inherent and numerical stability are discussed for corresponding analytical and graphic methods and numerical methods.
Sustainability science: accounting for nonlinear dynamics in policy and social-ecological systems
Resilience is an emergent property of complex systems. Understanding resilience is critical for sustainability science, as linked social-ecological systems and the policy process that governs them are characterized by non-linear dynamics. Non-linear dynamics in these systems mean...
Macrosimulation of nonlinear dynamic systems for wave-shaping applications
NASA Astrophysics Data System (ADS)
Ogrodzki, Jan; Bieńkowski, Piotr
2014-11-01
Macromodeling is a technique widely used in circuits simulation. Macromodels usually describe complex, repetitive parts of large systems. They are often created on the base of original circuits by their simplification, e.g. macromodels of operational amplifiers. Another group of macromodels makes use of the circuit response approximation. This approach is called behavioral macromodeling. Low numerical complexity of behavioral macromodels is especially useful in CAD systems where circuit simulation must be run many times. In this paper the behavioral macromodeling technique has been applied to the whole circuit not to its part. This technique may be understood as shaping of the circuit output response and so belongs to a class of wave-shaping methods. We have used it to nonlinear, dynamic circuits with periodic signals of finite spectra, as e.g. in audio systems. The macromodels shape their frequency and spectral characteristics with a sufficient simplicity to omit unwanted distortions and with a sufficient efficiency to run the simulator in real time. Elaboration of this wave-shaping simulator is based on dynamic circuits identification, Fourier approximation of signals and harmonic balance technique. The obtained macromodel can be run as a software substitute for a hardware audio system.
NASA Astrophysics Data System (ADS)
Komatsu, Kazuo; Takata, Hitoshi
2012-11-01
In this paper, we consider an observer design by using a formal linearization based on Fourier expansion for nonlinear dynamic and measurement systems. A non-linear dynamic system is given by a nonlinear ordinary differential equation, and a measurement sysetm is done by a nonlinear equation. Defining a linearization function which consists of the trigonometric functions considered up to the higher-order, a nonlinear dynamic system is transformed into an augmented linear one with respect to this linearization function by using Fourier expansion. Introducing an augmented measurement vector which consists of polynomials of measurement data, a measurement equation is transformed into an augmented linear one with respect to the linearization function in the same way. To these augmented linearized systems, a linear estimation theory is applied to design a new non-linear observer.
NASA Astrophysics Data System (ADS)
Errouissi, Rachid; Yang, Jun; Chen, Wen-Hua; Al-Durra, Ahmed
2016-08-01
In this paper, a robust nonlinear generalised predictive control (GPC) method is proposed by combining an integral sliding mode approach. The composite controller can guarantee zero steady-state error for a class of uncertain nonlinear systems in the presence of both matched and unmatched disturbances. Indeed, it is well known that the traditional GPC based on Taylor series expansion cannot completely reject unknown disturbance and achieve offset-free tracking performance. To deal with this problem, the existing approaches are enhanced by avoiding the use of the disturbance observer and modifying the gain function of the nonlinear integral sliding surface. This modified strategy appears to be more capable of achieving both the disturbance rejection and the nominal prescribed specifications for matched disturbance. Simulation results demonstrate the effectiveness of the proposed approach.
The Impact of Fiber Nonlinearities on Digital Optical Communication Systems
NASA Astrophysics Data System (ADS)
Chiang, Ting-Kuang
Wavelength-division multiplexing (WDM) enables high throughput fiber-optic networks by sending several optical channels through a single fiber. Even though the bandwidth of optical fibers is over 25 THz, fiber nonlinearities can limit the capacity of WDM communication systems. Cross -phase modulation (XPM) is one of the nonlinear effects that affect WDM systems. This thesis provides an in-depth understanding of the properties of XPM-induced phase shift and suggests techniques to suppress XPM in long-distance WDM optical networks. In this thesis, XPM is theoretically and experimentally investigated in fiber links with optical amplifiers and dispersion compensators. The theoretical analysis suggests that the XPM effect can be modeled as a phase modulator with inputs from the intensity of co-propagating waves. The frequency response of the phase modulator depends on fiber dispersion, wavelength separation, and fiber length. In non-dispersive fibers, XPM is frequency-independent; in dispersive fibers, the response is approximately inversely proportional to modulation frequency, fiber dispersion, and wavelength separation. In N-segment amplified links with no dispersion compensators, the XPM frequency response is increased N -fold, but only in very narrow frequency bands. In most other frequency bands, the increase is limited and almost independent of N. However, in N-segment amplified links with dispersion compensators, the frequency response of XPM is increased N-fold at all frequencies if the dispersion is compensated for within each fiber segment. The XPM-induced sensitivity penalty in multichannel continuous-phase frequency-shift-keying optical communication systems is investigated by theoretical analysis, computer simulations, and experimental measurements. It is shown that high-frequency components in the XPM-induced phase shift play a more important role in determining the sensitivity penalty than the low-frequency components. The XPM-induced sensitivity penalty
Donnelly, W J; Donnelly, J E; Thong, Y H
1987-01-01
Multivariate cluster analysis of data on 128 asthmatic children resulted in the identification of 8 major discriminating variables. Stepwise divisions by this computer programme resulted in the formation of 6 grades of severity. There was significant correlation between higher grades of severity and early onset of the disease (P less than 0.02). There was also significant correlation between higher grades of severity and greater use of interval medications (P less than 0.002). However, 27.3% were receiving inadequate interval medications in respect of their grade of severity. Assignation of a 5-point scale to each of the 8 major discriminating variables resulted in the generation of computer-designated scores commensurate with each grade of severity. This was coupled to current recommendations for stepwise maintenance medications appropriate for each grade. This Score Card system for maintenance management of childhood asthma may prove useful in busy clinical settings.
Neural Feedback Passivity of Unknown Nonlinear Systems via Sliding Mode Technique.
Yu, Wen
2015-07-01
Passivity method is very effective to analyze large-scale nonlinear systems with strong nonlinearities. However, when most parts of the nonlinear system are unknown, the published neural passivity methods are not suitable for feedback stability. In this brief, we propose a novel sliding mode learning algorithm and sliding mode feedback passivity control. We prove that for a wide class of unknown nonlinear systems, this neural sliding mode control can passify and stabilize them. This passivity method is validated with a simulation and real experiment tests.
Linear versus nonlinear response of a forced wave turbulence system.
Cadot, Olivier; Touzé, Cyril; Boudaoud, Arezki
2010-10-01
A vibrating plate is set into a chaotic state of wave turbulence by a forcing having periodic and random components. Both components are weighted in order to explore continuously intermediate forcing from the periodic to the random one, but keeping constant its rms value. The transverse velocity of the plate is measured at the application point of the force. It is found that whatever the detail of the forcing is, the velocity spectra exhibit a universal cascade for frequencies larger than the forcing frequency range. In contrast, the velocity spectra strongly depend on the nature of the forcing within the range of forcing frequencies. The coherence function is used to extract the contribution of the velocity fluctuations that display a linear relationship with the forcing. The nonlinear contribution to the velocity fluctuations is found to be almost constant, about 55% of the total velocity fluctuations whatever the nature of the forcing from random to periodic. On the other hand, the nonlinear contribution to the fluctuations of the injected power depends on the nature of the forcing; it is significantly larger for the periodic forcing (60%) and decreases continuously as the randomness is increased, reaching a value of 40% for the pure random forcing. For all the cases of intermediate forcing from random to periodic, a simple model of the velocity response recovers in a fairly good agreement the probability density function of the injected power. The consequence of the existence of a linear-response component is discussed in the context of the fluctuation-dissipation theorem validation in experiments of out-of-equilibrium systems. PMID:21230369
Nonlinear damage identification of breathing cracks in Truss system
NASA Astrophysics Data System (ADS)
Zhao, Jie; DeSmidt, Hans
2014-03-01
The breathing cracks in truss system are detected by Frequency Response Function (FRF) based damage identification method. This method utilizes damage-induced changes of frequency response functions to estimate the severity and location of structural damage. This approach enables the possibility of arbitrary interrogation frequency and multiple inputs/outputs which greatly enrich the dataset for damage identification. The dynamical model of truss system is built using the finite element method and the crack model is based on fracture mechanics. Since the crack is driven by tensional and compressive forces of truss member, only one damage parameter is needed to represent the stiffness reduction of each truss member. Assuming that the crack constantly breathes with the exciting frequency, the linear damage detection algorithm is developed in frequency/time domain using Least Square and Newton Raphson methods. Then, the dynamic response of the truss system with breathing cracks is simulated in the time domain and meanwhile the crack breathing status for each member is determined by the feedback from real-time displacements of member's nodes. Harmonic Fourier Coefficients (HFCs) of dynamical response are computed by processing the data through convolution and moving average filters. Finally, the results show the effectiveness of linear damage detection algorithm in identifying the nonlinear breathing cracks using different combinations of HFCs and sensors.
Adaptation with disturbance attenuation in nonlinear control systems
Basar, T.
1997-12-31
We present an optimization-based adaptive controller design for nonlinear systems exhibiting parametric as well as functional uncertainty. The approach involves the formulation of an appropriate cost functional that places positive weight on deviations from the achievement of desired objectives (such as tracking of a reference trajectory while the system exhibits good transient performance) and negative weight on the energy of the uncertainty. This cost functional also translates into a disturbance attenuation inequality which quantifies the effect of the presence of uncertainty on the desired objective, which in turn yields an interpretation for the optimizing control as one that optimally attenuates the disturbance, viewed as the collection of unknown parameters and unknown signals entering the system dynamics. In addition to this disturbance attenuation property, the controllers obtained also feature adaptation in the sense that they help with identification of the unknown parameters, even though this has not been set as the primary goal of the design. In spite of this adaptation/identification role, the controllers obtained are not of certainty-equivalent type, which means that the identification and the control phases of the design are not decoupled.
Robust Control Design for Uncertain Nonlinear Dynamic Systems
NASA Technical Reports Server (NTRS)
Kenny, Sean P.; Crespo, Luis G.; Andrews, Lindsey; Giesy, Daniel P.
2012-01-01
Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.
NASA Technical Reports Server (NTRS)
Anderson, B. D. O.; Brockett, R. W.; Byrnes, C. I.; Ghosh, B. K.; Stevens, P. K.
1983-01-01
The extent to which feedback can alter the dynamic characteristics (e.g., instability, oscillations) of a control system, possibly operating in one or more modes (e.g., failure versus nonfailure of one or more components) is examined.
The SWAN/NPSOL code system for multivariable multiconstraint shield optimization
Watkins, E.F.; Greenspan, E.
1995-12-31
SWAN is a useful code for optimization of source-driven systems, i.e., systems for which the neutron and photon distribution is the solution of the inhomogeneous transport equation. Over the years, SWAN has been applied to the optimization of a variety of nuclear systems, such as minimizing the thickness of fusion reactor blankets and shields, the weight of space reactor shields, the cost for an ICF target chamber shield, and the background radiation for explosive detection systems and maximizing the beam quality for boron neutron capture therapy applications. However, SWAN`s optimization module can handle up to a single constraint and was inefficient in handling problems with many variables. The purpose of this work is to upgrade SWAN`s optimization capability.
Some Thoughts on Stability in Nonlinear Periodic Focusing Systems
DOE R&D Accomplishments Database
McMillan, E. M.
1967-09-05
A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.
Microcomputer Simulation of Nonlinear Systems: From Oscillations to Chaos.
ERIC Educational Resources Information Center
Raw, Cecil J. G.; Stacey, Larry M.
1989-01-01
Presents two short microcomputer programs which illustrate features of nonlinear dynamics, including steady states, periodic oscillations, period doubling, and chaos. Logistic maps are explained, inclusion in undergraduate chemistry and physics courses to teach nonlinear equations is discussed, and applications in social and biological sciences…
Nonlinear behavior of coupled magnetostrictive material systems analytical/experimental
NASA Astrophysics Data System (ADS)
Roberts, Mark M.; Mitrovic, Milan; Carman, Gregory P.
1995-05-01
In this paper, we present a nonlinear constitutive relation for magnetostrictive materials that includes coupling between temperature/preload and magnetic field strengths. The nonlinear constitutive relations are also integrated into a 1-dimensional nonlinear finite element model for studying structural components or composite materials containing magnetostrictive materials. The accuracy of the nonlinear constitutive relation is evaluated by comparing experimental results obtained on a Terfenol-D rod operating under both magnetic field and stress biases with theoretical values present in the literature. Results indicate that the model adequately predicts the nonlinear strain/field relations in specific regimes. Experimental tests, conducted on monolithic samples of different geometry, suggests that size effects may be important. A manufacturing process and preliminary experimental tests are also presented for a 1 - 3 magnetostrictive composite sample.
AESOP: A computer-aided design program for linear multivariable control systems
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L. C.
1982-01-01
An interactive computer program (AESOP) which solves quadratic optimal control and is discussed. The program can also be used to perform system analysis calculations such as transient and frequency responses, controllability, observability, etc., in support of the control and filter design computations.
ERIC Educational Resources Information Center
Mather, Richard
2015-01-01
This paper explores the application of canonical gradient analysis to evaluate and visualize student performance and acceptance of a learning system platform. The subject of evaluation is a first year BSc module for computer programming. This uses "Ceebot," an animated and immersive game-like development environment. Multivariate…
Indicators are commonly used for evaluating relative sustainability for competing products and processes. When a set of indicators is chosen for a particular system of study, it is important to ensure that they are variable independently of each other. Often the number of indicat...
Mustonen, Satu M; Tissari, Soile; Huikko, Laura; Kolehmainen, Mikko; Lehtola, Markku J; Hirvonen, Arja
2008-05-01
The distribution of drinking water generates soft deposits and biofilms in the pipelines of distribution systems. Disturbances in water distribution can detach these deposits and biofilms and thus deteriorate the water quality. We studied the effects of simulated pressure shocks on the water quality with online analysers. The study was conducted with copper and composite plastic pipelines in a pilot distribution system. The online data gathered during the study was evaluated with Self-Organising Map (SOM) and Sammon's mapping, which are useful methods in exploring large amounts of multivariate data. The objective was to test the usefulness of these methods in pinpointing the abnormal water quality changes in the online data. The pressure shocks increased temporarily the number of particles, turbidity and electrical conductivity. SOM and Sammon's mapping were able to separate these situations from the normal data and thus make those visible. Therefore these methods make it possible to detect abrupt changes in water quality and thus to react rapidly to any disturbances in the system. These methods are useful in developing alert systems and predictive applications connected to online monitoring.
Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Marston, J. B.; Hastings, M. B.
2005-03-01
The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.
Nonlinear phase field model for electrodeposition in electrochemical systems
Liang, Linyun; Chen, Long-Qing
2014-12-29
A nonlinear phase-field model has been developed for describing the electrodeposition process in electrochemical systems that are highly out of equilibrium. Main thermodynamic driving forces for the electrode-electrolyte interface (EEI) evolution are limited to local variations of overpotential and ion concentration. Application of the model to Li-ion batteries describes the electrode interface motion and morphology change caused by charge mass transfer in the electrolyte, an electrochemical reaction at the EEI and cation deposition on the electrode surface during the charging operation. The Li electrodeposition rate follows the classical Butler-Volmer kinetics with exponentially and linearly depending on local overpotential and cation concentration at the electrode surface, respectively. Simulation results show that the Li deposit forms a fiber-like shape and grows parallel to the electric field direction. The longer and thicker deposits are observed both for higher current density and larger rate constant where the surface reaction rate is expected to be high. The proposed diffuse interface model well captures the metal electrodeposition phenomena in plenty of non-equilibrium electrochemical systems.
On classical mechanical systems with non-linear constraints
NASA Astrophysics Data System (ADS)
Terra, Gláucio; Kobayashi, Marcelo H.
2004-03-01
In the present work, we analyze classical mechanical systems with non-linear constraints in the velocities. We prove that the d'Alembert-Chetaev trajectories of a constrained mechanical system satisfy both Gauss' principle of least constraint and Hölder's principle. In the case of a free mechanics, they also satisfy Hertz's principle of least curvature if the constraint manifold is a cone. We show that the Gibbs-Maggi-Appell (GMA) vector field (i.e. the second-order vector field which defines the d'Alembert-Chetaev trajectories) conserves energy for any potential energy if, and only if, the constraint is homogeneous (i.e. if the Liouville vector field is tangent to the constraint manifold). We introduce the Jacobi-Carathéodory metric tensor and prove Jacobi-Carathéodory's theorem assuming that the constraint manifold is a cone. Finally, we present a version of Liouville's theorem on the conservation of volume for the flow of the GMA vector field.
Controlling Spatiotemporal Chaos in Active Dissipative-Dispersive Nonlinear Systems
NASA Astrophysics Data System (ADS)
Gomes, Susana; Pradas, Marc; Kalliadasis, Serafim; Papageorgiou, Demetrios; Pavliotis, Grigorios
2015-11-01
We present a novel generic methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. The methodology is exemplified with the generalized Kuramoto-Sivashinsky equation, the simplest possible prototype that retains that fundamental elements of any nonlinear process involving wave evolution. The equation is applicable on a wide variety of systems including falling liquid films and plasma waves with dispersion due to finite banana width. We show that applying the appropriate choice of time-dependent feedback controls via blowing and suction, we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, travelling waves and spatiotemporal chaos, but also use the controls obtained to stabilize the solutions to more general long wave models. We acknowledge financial support from Imperial College through a Roth PhD studentship, Engineering and Physical Sciences Research Council of the UK through Grants No. EP/H034587, EP/J009636, EP/K041134, EP/L020564 and EP/L024926 and European Research Council via Advanced Grant No. 247031.
A closed-loop identification protocol for nonlinear dynamical systems.
Feng, Xiao-jiang; Rabitz, Herschel; Turinici, Gabriel; Le Bris, Claude
2006-06-29
A previous work introduced an optimal identification (OI) technique for reliably extracting model parameters of biochemical reaction systems from tailored laboratory experiments. The notion of optimality enters through seeking an external control in the laboratory producing data that leads to minimum uncertainties in the identified parameter distributions. A number of algorithmic and operational improvements are introduced in this paper to OI, aiming to build a more practical and efficient closed-loop identification protocol/procedure (CLIP) for nonlinear dynamical systems. The improvements in CLIP include (a) inversion cost function modification to preferably search for the upper and lower boundaries of the parameter distributions consistent with the observed data, (b) dynamic search range updating of the unknown parameters to better exploit the information from the prior iterative experiments, (c) replacing the control genetic algorithm by the simplex method to enable better balance between operational cost and inversion quality, and (d) utilizing virtual sensitivity optimization techniques to further reduce the laboratory costs. The workings of CLIP utilizing these new algorithms are illustrated in indentifying a simulated tRNA proofreading model, and the results demonstrate enhanced performance of CLIP in terms of algorithmic reliability and efficiency. PMID:16789759
Identification of limit cycles in multi-nonlinearity, multiple path systems
NASA Technical Reports Server (NTRS)
Mitchell, J. R.; Barron, O. L.
1979-01-01
A method of analysis which identifies limit cycles in autonomous systems with multiple nonlinearities and multiple forward paths is presented. The FORTRAN code for implementing the Harmonic Balance Algorithm is reported. The FORTRAN code is used to identify limit cycles in multiple path and nonlinearity systems while retaining the effects of several harmonic components.
On the estimation of the attainability set of nonlinear control systems
Ekimov, A.V.; Balykina, Yu.E.; Svirkin, M.V.
2015-03-10
Analysis of the attainability set and construction of its estimates greatly facilitates the solution of a variety of problems in mathematical control theory. In the paper, the problem of boundedness of the integral funnel of nonlinear controlled system is considered. Some estimates of the attainability sets for a nonlinear controlled system are presented. Theorems on the boundedness of considered integral funnels are proved.
Applications to aeronautics of the theory of transformations of nonlinear systems
NASA Technical Reports Server (NTRS)
Meyer, G.; Su, R.; Hunt, L. R.
1982-01-01
The development of the transformation theory is discussed. Results and applications concerning the use of this design technique for automatic flight control of aircraft are presented. The theory examines the transformation of nonlinear systems to linear systems. The tracking of linear models by nonlinear plants is discussed. Results of manned simulation are also presented.
Global adaptive output feedback control for a class of nonlinear time-delay systems.
Zhai, Jun-yong; Zha, Wen-ting
2014-01-01
This paper addresses the problem of global output feedback control for a class of nonlinear time-delay systems. The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate. With a change of coordinates, a linear-like controller is constructed, which avoids the repeated derivatives of the nonlinearities depending on the observer states and the dynamic gain in backstepping approach and therefore, simplifies the design procedure. Using the idea of universal control, we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the nonlinear time-delay systems.
Multivariable closed loop control analysis and synthesis for complex flight systems
NASA Technical Reports Server (NTRS)
Schmidt, D. K.
1981-01-01
A flight control system analysis and synthesis method is presented that is intended to be especially suitable for application to vehicles exhibiting complex dynamic characteristics. For such vehicles quantitative handling qualities specifications are not usually available. Howver, handling qualities objectives are specifically introduced in this method via the hypothesis of correlation between pilot ratings and the objective function of an optimal control model of the human pilot. Further, since augmentation and pilot operate in parallel, simultaneous determination of the augmentation and pilot model gains is required. Desirable augmented dynamics are obtained for a variety of complex systems and the method is experimentally verified in the case of simple pilot damper gain selection for optimum pitch tracking performance.
?-optimisation and fixed poles of multivariable sampled-data systems with delay
NASA Astrophysics Data System (ADS)
Lampe, B. P.; Rosenwasser, E. N.
2015-04-01
Using the parametric transfer matrix (PTM) of sampled-data (SD) systems with pure time delay, the paper generalises the polynomial method for solving the ?-optimisation problem to the multiple-input multiple-output (MIMO) case. The generalisation is not only a formal act, because in the MIMO case, the PTM method leads to a minimisation problem for a singular quadratic functional, which is connected with honest technical difficulties. Therefore, the paper introduces a special transformation to overcome these difficulties. Some general properties of ?-optimal SD systems with delay are investigated. Notice that there always exists a subset of so-called fixed poles, which is responsible for a principal performance restriction of the ?-optimal control loop.
Multi-variable mathematical models for the air-cathode microbial fuel cell system
NASA Astrophysics Data System (ADS)
Ou, Shiqi; Kashima, Hiroyuki; Aaron, Douglas S.; Regan, John M.; Mench, Matthew M.
2016-05-01
This research adopted the version control system into the model construction for the single chamber air-cathode microbial fuel cell (MFC) system, to understand the interrelation of biological, chemical, and electrochemical reactions. The anodic steady state model was used to consider the chemical species diffusion and electric migration influence to the MFC performance. In the cathodic steady state model, the mass transport and reactions in a multi-layer, abiotic cathode and multi-bacteria cathode biofilm were simulated. Transport of hydroxide was assumed for cathodic pH change. This assumption is an alternative to the typical notion of proton consumption during oxygen reduction to explain elevated cathode pH. The cathodic steady state model provided the power density and polarization curve performance results that can be compared to an experimental MFC system. Another aspect considered was the relative contributions of platinum catalyst and microbes on the cathode to the oxygen reduction reaction (ORR). Simulation results showed that the biocatalyst in a cathode that includes a Pt/C catalyst likely plays a minor role in ORR, contributing up to 8% of the total power calculated by the models.
Multi-variable mathematical models for the air-cathode microbial fuel cell system
Ou, Shiqi; Kashima, Hiroyuki; Aaron, Douglas S.; Regan, John M.; Mench, Matthew M.
2016-03-10
This research adopted the version control system into the model construction for the single chamber air-cathode microbial fuel cell (MFC) system, to understand the interrelation of biological, chemical, and electrochemical reactions. The anodic steady state model was used to consider the chemical species diffusion and electric migration influence to the MFC performance. In the cathodic steady state model, the mass transport and reactions in a multi-layer, abiotic cathode and multi-bacteria cathode biofilm were simulated. Transport of hydroxide was assumed for cathodic pH change. This assumption is an alternative to the typical notion of proton consumption during oxygen reduction to explainmore » elevated cathode pH. The cathodic steady state model provided the power density and polarization curve performance results that can be compared to an experimental MFC system. Another aspect we considered was the relative contributions of platinum catalyst and microbes on the cathode to the oxygen reduction reaction (ORR). We found simulation results showed that the biocatalyst in a cathode that includes a Pt/C catalyst likely plays a minor role in ORR, contributing up to 8% of the total power calculated by the models.« less
Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems
NASA Technical Reports Server (NTRS)
Murthy, V. R.; Shultz, Louis A.
1994-01-01
The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.
Advanced data assimilation in strongly nonlinear dynamical systems
NASA Technical Reports Server (NTRS)
Miller, Robert N.; Ghil, Michael; Gauthiez, Francois
1994-01-01
Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.
Develop Advanced Nonlinear Signal Analysis Topographical Mapping System
NASA Technical Reports Server (NTRS)
Jong, Jen-Yi
1997-01-01
During the development of the SSME, a hierarchy of advanced signal analysis techniques for mechanical signature analysis has been developed by NASA and AI Signal Research Inc. (ASRI) to improve the safety and reliability for Space Shuttle operations. These techniques can process and identify intelligent information hidden in a measured signal which is often unidentifiable using conventional signal analysis methods. Currently, due to the highly interactive processing requirements and the volume of dynamic data involved, detailed diagnostic analysis is being performed manually which requires immense man-hours with extensive human interface. To overcome this manual process, NASA implemented this program to develop an Advanced nonlinear signal Analysis Topographical Mapping System (ATMS) to provide automatic/unsupervised engine diagnostic capabilities. The ATMS will utilize a rule-based Clips expert system to supervise a hierarchy of diagnostic signature analysis techniques in the Advanced Signal Analysis Library (ASAL). ASAL will perform automatic signal processing, archiving, and anomaly detection/identification tasks in order to provide an intelligent and fully automated engine diagnostic capability. The ATMS has been successfully developed under this contract. In summary, the program objectives to design, develop, test and conduct performance evaluation for an automated engine diagnostic system have been successfully achieved. Software implementation of the entire ATMS system on MSFC's OISPS computer has been completed. The significance of the ATMS developed under this program is attributed to the fully automated coherence analysis capability for anomaly detection and identification which can greatly enhance the power and reliability of engine diagnostic evaluation. The results have demonstrated that ATMS can significantly save time and man-hours in performing engine test/flight data analysis and performance evaluation of large volumes of dynamic test data.
Model predictive control for a class of systems with isolated nonlinearity.
Tao, Jili; Zhu, Yong; Fan, Qinru
2014-07-01
The paper is concerned with an overall convergent nonlinear model predictive control design for a kind of nonlinear mechatronic drive systems. The proposed nonlinear model predictive control results in the improvement of regulatory capacity for reference tracking and load disturbance rejection. The design of the nonlinear model predictive controller consists of two steps: the first step is to design a linear model predictive controller based on the linear part of the system at each sample instant, then an overall convergent nonlinear part is added to the linear model predictive controller to combine a nonlinear controller using error driven. The structure of the proposed controller is similar to that of classical PI optimal regulator but it also bears a set-point feed forward control loop, thus tracking ability and disturbance rejection are improved. The proposed method is compared with the results from recent literature, where control performance under both model match and mismatch cases are enlightened. PMID:24755053
Multivariate analysis and visualization of soil quality data for no-till systems.
Villamil, M B; Miguez, F E; Bollero, G A
2008-01-01
To evidence the multidimensionality of the soil quality concept, we propose the use of data visualization as a tool for exploratory data analyses, model building, and diagnostics. Our objective was to establish the best edaphic indicators for assessing soil quality in four no-till systems with regard to functioning as a medium for crop production and nutrient cycling across two Illinois locations. The compared situations were no-till corn-soybean rotations including either winter fallowing (C/S) or cover crops of rye (Secale cereale; C-R/S-R), hairy vetch (Vicia villosa; C-R/S-V), or their mixture (C-R/S-VR). The dataset included the variables bulk density (BD), penetration resistance (PR), water aggregate stability (WAS), soil reaction (pH), and the contents of soil organic matter (SOM), total nitrogen (TN), soil nitrates (NO(3)-N), and available phosphorus (P). Interactive data visualization along with canonical discriminant analysis (CDA) allowed us to show that WAS, BD, and the contents of P, TN, and SOM have the greatest potential as soil quality indicators in no-till systems in Illinois. It was more difficult to discriminate among WCC rotations than to separate these from C/S, considerably inflating the error rate associated with CDA. We predict that observations of no-till C/S will be classified correctly 51% of the time, while observations of no-till WCC rotations will be classified correctly 74% of the time. High error rates in CDA underscore the complexity of no-till systems and the need in this area for more long-term studies with larger datasets to increase accuracy to acceptable levels.
Bomb/no bomb: From multivariate analysis to artificial neural systems
NASA Astrophysics Data System (ADS)
Shea, Patrick; Liu, Felix; Yedidia, Barak
1992-05-01
Systems for the detection of explosives hidden in checked airline baggage have been under development at the Science Applications International Corporation (SAIC) for the FAA since 1985. In May of 1987, the first prototype was fielded for testing at San Francisco International Airport. In 1989, the first production unit was field at JFK Airport in New York. Since than, over 550,000 bags have been screened by SAIC units around the world. The system uses thermal neutron activation (TNA) to detect the presence of explosives. In this technique a suitcase on a conveyor belt moves past a source and an array of detectors. Neutrons from the source easily penetrate the luggage, and are absorbed by all of the materials present. Different elements will emit different energy gamma rays after absorbing these neutrons (much like fluorescence). These gamma rays are of a high enough energy that they easily penetrate the luggage, and are detected by a detector array which surrounds the cavity enclosing the suitcase and conveyor belt. The detectors record the number of gamma rays observed at each energy. The number of gamma rays of a characteristic energy which are observed depends on the amount of the element present, its location, the number of neutrons present, and the probability that the element will capture a thermal neutron and emit the gamma ray. Since this probability is a known constant for any particular element, and the number of neutrons present and the number of characteristic gamma rays are measured, the amount of each element and its location can, in theory, be determined from the array of signals. Commercial and military explosives, such as are used by terrorists, have several characteristics which distinguish them from most objects in luggage. On of these characteristics is a high density of nitrogen. A description of the decision algorithms is presented, and the artificial neural system (ANS) is discussed. On-line experience and decision surfaces are also covered.
Nonlinear System Identification for Aeroelastic Systems with Application to Experimental Data
NASA Technical Reports Server (NTRS)
Kukreja, Sunil L.
2008-01-01
Representation and identification of a nonlinear aeroelastic pitch-plunge system as a model of the Nonlinear AutoRegressive, Moving Average eXogenous (NARMAX) class is considered. A nonlinear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (1) the outputs of the NARMAX model closely match those generated using continuous-time methods, and (2) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.
Tesfalidet, Solomon; Geladi, Paul; Shimizu, Kenichi; Lindholm-Sethson, Britta
2016-03-31
Methotrexate (MTX), a common pharmaceutical drug in cancer therapy and treatment of rheumatic diseases, is known to cause severe adverse side effects at high dose. As the side effect may be life threatening, there is an urgent need for a continuous, bed-side monitoring of the nominal MTX serum level in a patient while the chemical is being administered. This article describes a detection of MTX using a flow system that consists two modified gold electrodes. Interaction of MTX with the antibodies fixed on the electrode surface is detected by electrochemical impedance spectroscopy and evaluated using singular value decomposition (SVD). The key finding of this work is that the change in the electrode capacitance is found to be quantitative with respect to the concentration of MTX. Moreover a calibration curve constructed using the principal component regression method has a linear range of six orders of magnitude and a detection limit of 1.65 × 10(-10) M.
A modal capacity method for nonlinear dynamic analysis on transputer systems
Nordhues, H.W.; Woerner, J.D.
1995-12-31
A new method to calculate the response of nonlinear behaving systems is described. The two fundamentals of the modal capacity method are the principle of a modal capacity method are the principle of a modal reduction on the one hand and the capacity design method on the other hand. The nonlinear behavior of systems can be expressed by nonlinear modes in combination with a new superposition method. The procedure can be used either for the design of systems [Nor95] or to derive existing systems similar to the ultimate load method [WSK91]. Because of the modal reduction of the modal capacity method transputer systems can be used in a very efficient way.
Intraband discrete breathers in disordered nonlinear systems. II. Localization
NASA Astrophysics Data System (ADS)
Kopidakis, G.; Aubry, S.
2000-05-01
We find spatially localized, time-periodic solutions (discrete breathers or DBs) in disordered nonlinear systems with frequency inside the linear phonon spectrum under conditions that strictly prohibit their existence in their periodic counterparts. For that purpose, we develop a new in situ method for the accurate calculation of these solutions which does not make use of any continuation from an anticontinuous limit. Using this method, we demonstrate that intraband localized modes (intraband discrete breathers or IDBs) at a given site with frequencies inside the discrete linear spectrum do exist, provided these frequencies do not belong to forbidden resonance gaps. Since there is a dense set of resonant frequencies, we illustrate numerically, in agreement with a theorem by Albanese and Fröhlich, that the localized DBs exist provided that their frequencies belong to fat Cantor sets (i.e., with finite measure). Such a set contains as accumulation points the linear frequency of the normal mode at the occupied site. We check that many of these solutions are linearly stable and conjecture that their frequency belongs to another smaller fat Cantor set. Our numerical methods provide a much wider set of exact solutions which are multisite breathers and suggest conjectures extending the existing theorems. The physical implications of the existence of IDBs and possible applications for glasses and the persistent spectral hole burning are discussed.
Nonlinearity management in fiber transmission systems with hybrid amplification
NASA Astrophysics Data System (ADS)
Ania-Castañón, J. D.; Nasieva, I. O.; Kurukitkoson, N.; Turitsyn, S. K.; Borsier, C.; Pincemin, E.
2004-04-01
Nonlinearity management in transmission lines with periodic dispersion compensation and hybrid Raman-Erbium doped fiber amplification is studied both analytically and numerically. Different transmission/compensating fiber pairs are considered, with particular focus on the SMF/DCF case.
Some Thoughts on Stability in Nonlinear Periodic Focusing Systems [Addendum
DOE R&D Accomplishments Database
McMillan, Edwin M.
1968-03-29
Addendum to September 5, 1967 report with the same title and with the abstract: A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.
Tsai, Jason S-H; Hsu, Wen-Teng; Lin, Long-Guei; Guo, Shu-Mei; Tann, Joseph W
2014-01-01
A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input-output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection.
Grönlund, J U; Jalonen, J; Korhonen, I; Rolfe, P; Välimäki, I A
1995-05-01
We studied the pulsatile component of cerebral circulation with transcephalic electrical impedance (delta Z) in six preterm newborns, three of whom had severe cerebral bleeding, peri-intraventricular haemorrhage (PIVH). The transcephalic electrical impedance delta Z signal, ECG, arterial blood pressure, (aBP) and respirogram were recorded on analogue magnetic tape for 30 min. Artefact-free stationary segments (lasting for 2 min) of the four signals were digitised. A digital multivariate autoregressive (MAR) model was used to study frequency-specific variability in the signals and to quantify interrelations between the variabilities of delta Z, HR, aBP and respiratory signals. MAR modelling describes a system where all the signals simultaneously explain each other. The inherent variability of delta Z was lower and the influences of respiration and aBP on delta Z significantly greater in infants with severe PIVH than in controls. These changes were observed at high frequencies corresponding to respiration and heart rate. This may be interpreted as a marker of pressure passivism in the cerebral circulation following PIVH. We conclude that in preterm babies the application of MAR modelling, together with transcephalic impedance, may be a new, helpful and quantitative method for the study of simultaneous interrelations between variables of cerebral and systemic circulations and respiration.
NASA Technical Reports Server (NTRS)
Behbehani, K.
1980-01-01
A new sensor/actuator failure analysis technique for turbofan jet engines was developed. Three phases of failure analysis, namely detection, isolation, and accommodation are considered. Failure detection and isolation techniques are developed by utilizing the concept of Generalized Likelihood Ratio (GLR) tests. These techniques are applicable to both time varying and time invariant systems. Three GLR detectors are developed for: (1) hard-over sensor failure; (2) hard-over actuator failure; and (3) brief disturbances in the actuators. The probability distribution of the GLR detectors and the detectability of sensor/actuator failures are established. Failure type is determined by the maximum of the GLR detectors. Failure accommodation is accomplished by extending the Multivariable Nyquest Array (MNA) control design techniques to nonsquare system designs. The performance and effectiveness of the failure analysis technique are studied by applying the technique to a turbofan jet engine, namely the Quiet Clean Short Haul Experimental Engine (QCSEE). Single and multiple sensor/actuator failures in the QCSEE are simulated and analyzed and the effects of model degradation are studied.
Lin, Tai-Chia; Belić, Milivoj R.; Petrović, Milan S.; Chen, Goong
2014-01-15
Counterpropagating optical beams in nonlinear media give rise to a host of interesting nonlinear phenomena such as the formation of spatial solitons, spatiotemporal instabilities, self-focusing and self-trapping, etc. Here we study the existence of ground state (the energy minimizer under the L{sup 2}-normalization condition) in two-dimensional (2D) nonlinear Schrödinger (NLS) systems with saturable nonlinearity, which describes paraxial counterpropagating beams in isotropic local media. The nonlinear coefficient of saturable nonlinearity exhibits a threshold which is crucial in determining whether the ground state exists. The threshold can be estimated by the Gagliardo-Nirenberg inequality and the ground state existence can be proved by the energy method, but not the concentration-compactness method. Our results also show the essential difference between 2D NLS equations with cubic and saturable nonlinearities.
Stability analysis and limit cycle in fractional system with Brusselator nonlinearities
NASA Astrophysics Data System (ADS)
Gafiychuk, V.; Datsko, B.
2008-07-01
The investigation of limit cycles in the fractional dynamical systems with Brusselator nonlinearities is considered. We present analysis of the stability domains as well as possible solutions realizing at different system parameters.
A method for zooming of nonlinear models of biochemical systems
2011-01-01
Background Models of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model. Results In this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in baker's yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved. Conclusions We introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to
A Nonlinear Lumped Model for Ultrasound Systems Using CMUT Arrays
Satir, Sarp; Degertekin, F. Levent
2015-01-01
We present a nonlinear lumped model that predicts the electrical input-output behavior of an ultrasonic system using CMUTs with arbitrary array/membrane/electrode geometry in different transmit-receive configurations and drive signals. The receive-only operation, where the electrical output signal of the CMUT array in response to incident pressure field is calculated, is included by modifying the boundary element based vibroacoustic formulation for a CMUT array in rigid baffle. Along with the accurate large signal transmit model, this formulation covers pitch-catch and pulse-echo operation when transmit and receive signals can be separated in time. In cases when this separation is not valid, such as CMUTs used in continuous wave transmit-receive mode, pulse-echo mode with a nearby hard or soft wall or in a bounded space such as in a microfluidic channel, an efficient formulation based on the method of images is used. Some of these particular applications and the overall modeling approach have been validated through comparison with finite element analysis on specific examples including CMUTs with multiple electrodes. To further demonstrate the capability of the model for imaging applications, the two-way response of a partial dual-ring intravascular ultrasound array is simulated using a parallel computing cluster, where the output currents of individual array elements are calculated for given input pulse and compared with experimental results. With its versatility, the presented model can be a useful tool for rapid iterative CMUT-based system design and simulation for a broad range of ultrasonic applications. PMID:26470049
Liu, Yan-Jun; Gao, Ying; Tong, Shaocheng; Chen, C L Philip
2016-01-01
In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.
Liu, Yan-Jun; Gao, Ying; Tong, Shaocheng; Chen, C L Philip
2016-01-01
In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example. PMID:26353383
Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials
Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane
2014-01-01
In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. PMID:25485293
Numerical solutions of the nonlinear fractional-order brusselator system by Bernstein polynomials.
Khan, Hasib; Jafari, Hossein; Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane
2014-01-01
In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. PMID:25485293
NASA Technical Reports Server (NTRS)
Kelkar, Atul G.; Joshi, Suresh M.
1994-01-01
Global asymptotic stability of a class of nonlinear multibody flexible space-stnuctures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore for the second case the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems including flexible space-structures with articulated flexible appendages.
NASA Technical Reports Server (NTRS)
Kelkar, Atul G.; Joshi, Suresh M.
1994-01-01
Global asymptotic stability of a class of nonlinear multibody flexible space structures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore, for the second case, the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems, including flexible space structures with articulated flexible appendages.
A nonlinear screen as an element for sound absorption and frequency conversion systems
NASA Astrophysics Data System (ADS)
Rudenko, O. V.
2016-01-01
The paper discusses a model for a screen with dissipative and nonlinear elastic properties that can be used in acoustic sound absorption and frequency conversion systems. Calculation and estimation schemes are explained that are necessary for understanding the functional capabilities of the device. Examples of the nonlinear elements in the screen and promising applications are described.
On asymptotic completeness of scattering in the nonlinear Lamb system, II
NASA Astrophysics Data System (ADS)
Komech, A. I.; Merzon, A. E.
2013-01-01
We establish the asymptotic completeness in the nonlinear Lamb system for hyperbolic stationary states. For the proof we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ordinary differential equation) converging to a hyperbolic stationary point using the inverse function theorem in a Banach space. We give counterexamples which show nonexistence of such trajectories for nonhyperbolic stationary points.
Nonlinear System Of Equations For Multicomponent Analysis Of Artificial Food Coloring
NASA Astrophysics Data System (ADS)
Santosa, I. E.; Budiasih, L. K.
2010-12-01
In multicomponent analysis of artificial food coloring (AFC), nonlinear relation of the absorbance and the concentration forms a nonlinear system of equations. The Newton's method based algorithm has been used to calculate individual AFC concentration in the mixture of two AFCs. The absorbance was measured using a spectrophotometer at two different wavelengths.
Is DNA a nonlinear dynamical system where solitary conformational waves are possible?
Yakushevich, L V
2001-09-01
DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The history of the approach, the main results, and arguments in favour and against are presented. Perspectives are discussed pertaining to studies of DNA's nonlinear properties. PMID:11568475
A method for high order linear system reduction and nonlinear system simplification
NASA Technical Reports Server (NTRS)
Desrochers, A. A.; Al-Jaar, R. Y.
1985-01-01
Least-squares-type algorithms for reducing the order of linear systems in the frequency domain and simplifying nonlinear systems in time domain are developed and demonstrated. The possible model structures are represented as nodes in a tree, and costs along the branches are assigned using the repeated-Gram-Schmidt orthogonalization procedure of Desrochers and Saridis (1980), permitting identification of the optimal n-term model by searching the tree to depth n, with no need for parameter identification. The efficiency and flexibility of the algorithms is shown in applications to the eighth-order linear system studied by Hsia (1972), a three-state eight-nonlinear-term aircraft-dynamics problem, and the related linear-controller problem (Garrard and Jordan, 1977).
Nonlinear systems identification and control via dynamic multitime scales neural networks.
Fu, Zhi-Jun; Xie, Wen-Fang; Han, Xuan; Luo, Wei-Dong
2013-11-01
This paper deals with the adaptive nonlinear identification and trajectory tracking via dynamic multilayer neural network (NN) with different timescales. Two NN identifiers are proposed for nonlinear systems identification via dynamic NNs with different timescales including both fast and slow phenomenon. The first NN identifier uses the output signals from the actual system for the system identification. In the second NN identifier, all the output signals from nonlinear system are replaced with the state variables of the NNs. The online identification algorithms for both NN identifier parameters are proposed using Lyapunov function and singularly perturbed techniques. With the identified NN models, two indirect adaptive NN controllers for the nonlinear systems containing slow and fast dynamic processes are developed. For both developed adaptive NN controllers, the trajectory errors are analyzed and the stability of the systems is proved. Simulation results show that the controller based on the second identifier has better performance than that of the first identifier.
Causality networks from multivariate time series and application to epilepsy.
Siggiridou, Elsa; Koutlis, Christos; Tsimpiris, Alkiviadis; Kimiskidis, Vasilios K; Kugiumtzis, Dimitris
2015-08-01
Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks from multivariate time series are assessed. For this, realizations on high dimensional coupled dynamical systems are considered and the performance of the Granger causality measures is evaluated, seeking for the measures that form networks closest to the true network of the dynamical system. In particular, the comparison focuses on Granger causality measures that reduce the state space dimension when many variables are observed. Further, the linear and nonlinear Granger causality measures of dimension reduction are compared to a standard Granger causality measure on electroencephalographic (EEG) recordings containing episodes of epileptiform discharges.
The peak response distributions of structure-DVA systems with nonlinear damping
NASA Astrophysics Data System (ADS)
Love, J. S.; Tait, M. J.
2015-07-01
Dynamic vibration absorbers (DVAs) with nonlinear damping are often modelled using a power-law equivalent viscous damping relationship. There is currently not a method available to predict the peak response of this type of nonlinear DVA without resorting to computationally expensive nonlinear simulations. Since the peak response of the DVA is required during the design process, it is advantageous to have a simplified method to estimate the peak response. In this study, statistical linearization is employed to represent the nonlinear damping as amplitude-dependent viscous damping and predict the rms response of the structure-DVA system. Subsequently, statistical nonlinearization is used to describe the probability density function of the DVA response amplitude. A probability density function is developed, which enables the peak response expected during an interval of time (e.g. 1-h) to be estimated from the rms response of the structure-DVA system. Higher power-law damping exponents are shown to result in smaller peak factors. Results of nonlinear simulations reveal that the model can estimate the peak structural and DVA responses with acceptable accuracy. A plot is developed to show the peak factors for nonlinear DVAs as a function of the number of system cycles for several power-law damping exponents. This plot can be used to estimate the peak response of a nonlinear DVA as a function of its rms response.
Ouari, Kamel; Rekioua, Toufik; Ouhrouche, Mohand
2014-01-01
In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller.
Modeling a multivariable reactor and on-line model predictive control.
Yu, D W; Yu, D L
2005-10-01
A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown.
Altet, J; Mateo, D; Perpiñà, X; Grauby, S; Dilhaire, S; Jordà, X
2011-09-01
This work presents an alternative characterization strategy to quantify the nonlinear behavior of temperature sensing systems. The proposed approach relies on measuring the temperature under thermal sinusoidal steady state and observing the intermodulation products that are generated within the sensing system itself due to its nonlinear temperature-output voltage characteristics. From such intermodulation products, second-order interception points can be calculated as a figure of merit of the measuring system nonlinear behavior. In this scenario, the present work first shows a theoretical analysis. Second, it reports the experimental results obtained with three thermal sensing techniques used in integrated circuits.
Discrete-time neural inverse optimal control for nonlinear systems via passivation.
Ornelas-Tellez, Fernando; Sanchez, Edgar N; Loukianov, Alexander G
2012-08-01
This paper presents a discrete-time inverse optimal neural controller, which is constituted by combination of two techniques: 1) inverse optimal control to avoid solving the Hamilton-Jacobi-Bellman equation associated with nonlinear system optimal control and 2) on-line neural identification, using a recurrent neural network trained with an extended Kalman filter, in order to build a model of the assumed unknown nonlinear system. The inverse optimal controller is based on passivity theory. The applicability of the proposed approach is illustrated via simulations for an unstable nonlinear system and a planar robot. PMID:24807528
Analysis of start-up transient for a powertrain system with a nonlinear clutch damper
NASA Astrophysics Data System (ADS)
Li, Laihang; Singh, Rajendra
2015-10-01
The transient vibration phenomenon in a vehicle powertrain system during the start-up (or shut-down) process is studied with a focus on the nonlinear characteristics of a multi-staged clutch damper. First, a four-degree-of-freedom torsional model with multiple discontinuous nonlinearities under flywheel motion input is developed, and the powertrain transient event is validated with a vehicle start-up experiment. Second, the role of the nonlinear torsional path on the transient event is investigated in the time and time-frequency domains; interactions between the clutch damper and the transmission transients are estimated by using two metrics. Third, the harmonic balance method is applied to examine the nonlinear characteristics of clutch damper during a slowly varying non-stationary process in a simplified and validated single-degree-of-freedom powertrain system model. Finally, analytical formulas are successfully developed and verified to approximate the nonlinear amplification level for a rapidly varying process.
Control synthesis of continuous-time T-S fuzzy systems with local nonlinear models.
Dong, Jiuxiang; Wang, Youyi; Yang, Guang-Hong
2009-10-01
This paper is concerned with the problem of designing fuzzy controllers for a class of nonlinear dynamic systems. The considered nonlinear systems are described by T-S fuzzy models with nonlinear local models, and the fuzzy models have fewer fuzzy rules than conventional T-S fuzzy models with local linear models. A new fuzzy control scheme with local nonlinear feedbacks is proposed, and the corresponding control synthesis conditions are given in terms of solutions to a set of linear matrix inequalities (LMIs). In contrast to the existing methods for fuzzy control synthesis, the new proposed control design method is based on fewer fuzzy rules and less computational burden. Moreover, the local nonlinear feedback laws in the new fuzzy controllers are also helpful in achieving good control effects. Numerical examples are given to illustrate the effectiveness of the proposed method.
Non-linear substructure approach for dynamic analysis of rigid-flexible multibody systems
NASA Astrophysics Data System (ADS)
Liu, A. Q.; Liew, K. M.
1994-04-01
This paper presents a substructure synthesis method (SSM) for nonlinear analysis of multibody systems. The detailed derivation of the equation of motion which takes into account the geometric nonlinear effects of large rotation undergoing small strain elastic deformation is presented. Using the substructure synthesis approach, the equation of motion is condensed through the boundary conditions at the interface between the flexible and rigid substructures. As a result, equations of motion for multi-flexible-body systems including the geometric non-linear effects of large rotation are derived. To demonstrate the applicability and accuracy of the proposed approach, an example of a two-link manipulator was chosen for this presentation. The results using the linear and nonlinear models are presented to highlight the effects of geometric nonlinearities.
Correlation techniques to determine model form in robust nonlinear system realization/identification
NASA Technical Reports Server (NTRS)
Stry, Greselda I.; Mook, D. Joseph
1991-01-01
The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.
Noise-induced transitions and resonant effects in nonlinear systems
NASA Astrophysics Data System (ADS)
Zaikin, Alexei
2003-02-01
Our every-day experience is connected with different acoustical noise or music. Usually noise plays the role of nuisance in any communication and destroys any order in a system. Similar optical effects are known: strong snowing or raining decreases quality of a vision. In contrast to these situations noisy stimuli can also play a positive constructive role, e.g. a driver can be more concentrated in a presence of quiet music. Transmission processes in neural systems are of especial interest from this point of view: excitation or information will be transmitted only in the case if a signal overcomes a threshold. Dr. Alexei Zaikin from the Potsdam University studies noise-induced phenomena in nonlinear systems from a theoretical point of view. Especially he is interested in the processes, in which noise influences the behaviour of a system twice: if the intensity of noise is over a threshold, it induces some regular structure that will be synchronized with the behaviour of neighbour elements. To obtain such a system with a threshold one needs one more noise source. Dr. Zaikin has analyzed further examples of such doubly stochastic effects and developed a concept of these new phenomena. These theoretical findings are important, because such processes can play a crucial role in neurophysics, technical communication devices and living sciences. Unsere alltägliche Erfahrung ist mit verschiedenen akustischen Einfluessen wie Lärm, aber auch Musik verbunden. Jeder weiss, wie Lärm stören kann und Kommunikation behindert oder gar unterbindet. Ähnliche optische Effekte sind bekannt: starkes Schneetreiben oder Regengüsse verschlechtern die Sicht und lassen uns Umrisse nur noch schemenhaft erkennen. Jedoch koennen ähnliche Stimuli auch sehr positive Auswirkungen haben: Autofahrer fahren bei leiser Musik konzentrierter -- die Behauptung von Schulkindern, nur bei dröhnenden Bässen die Mathehausaufgaben richtig rechnen zu können, ist allerdings nicht wissenschaftlich
MacDonald, Shannon E; Schopflocher, Donald P; Vaudry, Wendy
2014-01-01
Children who begin but do not fully complete the recommended series of childhood vaccines by 2 y of age are a much larger group than those who receive no vaccines. While parents who refuse all vaccines typically express concern about vaccine safety, it is critical to determine what influences parents of 'partially' immunized children. This case-control study examined whether parental concern about vaccine safety was responsible for partial immunization, and whether other personal or system-level factors played an important role. A random sample of parents of partially and completely immunized 2 y old children were selected from a Canadian regional immunization registry and completed a postal survey assessing various personal and system-level factors. Unadjusted odds ratios (OR) and adjusted ORs (aOR) were calculated with logistic regression. While vaccine safety concern was associated with partial immunization (OR 7.338, 95% CI 4.138-13.012), other variables were more strongly associated and reduced the strength of the relationship between concern and partial immunization in multivariable analysis (aOR 2.829, 95% CI 1.151-6.957). Other important factors included perceived disease susceptibility and severity (aOR 4.629, 95% CI 2.017-10.625), residential mobility (aOR 3.908, 95% CI 2.075-7.358), daycare use (aOR 0.310, 95% CI 0.144-0.671), number of needles administered at each visit (aOR 7.734, 95% CI 2.598-23.025) and access to a regular physician (aOR 0.219, 95% CI 0.057-0.846). While concern about vaccine safety may be addressed through educational strategies, this study suggests that additional program and policy-level strategies may positively impact immunization uptake.
NASA Technical Reports Server (NTRS)
Silva, Walter A.
1993-01-01
A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.
Robust Model-Based Sensor Fault Monitoring System for Nonlinear Systems in Sensor Networks
Wang, Dejun; Song, Shiyao
2014-01-01
A new model-based sensor fault diagnosis (FD) scheme, using an equivalent model, is developed for a kind of Multiple Inputs Multiple Outputs (MIMO) nonlinear system which fulfills the Lipschitz condition. The equivalent model, which is a bank of one-dimensional linear state equations with the bounded model uncertainty, can take the place of a plant's exact nonlinear model in the case of sensor FD. This scheme shows a new perspective whereby, by using the equivalent model, it doesn't have to study the nonlinear internal structure character or get the exact model. The influence of the model uncertainty on the residuals is explained in this paper. A method, called pretreatment, is utilized to minimize the model uncertainty. The eigenstructure assignment method with assistant state is employed to solve the problem of perfect decoupling against the model uncertainty, disturbance, system faults, the relevant actuator faults, or even the case of no input from the relevant actuator. The realization of the proposed scheme is given by an algorithm according to a single sensor FD, and verified by a simulation example. Depending on the above, a sensor fault monitoring system is established by the sensor network and diagnosis logic, then the effectiveness is testified by a simulation. PMID:25320904
Fault-tolerant control for a class of non-linear systems with dead-zone
NASA Astrophysics Data System (ADS)
Chen, Mou; Jiang, Bin; Guo, William W.
2016-05-01
In this paper, a fault-tolerant control scheme is proposed for a class of single-input and single-output non-linear systems with the unknown time-varying system fault and the dead-zone. The non-linear state observer is designed for the non-linear system using differential mean value theorem, and the non-linear fault estimator that estimates the unknown time-varying system fault is developed. On the basis of the designed fault estimator, the observer-based fault-tolerant tracking control is then developed using the backstepping technique for non-linear systems with the dead-zone. The stability of the whole closed-loop system is rigorously proved via Lyapunov analysis and the satisfactory tracking control performance is guaranteed in the presence of the unknown time-varying system fault and the dead-zone. Numerical simulation results are presented to illustrate the effectiveness of the proposed backstepping fault-tolerant control scheme for non-linear systems.
Adaptive robust stabilisation for a class of uncertain nonlinear time-delay dynamical systems
NASA Astrophysics Data System (ADS)
Wu, Hansheng
2013-02-01
The problem of adaptive robust stabilisation is considered for a class of uncertain nonlinear dynamical systems with multiple time-varying delays. It is assumed that the upper bounds of the nonlinear delayed state perturbations are unknown and that the time-varying delays are any non-negative continuous and bounded functions which do not require that their derivatives have to be less than one. In particular, it is only required that the nonlinear uncertainties, which can also include time-varying delays, are bounded in any non-negative nonlinear functions which are not required to be known for the system designer. For such a class of uncertain nonlinear time-delay systems, a new method is presented whereby a class of continuous memoryless adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain nonlinear time-delay systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. Finally, as an application, an uncertain nonlinear time-delay ecosystem with two competing species is given to demonstrate the validity of the results.
Multiscale analysis of nonlinear systems using computational homology
Konstantin Mischaikow, Rutgers University /Georgia Institute of Technology, Michael Schatz, Georgia Institute of Technology, William Kalies, Florida Atlantic University, Thomas Wanner,George Mason University
2010-05-19
- We extended our previous work on studying the time evolution of patterns associated with phase separation in conserved concentration fields. (6) Probabilistic Homology Validation - work on microstructure characterization is based on numerically studying the homology of certain sublevel sets of a function, whose evolution is described by deterministic or stochastic evolution equations. (7) Computational Homology and Dynamics - Topological methods can be used to rigorously describe the dynamics of nonlinear systems. We are approaching this problem from several perspectives and through a variety of systems. (8) Stress Networks in Polycrystals - we have characterized stress networks in polycrystals. This part of the project is aimed at developing homological metrics which can aid in distinguishing not only microstructures, but also derived mechanical response fields. (9) Microstructure-Controlled Drug Release - This part of the project is concerned with the development of topological metrics in the context of controlled drug delivery systems, such as drug-eluting stents. We are particularly interested in developing metrics which can be used to link the processing stage to the resulting microstructure, and ultimately to the achieved system response in terms of drug release profiles. (10) Microstructure of Fuel Cells - we have been using our computational homology software to analyze the topological structure of the void, metal and ceramic components of a Solid Oxide Fuel Cell.
Multiscale analysis of nonlinear systems using computational homology
Konstantin Mischaikow; Michael Schatz; William Kalies; Thomas Wanner
2010-05-24
- We extended our previous work on studying the time evolution of patterns associated with phase separation in conserved concentration fields. (6) Probabilistic Homology Validation - work on microstructure characterization is based on numerically studying the homology of certain sublevel sets of a function, whose evolution is described by deterministic or stochastic evolution equations. (7) Computational Homology and Dynamics - Topological methods can be used to rigorously describe the dynamics of nonlinear systems. We are approaching this problem from several perspectives and through a variety of systems. (8) Stress Networks in Polycrystals - we have characterized stress networks in polycrystals. This part of the project is aimed at developing homological metrics which can aid in distinguishing not only microstructures, but also derived mechanical response fields. (9) Microstructure-Controlled Drug Release - This part of the project is concerned with the development of topological metrics in the context of controlled drug delivery systems, such as drug-eluting stents. We are particularly interested in developing metrics which can be used to link the processing stage to the resulting microstructure, and ultimately to the achieved system response in terms of drug release profiles. (10) Microstructure of Fuel Cells - we have been using our computational homology software to analyze the topological structure of the void, metal and ceramic components of a Solid Oxide Fuel Cell.
Static feedback stabilization of nonlinear systems with single sensor and single actuator.
Wang, Jiqiang; Hu, Zhongzhi; Ye, Zhifeng
2014-01-01
This paper considers a single sensor and single actuator approach to the static feedback stabilization of nonlinear systems. This is essentially a remote control problem that is present in many engineering applications. The proposed method solves this problem that is less expensive to implement and more reliable in practice. Significant results are obtained on the design of controllers for stabilizing the nonlinear systems. Important issues on control implementation are also discussed. The proposed design method is validated through its application to nonlinear control of aircraft engines.
Nonlinear analysis of a closed-loop tractor-semitrailer vehicle system with time delay
NASA Astrophysics Data System (ADS)
Liu, Zhaoheng; Hu, Kun; Chung, Kwok-wai
2016-08-01
In this paper, a nonlinear analysis is performed on a closed-loop system of articulated heavy vehicles with driver steering control. The nonlinearity arises from the nonlinear cubic tire force model. An integration method is employed to derive an analytical periodic solution of the system in the neighbourhood of the critical speed. The results show that excellent accuracy can be achieved for the calculation of periodic solutions arising from Hopf bifurcation of the vehicle motion. A criterion is obtained for detecting the Bautin bifurcation which separates branches of supercritical and subcritical Hopf bifurcations. The integration method is compared to the incremental harmonic balance method in both supercritical and subcritical scenarios.
Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems
NASA Astrophysics Data System (ADS)
Colli, Pierluigi; Fukao, Takeshi
2016-05-01
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media equation, Hele-Shaw profile, nonlinear diffusion of singular logarithmic type, nonlinear diffusion of Penrose-Fife type, fast diffusion equation and so on. Namely, by setting the suitable potential of the Cahn-Hilliard systems, all these problems can be obtained as limits of the Cahn-Hilliard related problems. Convergence results and error estimates are proved.
Vacuum Rabi splitting effect in nanomechanical QED system with nonlinear resonator
NASA Astrophysics Data System (ADS)
Zhao, MingYue; Gao, YiBo
2016-08-01
Considering the intrinsic nonlinearity in a nanomechanical resonator coupled to a charge qubit, vacuum Rabi splitting effect is studied in a nanomechanical QED (qubit-resonator) system. A driven nonlinear Jaynes-Cummings model describes the dynamics of this qubit-resonator system. Using quantum regression theorem and master equation approach, we have calculated the two-time correlation spectrum analytically. In the weak driving limit, these analytical results clarify the influence of the driving strength and nonlinearity parameter on the correlation spectrum. Also, numerical calculations confirm these analytical results.
Finite-time H∞ filtering for non-linear stochastic systems
NASA Astrophysics Data System (ADS)
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Synthesis of nonlinear discrete control systems via time-delay affine Takagi-Sugeno fuzzy models.
Chang, Wen-Jer; Chang, Wei
2005-04-01
The affine Takagi-Sugeno (TS) fuzzy model played a more important role in nonlinear control because it can be used to approximate the nonlinear systems more than the homogeneous TS fuzzy models. Besides, it is known that the time delays exist in physical systems and the previous works did not consider the time delay effects in the analysis of affine TS fuzzy models. Hence a parallel distributed compensation based fuzzy controller design issue for discrete time-delay affine TS fuzzy models is considered in this paper. The time-delay effect is considered in the discrete affine TS fuzzy models and the stabilization issue is developed for the nonlinear time-delay systems. Finally, a numerical simulation for a time-delayed nonlinear truck-trailer system is given to show the applications of the present approach.
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method.
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method. PMID:25420238
Vibration control of a nonlinear quarter-car active suspension system by reinforcement learning
NASA Astrophysics Data System (ADS)
Bucak, İ. Ö.; Öz, H. R.
2012-06-01
This article presents the investigation of performance of a nonlinear quarter-car active suspension system with a stochastic real-valued reinforcement learning control strategy. As an example, a model of a quarter car with a nonlinear suspension spring subjected to excitation from a road profile is considered. The excitation is realised by the roughness of the road. The quarter-car model to be considered here can be approximately described as a nonlinear two degrees of freedom system. The experimental results indicate that the proposed active suspension system suppresses the vibrations greatly. A simulation of a nonlinear quarter-car active suspension system is presented to demonstrate the effectiveness and examine the performance of the learning control algorithm.
NASA Astrophysics Data System (ADS)
Venkatapathi, Murugesan; Rajwa, Bartek; Ragheb, Kathy; Banada, Padmapriya P.; Lary, Todd; Robinson, J. Paul; Hirleman, E. Daniel
2008-02-01
We describe a model-based instrument design combined with a statistical classification approach for the development and realization of high speed cell classification systems based on light scatter. In our work, angular light scatter from cells of four bacterial species of interest, Bacillus subtilis, Escherichia coli, Listeria innocua, and Enterococcus faecalis, was modeled using the discrete dipole approximation. We then optimized a scattering detector array design subject to some hardware constraints, configured the instrument, and gathered experimental data from the relevant bacterial cells. Using these models and experiments, it is shown that optimization using a nominal bacteria model (i.e., using a representative size and refractive index) is insufficient for classification of most bacteria in realistic applications. Hence the computational predictions were constituted in the form of scattering-data-vector distributions that accounted for expected variability in the physical properties between individual bacteria within the four species. After the detectors were optimized using the numerical results, they were used to measure scatter from both the known control samples and unknown bacterial cells. A multivariate statistical method based on a support vector machine (SVM) was used to classify the bacteria species based on light scatter signatures. In our final instrument, we realized correct classification of B. subtilis in the presence of E. coli,L. innocua, and E. faecalis using SVM at 99.1%, 99.6%, and 98.5%, respectively, in the optimal detector array configuration. For comparison, the corresponding values for another set of angles were only 69.9%, 71.7%, and 70.2% using SVM, and more importantly, this improved performance is consistent with classification predictions.
Time domain simulation of nonlinear response of a coupled TLP system in random seas
Kim, C.H.; Kim, M.H.; Liu, Y.H.; Zhao, C.T.
1994-12-31
This paper presents a result of an analysis of the nonlinear interaction and response of the coupled ISSC-TLP System to the random seas in the time domain. The environmental load also includes the effect of the concurrent steady winds and currents. The first- and second-order wave-exciting forces are calculated using a robust higher-order boundary element method (HOBEM), while the nonlinear tendon dynamic analysis is performed using the three-dimensional hybrid element method with the upgated Lagrangian formulation. The Morison equation is employed for the wave and current load on slender structures. The analysis is focused on the nonlinear responses due to the nonlinear environmental load and nonlinear interaction between the platform and tendons that includes the offset, setdown, large coupled surge-heave motion in the low frequency and resonant heave/pitch responses with the springing loads in the high frequency.
NASA Astrophysics Data System (ADS)
Collin, E.; Bunkov, Yu. M.; Godfrin, H.
2010-12-01
We report on low-temperature measurements performed on microelectromechanical systems driven deeply into the nonlinear regime. The materials are kept in their elastic domain while the observed nonlinearity is purely of geometrical origin. Two techniques are used, harmonic drive and free decay. For each case, we present an analytic theory fitting the data. The harmonic drive is fit with a modified Lorentzian line shape obtained from an extended version of Landau and Lifshitz’s nonlinear theory. The evolution in the time domain is fit with an amplitude-dependent frequency decaying function derived from the Lindstedt-Poincaré theory of nonlinear differential equations. The technique is perfectly generic and can be straightforwardly adapted to any mechanical device made of ideally elastic constituents, and which can be reduced to a single degree of freedom, for an experimental definition of its nonlinear dynamics equation.
The effect of problem perturbations on nonlinear dynamical systems and their reduced order models
Serban, R; Homescu, C; Petzold, L
2005-03-03
Reduced order models are used extensively in many areas of science and engineering for simulation, design, and control. Reduction techniques for nonlinear dynamical systems produce models that depend strongly on the nominal set of parameters for which the reduction is carried out. In this paper we address the following two questions: 'What is the effect of perturbations in the problem parameters on the output functional of a nonlinear dynamical system?' and 'To what extent does the reduced order model capture this effect?'
Dual objective active suspension system based on a novel nonlinear disturbance compensator
NASA Astrophysics Data System (ADS)
Deshpande, Vaijayanti S.; Shendge, P. D.; Phadke, S. B.
2016-09-01
This paper proposes an active suspension system to fulfil the dual objective of improving ride comfort while trying to keep the suspension deflection within the limits of the rattle space. The scheme is based on a novel nonlinear disturbance compensator which employs a nonlinear function of the suspension deflection. The scheme is analysed and validated by simulation and experimentation on a laboratory setup. The performance is compared with a passive suspension system for a variety of road profiles.
Approximated Stable Inversion for Nonlinear Systems with Nonhyperbolic Internal Dynamics. Revised
NASA Technical Reports Server (NTRS)
Devasia, Santosh
1999-01-01
A technique to achieve output tracking for nonminimum phase nonlinear systems with non- hyperbolic internal dynamics is presented. The present paper integrates stable inversion techniques (that achieve exact-tracking) with approximation techniques (that modify the internal dynamics) to circumvent the nonhyperbolicity of the internal dynamics - this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques. The theory is developed for nonlinear systems and the method is applied to a two-cart with inverted-pendulum example.
Phonon mechanisms of nonlinear decay and dephasing of mesoscopic vibrational systems
NASA Astrophysics Data System (ADS)
Atalaya, Juan; Kenny, Thomas W.; Dykman, Mark I.
2015-03-01
The frequencies and the decay rates of mesoscopic oscillators depend on vibration amplitudes. Nonlinear decay has been seen recently in various nano- and micro-mechanical systems. Here we consider a microscopic mechanism of nonlinear decay, the nonlinear coupling of the vibrational mode of interest, for example, a flexural mode, to other vibrations. Typically, the modes of interest have low eigenfrequencies ω0. Their decay comes from the coupling to acoustic-phonon type vibrations with much higher frequency and density of states. Thus, nonlinear decay requires quartic anharmonic coupling or cubic anharmonicity in the higher order. We find the decay rate for the inverse lifetime of the involved phonons, which is determined by the internal nonlinearity and the boundary scattering, being either much larger or smaller than ω0. The results extend the thermo-elastic, Akhiezer, and Landau-Rumer decay theory to nonlinear decay of mesoscopic modes and make specific predictions on the temperature and frequency dependence of the decay rate for different types of systems. We show that nonlinear decay is invariably accompanied by dephasing. We also show that in nano-electro-mechanical systems the decay rate can be electrostatically controlled.
Esfandiari, Kasra; Abdollahi, Farzaneh; Talebi, Heidar Ali
2015-10-01
This paper presents a tracking control methodology for a class of uncertain nonlinear systems subject to input saturation constraint and external disturbances. Unlike most previous approaches on saturated systems, which assumed affine nonlinear systems, in this paper, tracking control problem is solved for uncertain nonaffine nonlinear systems with input saturation. To deal with the saturation constraint, an auxiliary system is constructed and a modified tracking error is defined. Then, by employing implicit function theorem, mean value theorem, and modified tracking error, updating rules are derived based on the well-known back-propagation (BP) algorithm, which has been proven to be the most relevant updating rule to control problems. However, most of the previous approaches on BP algorithm suffer from lack of stability analysis. By injecting a damping term to the standard BP algorithm, uniformly ultimately boundedness of all the signals of the closed-loop system is ensured via Lyapunov's direct method. Furthermore, the presented approach employs nonlinear in parameter neural networks. Hence, the proposed scheme is applicable to systems with higher degrees of nonlinearity. Using a high-gain observer to reconstruct the states of the system, an output feedback controller is also presented. Finally, the simulation results performed on a Duffing-Holmes chaotic system, a generalized pendulum-type system, and a numerical system are presented to demonstrate the effectiveness of the suggested state and output feedback control schemes. PMID:25532213
Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data
NASA Technical Reports Server (NTRS)
Kukreja, Sunil L.
2008-01-01
Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.
IDENTIFICATION OF NONLINEARITIES IN AN 8-DOF SYSTEM THROUGH SPECTRAL FEEDBACK
B. ARCAND; J. WAIT
2000-08-01
The accurate detection and characterization of nonlinearities associated with damage in structural systems is an area of vibration analysis that is being widely researched. In this paper, nonlinear behavior is considered a potential indicator of damage. Most conventional damage detection methods, such as those based on resonant frequencies and mode shapes, do not accurately identify the location and extent of nonlinearities present in a given structural system. As an extension of previous work at LANL, an effort is made to validate a damage detection method proposed by Adams. This method states that the frequency response function (FRF) matrix obtained from a low-level vibration test approximates the underlying linear FRF matrix of the system. The nonlinear systems' responses to high level excitation are combined with the linear FRF in a classic feedback loop to obtain the contributions of nonlinear internal forces. The temporal and spatial characteristics of the nonlinearities present in a structural system are identified. An 8-DOF system is used as a test case to validate the aforementioned method. Results of the tests and important issues concerning the method are presented.
Estimation on nonlinear damping in second order distributed parameter systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1989-01-01
An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.
Ming, Yi; Li, Hui-Min; Ding, Ze-Jun
2016-03-01
Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011)]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.
NASA Astrophysics Data System (ADS)
Ming, Yi; Li, Hui-Min; Ding, Ze-Jun
2016-03-01
Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011), 10.1038/nnano.2011.71]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.
NASA Astrophysics Data System (ADS)
Duan, Zhaoxia; Xiang, Zhengrong; Karimi, Hamid Reza
2014-07-01
This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality-based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired controller gains is derived. An illustrative example is provided to show the usefulness and effectiveness of the proposed method.
Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances
Miroshnichenko, Andrey E.; Kivshar, Yuri S.; Malomed, Boris A.
2011-07-15
We consider a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (in other words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system in the form of a dimer, symmetric and asymmetric eigenstates, including multistable ones, are found analytically. We demonstrate that, if coupled to a linear chain, such a nonlinear PT-symmetric dimer generates previously unexplored types of nonlinear Fano resonances, with completely suppressed or greatly amplified transmission, as well as a regime similar to the electromagnetically induced transparency. The implementation of the systems is possible in various media admitting controllable linear and nonlinear amplification of waves.
Al-Khateeb, Mohammad A Z; McCarthy, Mary; Sánchez, Christian; Ellis, Andrew
2016-04-15
In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dBSNR/dBPower suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error. PMID:27082361
A frozen matrix hybrid optical nonlinear system enhanced by a particle lens
NASA Astrophysics Data System (ADS)
Chen, Lianwei; Zheng, Xiaorui; Du, Zheren; Jia, Baohua; Gu, Min; Hong, Minghui
2015-09-01
In this work, a Graphene Oxide (GO) nano-sheet and SiO2 micro-bead hybrid system based on a frozen matrix was investigated for its enhanced optical nonlinear performance. A frozen matrix is a novel approach that hosts the optical nonlinear nano-particles, which combines the strengths from both liquid and solid phase systems for high performance photonic applications. SiO2 micro-beads were used to induce a local field enhancement effect that improved the optical nonlinearity of GO nano-sheets. The nonlinear performance of the hybrid system is several orders higher than the existing GO nano-sheet liquid dispersion. In addition, this frozen matrix and the local field enhancement effect are two facile and versatile methods that can be applied to many types of nano-particle dispersions.In this work, a Graphene Oxide (GO) nano-sheet and SiO2 micro-bead hybrid system based on a frozen matrix was investigated for its enhanced optical nonlinear performance. A frozen matrix is a novel approach that hosts the optical nonlinear nano-particles, which combines the strengths from both liquid and solid phase systems for high performance photonic applications. SiO2 micro-beads were used to induce a local field enhancement effect that improved the optical nonlinearity of GO nano-sheets. The nonlinear performance of the hybrid system is several orders higher than the existing GO nano-sheet liquid dispersion. In addition, this frozen matrix and the local field enhancement effect are two facile and versatile methods that can be applied to many types of nano-particle dispersions. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr03304g
Multivariate respiratory motion prediction
NASA Astrophysics Data System (ADS)
Dürichen, R.; Wissel, T.; Ernst, F.; Schlaefer, A.; Schweikard, A.
2014-10-01
In extracranial robotic radiotherapy, tumour motion is compensated by tracking external and internal surrogates. To compensate system specific time delays, time series prediction of the external optical surrogates is used. We investigate whether the prediction accuracy can be increased by expanding the current clinical setup by an accelerometer, a strain belt and a flow sensor. Four previously published prediction algorithms are adapted to multivariate inputs—normalized least mean squares (nLMS), wavelet-based least mean squares (wLMS), support vector regression (SVR) and relevance vector machines (RVM)—and evaluated for three different prediction horizons. The measurement involves 18 subjects and consists of two phases, focusing on long term trends (M1) and breathing artefacts (M2). To select the most relevant and least redundant sensors, a sequential forward selection (SFS) method is proposed. Using a multivariate setting, the results show that the clinically used nLMS algorithm is susceptible to large outliers. In the case of irregular breathing (M2), the mean root mean square error (RMSE) of a univariate nLMS algorithm is 0.66 mm and can be decreased to 0.46 mm by a multivariate RVM model (best algorithm on average). To investigate the full potential of this approach, the optimal sensor combination was also estimated on the complete test set. The results indicate that a further decrease in RMSE is possible for RVM (to 0.42 mm). This motivates further research about sensor selection methods. Besides the optical surrogates, the sensors most frequently selected by the algorithms are the accelerometer and the strain belt. These sensors could be easily integrated in the current clinical setup and would allow a more precise motion compensation.
NASA Astrophysics Data System (ADS)
Hamel, Sarah; Boulkroune, Abdesselem
2016-08-01
In this paper, a modified generalized function projective synchronization scheme for a class of master-slave chaotic systems subject to dynamic disturbances and input nonlinearities (dead-zone and sector nonlinearities) is investigated. This synchronization system can be seen as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization and so on), in the sense that the master system has a scaling function matrix and the slave system has a scaling factor matrix. To practically achieve this generalized function synchronization, an adaptive fuzzy variable-structure control system is designed. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is employed to prove the boundedness of all signals of the closed-loop control system as well as the exponential convergence of the synchronization errors to an adjustable region. Simulations results are presented to illustrate the effectiveness of the proposed generalized function PS scheme.
Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity
Zhan, Kaiyun; Tian, Hao; Li, Xin; Xu, Xianfeng; Jiao, Zhiyong; Jia, Yulei
2016-01-01
We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain. PMID:27596716
Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity.
Zhan, Kaiyun; Tian, Hao; Li, Xin; Xu, Xianfeng; Jiao, Zhiyong; Jia, Yulei
2016-01-01
We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain. PMID:27596716
Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity
NASA Astrophysics Data System (ADS)
Zhan, Kaiyun; Tian, Hao; Li, Xin; Xu, Xianfeng; Jiao, Zhiyong; Jia, Yulei
2016-09-01
We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain.
Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan
2016-01-01
In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite
NASA Astrophysics Data System (ADS)
Lin, Raymond Chao
The handling qualities evaluation of nonlinear aircraft systems is an area of concern in loss-of-control (LOC) prevention. The Get Transfer Function (GetTF) method was demonstrated for evaluating the handling qualities of flight control systems and aircraft containing nonlinearities. NASA's Generic Transport Model (GTM), a nonlinear model of a civilian jet transport aircraft, was evaluated. Using classical techniques, the stability, control, and augmentation (SCAS) systems were designed to control pitch rate, roll rate, and airspeed. Hess's structural pilot model was used to model pilot dynamics in pitch and roll-attitude tracking. The simulated task was simultaneous tracking of, both, pitch and roll attitudes. Eight cases were evaluated: 1) gain increase of pitch-attitude command signal, 2) gain increase of roll-attitude command signal, 3) gain reduction of elevator command signal, 4) backlash in elevator actuator, 5) combination 3 and 4 in elevator actuator, 6) gain reduction of aileron command signal, 7) backlash in aileron actuator, and 8) combination of 6 and 7 in aileron actuator. The GetTF method was used to estimate the transfer function approximating a linear relationship between the proprioceptive signal of the pilot model and the command input. The transfer function was then used to predict the handling qualities ratings (HQR) and pilot-induced oscillation ratings (PIOR). The HQR is based on the Cooper-Harper rating scale. In pitch-attitude tracking, the nominal aircraft is predicted to have Level 2* HQRpitch and 2 < PIORpitch < 4. The GetTF method generally predicted degraded handling qualities for cases with impaired actuators. The results demonstrate GetTF's utility in evaluating the handling qualities during the design phase of flight control and aircraft systems. A limited human-in-the-loop pitch tracking exercise was also conducted to validate the structural pilot model.
Bui, Lam Anh; Mitchell, Arnan
2013-04-01
A novel remoted instantaneous frequency measurement system using all optical mixing is demonstrated. This system copies an input intensity modulated optical carrier using four wave mixing, delays this copy and then mixes it with the original signal, to produce an output idler tone. The intensity of this output can be used to determine the RF frequency of the input signal. This system is inherently broadband and can be easily scaled beyond 40 GHz while maintaining a DC output which greatly simplifies receiving electronics. The remoted configuration isolates the sensitive and expensive receiver hardware from the signal sources and importantly allows the system to be added to existing microwave photonic implementations without modification of the transmission module. PMID:23571944
Iterative methods for large scale nonlinear and linear systems. Final report, 1994--1996
Walker, H.F.
1997-09-01
The major goal of this research has been to develop improved numerical methods for the solution of large-scale systems of linear and nonlinear equations, such as occur almost ubiquitously in the computational modeling of physical phenomena. The numerical methods of central interest have been Krylov subspace methods for linear systems, which have enjoyed great success in many large-scale applications, and newton-Krylov methods for nonlinear problems, which use Krylov subspace methods to solve approximately the linear systems that characterize Newton steps. Krylov subspace methods have undergone a remarkable development over the last decade or so and are now very widely used for the iterative solution of large-scale linear systems, particularly those that arise in the discretization of partial differential equations (PDEs) that occur in computational modeling. Newton-Krylov methods have enjoyed parallel success and are currently used in many nonlinear applications of great scientific and industrial importance. In addition to their effectiveness on important problems, Newton-Krylov methods also offer a nonlinear framework within which to transfer to the nonlinear setting any advances in Krylov subspace methods or preconditioning techniques, or new algorithms that exploit advanced machine architectures. This research has resulted in a number of improved Krylov and Newton-Krylov algorithms together with applications of these to important linear and nonlinear problems.
Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Killingsworth, W. R., Jr.
1972-01-01
The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.
Hybrid Takagi-Sugeno Fuzzy FED PID Control of Nonlinear Systems
NASA Astrophysics Data System (ADS)
Hamed, Basil; El Khateb, Ahmad
2008-06-01
The new method of proportional-integral-derivative (PID) controller is proposed in this paper for a hybrid fuzzy PID controller for nonlinear system. The important feature of the proposed approach is that it combines the fuzzy gain scheduling method and a fuzzy fed PID controller to solve the nonlinear control problem. The resultant fuzzy rule base of the proposed controller contains one part. This single part of the rules uses the Takagi-Sugeno method for solving the nonlinear problem. The simulation results of a nonlinear system show that the performance of a fed PID Hybrid Takagi-Sugeno fuzzy controller is better than that of the conventional fuzzy PID controller or Hybrid Mamdani fuzzy FED PID controller.
NASA Astrophysics Data System (ADS)
Mokaddem, S.; Khaber, F.
2008-06-01
This work presents a development of adaptive type-1 and type-2 fuzzy controls for uncertain nonlinear systems. Using the adaptive type-1 fuzzy control, the dynamic of the nonlinear systems is approximated with type-1 fuzzy systems whose parameters are adjusted by appropriate law adaptation. For adaptive type-2 fuzzy control, the dynamic of the nonlinear systems is approximated with interval type-2 fuzzy systems. The use of this type-2 control requires an additional operation witch is the type reduction, in comparing with typ-1 control. The closed-loop system stability is guaranteed by the Lyaponov synthesis. To show the performance of the developed controls, a comparative study is realized through the application of these controls so that an inverted pendulum tracks a given trajectory in presence of disturbances.
Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan
2016-01-01
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740
Solving nonlinear evolution equation system using two different methods
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.
2015-12-01
This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.
Ryali, Srikanth; Ian Shih, Yen-Yu; Chen, Tianwen; Kochalka, John; Albaugh, Daniel; Fang, Zhongnan; Supekar, Kaustubh; Lee, Jin Hyung; Menon, Vinod
2016-01-01
State-space multivariate dynamical systems (MDS) (Ryali et al., 2011) and other causal estimation models are being increasingly used to identify directed functional interactions between brain regions. However, the validity and accuracy of such methods is poorly understood. Performance evaluation based on computer simulations of small artificial causal networks can address this problem to some extent, but they often involve simplifying assumptions that reduce biological validity of the resulting data. Here, we use a novel approach taking advantage of recently developed optogenetic fMRI (ofMRI) techniques to selectively stimulate brain regions while simultaneously recording high-resolution whole-brain fMRI data. ofMRI allows for a more direct investigation of causal influences from the stimulated site to brain regions activated downstream and is therefore ideal for evaluating causal estimation methods in vivo. We used ofMRI to investigate whether MDS models for fMRI can accurately estimate causal functional interactions between brain regions. Two cohorts of ofMRI data were acquired, one at Stanford University and the University of California Los Angeles (Cohort 1) and the other at the University of North Carolina Chapel Hill (Cohort 2). In each cohort optical stimulation was delivered to the right primary motor cortex (M1). General linear model analysis revealed prominent downstream thalamic activation in Cohort 1, and caudate-putamen (CPu) activation in Cohort 2. MDS accurately estimated causal interactions from M1 to thalamus and from M1 to CPu in Cohort 1 and Cohort 2, respectively. As predicted, no causal influences were found in the reverse direction. Additional control analyses demonstrated the specificity of causal interactions between stimulated and target sites. Our findings suggest that MDS state-space models can accurately and reliably estimate causal interactions in ofMRI data and further validate their use for estimating causal interactions in fMRI. More
Nonlinear stability research on the hydraulic system of double-side rolling shear.
Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu
2015-10-01
This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation. PMID:26520981
Nonlinear stability research on the hydraulic system of double-side rolling shear
NASA Astrophysics Data System (ADS)
Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu
2015-10-01
This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.
PID controller design of nonlinear systems using an improved particle swarm optimization approach
NASA Astrophysics Data System (ADS)
Chang, Wei-Der; Shih, Shun-Peng
2010-11-01
In this paper, an improved particle swarm optimization is presented to search for the optimal PID controller gains for a class of nonlinear systems. The proposed algorithm is to modify the velocity formula of the general PSO systems in order for improving the searching efficiency. In the improved PSO-based nonlinear PID control system design, three PID control gains, i.e., the proportional gain Kp, integral gain Ki, and derivative gain Kd are required to form a parameter vector which is called a particle. It is the basic component of PSO systems and many such particles further constitute a population. To derive the optimal PID gains for nonlinear systems, two principle equations, the modified velocity updating and position updating equations, are employed to move the positions of all particles in the population. In the meanwhile, an objective function defined for PID controller optimization problems may be minimized. To validate the control performance of the proposed method, a typical nonlinear system control, the inverted pendulum tracking control, is illustrated. The results testify that the improved PSO algorithm can perform well in the nonlinear PID control system design.
Nonlinear dynamical systems and control for large-scale, hybrid, and network systems
NASA Astrophysics Data System (ADS)
Hui, Qing
In this dissertation, we present several main research thrusts involving thermodynamic stabilization via energy dissipating hybrid controllers and nonlinear control of network systems. Specifically, a novel class of fixed-order, energy-based hybrid controllers is presented as a means for achieving enhanced energy dissipation in Euler-Lagrange, lossless, and dissipative dynamical systems. These dynamic controllers combine a logical switching architecture with continuous dynamics to guarantee that the system plant energy is strictly decreasing across switching. In addition, we construct hybrid dynamic controllers that guarantee the closed-loop system is consistent with basic thermodynamic principles. In particular, the existence of an entropy function for the closed-loop system is established that satisfies a hybrid Clausius-type inequality. Special cases of energy-based hybrid controllers involving state-dependent switching are described, and the framework is applied to aerospace system models. The overall framework demonstrates that energy-based hybrid resetting controllers provide an extremely efficient mechanism for dissipating energy in nonlinear dynamical systems. Next, we present finite-time coordination controllers for multiagent network systems. Recent technological advances in communications and computation have spurred a broad interest in autonomous, adaptable vehicle formations. Distributed decision-making for coordination of networks of dynamic agents addresses a broad area of applications including cooperative control of unmanned air vehicles, microsatellite clusters, mobile robotics, and congestion control in communication networks. In this dissertation we focus on finite-time consensus protocols for networks of dynamic agents with undirected information flow. The proposed controller architectures are predicated on the recently developed notion of system thermodynamics resulting in thermodynamically consistent continuous controller architectures
Eliminating Nonlinear Acoustical Effects From Thermoacoustic Refrigeration Systems
NASA Astrophysics Data System (ADS)
Garrett, Steven L.; Smith, Robert W. M.; Poese, Matthew E.
2006-05-01
Nonlinear acoustical effects dissipate energy that degrades thermoacoustic refrigerator performance. The largest of these effects occur in acoustic resonators and include shock formation; turbulence and boundary layer disruption; and entry/exit (minor) losses induced by changes in resonator cross-sectional area. Effects such as these also make the creation of accurate performance models more complicated. Suppression of shock formation by intentional introduction of resonator anharmonicity has been common practice for the past two decades. Recent attempts to increase cooling power density by increasing pressure amplitudes has required reduction of turbulence and minor loss by using an new acousto-mechanical resonator topology. The hybrid resonator still stores potential energy in the compressibility of the gaseous working fluid, but stores kinetic energy in the moving (solid) mass of the motor and piston. This talk will first present nonlinear acoustical loss measurements obtained in a "conventional" double-Helmholtz resonator geometry (TRITON) that dissipated four kilowatts of acoustic power. We will then describe the performance of the new "bellows bounce" resonator configuration and "vibromechanical multiplier" used in the first successful implementation of this approach that created an ice cream freezer produced at Penn State for Ben & Jerry's.
Adaptive discrete-time sliding-mode control of nonlinear systems described by Wiener models
NASA Astrophysics Data System (ADS)
Salhi, Houda; Kamoun, Samira; Essounbouli, Najib; Hamzaoui, Abdelaziz
2016-03-01
In this paper, we propose an adaptive control scheme that can be applied to nonlinear systems with unknown parameters. The considered class of nonlinear systems is described by the block-oriented models, specifically, the Wiener models. These models consist of dynamic linear blocks in series with static nonlinear blocks. The proposed adaptive control method is based on the inverse of the nonlinear function block and on the discrete-time sliding-mode controller. The parameters adaptation are performed using a new recursive parametric estimation algorithm. This algorithm is developed using the adjustable model method and the least squares technique. A recursive least squares (RLS) algorithm is used to estimate the inverse nonlinear function. A time-varying gain is proposed, in the discrete-time sliding mode controller, to reduce the chattering problem. The stability of the closed-loop nonlinear system, with the proposed adaptive control scheme, has been proved. An application to a pH neutralisation process has been carried out and the simulation results clearly show the effectiveness of the proposed adaptive control scheme.
NASA Technical Reports Server (NTRS)
Meyer, G.; Cicolani, L.
1981-01-01
A practical method for the design of automatic flight control systems for aircraft with complex characteristics and operational requirements, such as the powered lift STOL and V/STOL configurations, is presented. The method is effective for a large class of dynamic systems requiring multi-axis control which have highly coupled nonlinearities, redundant controls, and complex multidimensional operational envelopes. It exploits the concept of inverse dynamic systems, and an algorithm for the construction of inverse is given. A hierarchic structure for the total control logic with inverses is presented. The method is illustrated with an application to the Augmentor Wing Jet STOL Research Aircraft equipped with a digital flight control system. Results of flight evaluation of the control concept on this aircraft are presented.
Green, P. L.; Worden, K.
2015-01-01
In this paper, the authors outline the general principles behind an approach to Bayesian system identification and highlight the benefits of adopting a Bayesian framework when attempting to identify models of nonlinear dynamical systems in the presence of uncertainty. It is then described how, through a summary of some key algorithms, many of the potential difficulties associated with a Bayesian approach can be overcome through the use of Markov chain Monte Carlo (MCMC) methods. The paper concludes with a case study, where an MCMC algorithm is used to facilitate the Bayesian system identification of a nonlinear dynamical system from experimentally observed acceleration time histories. PMID:26303916
Stability analysis of a general family of nonlinear positive discrete time-delay systems
NASA Astrophysics Data System (ADS)
Nam, P. T.; Phat, V. N.; Pathirana, P. N.; Trinh, H.
2016-07-01
In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.
Influence of adaptation on the nonlinear dynamics of a system of competing populations
NASA Astrophysics Data System (ADS)
Dimitrova, Zlatinka I.; Vitanov, Nikolay K.
2000-08-01
We investigate the nonlinear dynamics of a system of populations competing for the same limited resource assuming that they can adapt their growth rates and competition coefficients with respect to the number of individuals of each population. The adaptation leads to an enrichment of the nonlinear dynamics of the system which is demonstrated by a discussion of new orbits in the phase space of the system, completely dependent on the adaptation parameters, as well as by an investigation of the influence of the adaptation parameters on the dynamics of a strange attractor of the model system of ODEs.
Time-evolution of quantum systems via a complex nonlinear Riccati equation. II. Dissipative systems
NASA Astrophysics Data System (ADS)
Cruz, Hans; Schuch, Dieter; Castaños, Octavio; Rosas-Ortiz, Oscar
2016-10-01
In our former contribution (Cruz et al., 2015), we have shown the sensitivity to the choice of initial conditions in the evolution of Gaussian wave packets via the nonlinear Riccati equation. The formalism developed in the previous work is extended to effective approaches for the description of dissipative quantum systems. By means of simple examples we show the effects of the environment on the quantum uncertainties, correlation function, quantum energy contribution and tunnelling currents. We prove that the environmental parameter γ is strongly related with the sensitivity to the choice of initial conditions.
Describing the Elephant: Structure and Function in Multivariate Data.
ERIC Educational Resources Information Center
McDonald, Roderick P.
1986-01-01
There is a unity underlying the diversity of models for the analysis of multivariate data. Essentially, they constitute a family of models, most generally nonlinear, for structural/functional relations between variables drawn from a behavior domain. (Author)