NASA Astrophysics Data System (ADS)
Chang, Wei-Der; Yan, Jun-Juh
2006-10-01
In this paper, we propose a novel genetic algorithm (GA) with a multi-crossover fashion to estimate the associated coefficients for a class of nonlinear discrete-time multivariable dynamical systems. Unlike the traditional crossover method of using two chromosomes, the proposed method uses three chromosomes to achieve a crossover. According to the adjusting direction by crossing three chromosomes, more excellent offspring can be produced. To solve the identification problem of multivariable nonlinear discrete-time systems, each of estimated system coefficients represents a gene, and a collection of genes is referred to as a chromosome in the view of GA. The chromosomes in the population are then evolved using the proposed multi-crossover method. An illustrative example of multivariable nonlinear systems is given to demonstrate the effectiveness, as compared with the traditional crossover method, of the proposed method.
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
NASA Astrophysics Data System (ADS)
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.
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.
NASA Technical Reports Server (NTRS)
Sidar, M.
1976-01-01
The problem of identifying constant and variable parameters in multi-input, multi-output, linear and nonlinear systems is considered, using the maximum likelihood approach. An iterative algorithm, leading to recursive identification and tracking of the unknown parameters and the noise covariance matrix, is developed. Agile tracking and accurate and unbiased identified parameters are obtained. Necessary conditions for a globally asymptotically stable identification process are provided; the conditions proved to be useful and efficient. Among different cases studied, the stability derivatives of an aircraft were identified and some of the results are shown as examples.
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. PMID:12424811
Multivariate Padé Approximations For Solving Nonlinear Diffusion Equations
NASA Astrophysics Data System (ADS)
Turut, V.
2015-11-01
In this paper, multivariate Padé approximation is applied to power series solutions of nonlinear diffusion equations. As it is seen from tables, multivariate Padé approximation (MPA) gives reliable solutions and numerical results.
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.
Different approaches to multivariate calibration of nonlinear sensor data.
Dieterle, Frank; Busche, Stefan; Gauglitz, Günter
2004-10-01
In this study, different approaches to the multivariate calibration of the vapors of two refrigerants are reported. As the relationships between the time-resolved sensor signals and the concentrations of the analytes are nonlinear, the widely used partial least-squares regression (PLS) fails. Therefore, different methods are used, which are known to be able to deal with nonlinearities present in data. First, the Box-Cox transformation, which transforms the dependent variables nonlinearly, was applied. The second approach, the implicit nonlinear PLS regression, tries to account for nonlinearities by introducing squared terms of the independent variables to the original independent variables. The third approach, quadratic PLS (QPLS), uses a nonlinear quadratic inner relationship for the model instead of a linear relationship such as PLS. Tree algorithms are also used, which split a nonlinear problem into smaller subproblems, which are modeled using linear methods or discrete values. Finally, neural networks are applied, which are able to model any relationship. Different special implementations, like genetic algorithms with neural networks and growing neural networks, are also used to prevent an overfitting. Among the fast and simpler algorithms, QPLS shows good results. Different implementations of neural networks show excellent results. Among the different implementations, the most sophisticated and computing-intensive algorithms (growing neural networks) show the best results. Thus, the optimal method for the data set presented is a compromise between quality of calibration and complexity of the algorithm. PMID:15156303
System identification for multivariable control
NASA Astrophysics Data System (ADS)
Vanzee, G. A.
1981-05-01
System identification methods and modern control theory are applied to industrial processes. These processes must often be controlled in order to meet certain requirements with respect to the product quality, safety, energy consumption, and environmental load. Modern control system design methods which take the occurring interaction phenomena and stochastic disturbances into account are used. An accurate dynamic mathematical model of the process, by theoretical modelling and/or by system identification is obtained. The computational aspects of two important types of identifications methods, i.e., stochastic realization and prediction error based parameter estimation are studied. The studied computational aspects are the robustness, the accuracy, and the computational costs of the methods. Theoretical analyses and applications to a multivariable pilot scale process, operating under closed loop conditions are investigated.
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.
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.
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.
Output feedback for linear multivariable systems with parameter uncertainty.
NASA Technical Reports Server (NTRS)
Basuthakur, S.; Knapp, C. H.
1973-01-01
A minimax design method is applied to the problem of obtaining an acceptable output feedback matrix for linear multivariable systems with parameter uncertainty. The result is a set of nonlinear matrix equations (similar to those obtained by Levine and Athans (1970)), which must be solved for the feedback matrix. An example illustrates the technique and the fact that better results are achieved for large parameter variation than with a purely nominal design.
Multivariate optimization of production systems
Carroll, J.A.; Horne, R.N. )
1992-07-01
This paper reports that mathematically, optimization involves finding the extreme values of a function. Given a function of several variables, Z = {integral}({rvec x}{sub 1}, {rvec x}{sub 2},{rvec x}{sub 3},{yields}x{sub n}), an optimization scheme will find the combination of these variables that produces an extreme value in the function, whether it is a minimum or a maximum value. Many examples of optimization exist. For instance, if a function gives and investor's expected return on the basis of different investments, numerical optimization of the function will determine the mix of investments that will yield the maximum expected return. This is the basis of modern portfolio theory. If a function gives the difference between a set of data and a model of the data, numerical optimization of the function will produce the best fit of the model to the data. This is the basis for nonlinear parameter estimation. Similar examples can be given for network analysis, queuing theory, decision analysis, etc.
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. PMID:22106143
Estimating the decomposition of predictive information in multivariate systems.
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. PMID:25871169
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.
Intermittent control of unstable multivariate systems.
Loram, I; Gawthrop, P; Gollee, H
2015-08-01
A sensorimotor architecture inspired from biological, vertebrate control should (i) explain the interface between high dimensional sensory analysis, low dimensional goals and high dimensional motor mechanisms and (ii) provide both stability and flexibility. Our interest concerns whether single-input-single-output intermittent control (SISO_IC) generalized to multivariable intermittent control (MIC) can meet these requirements.We base MIC on the continuous-time observer-predictorstate-feedback architecture. MIC uses event detection. A system matched hold (SMH), using the underlying continuoustime optimal control design, generates multivariate open-loop control signals between samples of the predicted state. Combined, this serial process provides a single-channel of control with optimised sensor fusion and motor synergies. Quadratic programming provides constrained, optimised equilibrium control design to handle unphysical configurations, redundancy and provides minimum, necessary reduction of open loop instability through optimised joint impedance. In this multivariate form, dimensionality is linked to goals rather than neuromuscular or sensory degrees of freedom. The biological and engineering rationale for intermittent rather than continuous multivariate control, is that the generalised hold sustains open loop predictive control while the open loop interval provides time within the feedback loop for online centralised, state dependent optimisation and selection. PMID:26736539
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
NASA Astrophysics Data System (ADS)
Leeds, W. B.; Wikle, C. K.
2012-12-01
Spatio-temporal statistical models, and in particular Bayesian hierarchical models (BHMs), have become increasingly popular as means of representing natural processes such as climate and weather that evolve over space and time. Hierarchical models make it possible to specify separate, conditional probability distributions that account for uncertainty in the observations, the underlying process, and parameters in situations when specifying these sources of uncertainty in a joint probability distribution may be difficult. As a result, BHMs are a natural setting for climatologists, meteorologists, and other environmental scientists to incorporate scientific information (e.g., PDEs, IDEs, etc.) a priori into a rigorous statistical framework that accounts for error in measurements, uncertainty in the understanding of the true underlying process, and uncertainty in the parameters that describe the process. While much work has been done in the development of statistical models for linear dynamic spatio-temporal processes, statistical modeling for nonlinear (and particularly, multivariate nonlinear) spatio-temporal dynamical processes is still a relatively open area of inquiry. As a result, general statistical models for environmental scientists to model complicated nonlinear processes is limited. We address this limitation in the methodology by introducing a multivariate "general quadratic nonlinear" framework for modeling multivariate, nonlinear spatio-temporal random processes inside of a BHM in a way that is especially applicable for problems in the ocean and atmospheric sciences. We show that in addition to the fact that this model addresses the previously mentioned sources of uncertainty for a wide spectrum of multivariate, nonlinear spatio-temporal processes, it is also a natural framework for data assimilation, allowing for the fusing of observations with computer models, computer model emulators, computer model output, or "mechanistically motivated" statistical
Compensator improvement for multivariable control systems
NASA Technical Reports Server (NTRS)
Mitchell, J. R.; Mcdaniel, W. L., Jr.; Gresham, L. L.
1977-01-01
A theory and the associated numerical technique are developed for an iterative design improvement of the compensation for linear, time-invariant control systems with multiple inputs and multiple outputs. A strict constraint algorithm is used in obtaining a solution of the specified constraints of the control design. The result of the research effort is the multiple input, multiple output Compensator Improvement Program (CIP). The objective of the Compensator Improvement Program is to modify in an iterative manner the free parameters of the dynamic compensation matrix so that the system satisfies frequency domain specifications. In this exposition, the underlying principles of the multivariable CIP algorithm are presented and the practical utility of the program is illustrated with space vehicle related examples.
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
Tortajada-Genaro, L A; Campíns-Falcó, P
2007-05-15
Multivariate standardisation is proposed for the successful chemiluminescence determination of chromium based on luminol-hydrogen peroxide reaction. In an extended concentration range, non-linear calibration model is needed. The studied instrumental situations were different detection cells, instruments, assemblies, time and their possible combinations. Chemiluminescence kinetic registers have been transferred using piecewise direct standardisation (PDS) method. The optimisation of transfer parameters has been carried out based on the prediction residual error criteria. Non-linear principal component regression (NL-PCR) and non-linear partial least square regression (NL-PLS) were chosen for modelling the relationship signal-concentration of transferred registers. Good accuracy and precision were obtained for water samples. The concentrations of chromium were statistically in agreement with reference method values and with recovery studies. Therefore, it is possible to transfer chemiluminescence curves without loosing ability of prediction, even the presence of a non-linear behaviour. PMID:19071716
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.
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.
Dr. Katja Lindenberg
2005-11-20
During the one-year period 2004-2005 our work continued to focus on nonlinear noisy systems, with special attention to spatially extended systems. There is a history of many decades of research in the sciences and engineering on the behavior of noninear noisy systems, but only in the past ten years or so has a theoretical understanding of spatially extended systems begun to emerge. This has been the outcome of a symbiosis of numerical simulations not possible until recently, laboratory experiments, and new analytic methods.
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
NASA Astrophysics Data System (ADS)
Irving, A. D.; Dewson, T.
1997-02-01
A new method is described for extracting mixed linear-nonlinear coupled differential equations from multivariate discrete time series data. It is assumed in the present work that the solution of the coupled ordinary differential equations can be represented as a multivariate Volterra functional expansion. A tractable hierarchy of moment equations is generated by operating on a suitably truncated Volterra functional expansion. The hierarchy facilitates the calculation of the coefficients of the coupled differential equations. In order to demonstrate the method's ability to accurately estimate the coefficients of the governing differential equations, it is applied to data derived from the numerical solution of the Lorenz equations with additive noise. The method is then used to construct a dynamic global mid- and high-magnetic latitude ionospheric model where nonlinear phenomena such as period doubling and quenching occur. It is shown that the estimated inhomogeneous coupled second-order differential equation model for the ionospheric foF2 peak plasma density can accurately forecast the future behaviour of a set of ionosonde stations which encompass the earth. Finally, the method is used to forecast the future behaviour of a portfolio of Japanese common stock prices. The hierarchy method can be used to characterise the observed behaviour of a wide class of coupled linear and mixed linear-nonlinear phenomena.
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.
NASA Astrophysics Data System (ADS)
Kourehli, S. S.
2015-07-01
Damage detection and estimation in structures using incomplete modal data is presented. In the proposed approach, damage location and severity is determined by solving an optimization problem using the constrained nonlinear multivariable function of Matlab (so- called fmincon) to perform constrained minimization. The feasibility of the presented method is validated with a three-story plane frame as numerical example containing one or several damages with different value of damage severity. The obtained results indicated that proposed method is effective and robust in detection and estimation of damage.
NASA Technical Reports Server (NTRS)
Turner, L. R.
1960-01-01
The problem of solving systems of nonlinear equations has been relatively neglected in the mathematical literature, especially in the textbooks, in comparison to the corresponding linear problem. Moreover, treatments that have an appearance of generality fail to discuss the nature of the solutions and the possible pitfalls of the methods suggested. Probably it is unrealistic to expect that a unified and comprehensive treatment of the subject will evolve, owing to the great variety of situations possible, especially in the applied field where some requirement of human or mechanical efficiency is always present. Therefore we attempt here simply to pose the problem and to describe and partially appraise the methods of solution currently in favor.
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 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 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.
Power system stability improvement with multivariable self-tuning control
Fan, J.Y.; Ortmeyer, T.H.; Mukundan, R. )
1990-02-01
A multivariable self-tuning adaptive control scheme is presented. This scheme is of a decentralized nature and is implemented locally for individual generating units. A discrete multivariable auto-regressive-moving-average model is developed to represent a generating unit. The recursive-least-squares (RLS) estimation algorithm with variable-forgetting factor and the generalized-minimum-variance control technique are utilized to synthesize the local controllers. A dynamic goal-point-generating model is introduced to provide varying goal point for the local controller which leads the subsystem output to its equilibrium gradually. Extensive simulations are performed on the IEEE 10-machine test system. The results show that the proposed multivariable adaptive control scheme is effective in damping the severe oscillations after large disturbances as well as improving the system dynamics under small oscillations and is better than the conventional PSS method. The controller demonstrates robustness and is compatible with the existing conventional controllers in multimachine systems.
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.
NASA Astrophysics Data System (ADS)
Deng, Linhua
2015-07-01
Three nonlinear analysis techniques, including cross-recurrence plot, line of synchronization, and cross-wavelet transform, are proposed to estimate the coherent phase vibrations of nonlinear and non-stationary time series. The case study utilizes the monthly averages of sunspot areas during the time interval from May 1874 to August 2014. The following prominent results are found: (1) the phase-leading hemisphere of long-term sunspot areas has changed twice in the past 140 years, indicating that the hemispheric imbalances and apparent phase differences on both hemispheres are a prevalent behavior and are not anomalous; (2) the alternating regularity of hemispheric asynchronism exhibits a cyclical pattern of 4.5+3.5 cycles, and the magnetic flux excess in a certain hemisphere during the ascending branch of a cycle can be taken as an indication of the phase-leading hemisphere in this cycle. We firmly believe that powerful nonlinear approaches are more advanced than classical linear methods when they are combined to determine the dynamic complexity of nonlinear physical systems.
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.
Nonlinear dynamical systems analyzer
NASA Astrophysics Data System (ADS)
Coffey, Adrian S.; Johnson, Martin; Jones, Robin
1994-10-01
Computationally intensive algorithms are an ever more common requirement of modern signal processing. Following the work of Gentleman and Kung, McWhirter, Shepherd and Proudler suggested that certain matrix-orientated algorithms can be mapped onto systolic array architectures for adaptive linear signal processing. This has been extended by Broomhead et al. to the calculation of nonlinear predictive models and applied by Jones et al. to target identification and recognition. We shall show that predictive models are extremely sharp discriminators. Our chosen problem, if implemented as a systolic array, would require 3403 processors which would result in high through-put rate at excessive cost. We are developing an efficient sub-optimally implemented systolic array; one processor servicing more than one systolic node. We describe a prototype Heuristic Processor which computes a multi- dimensional, nonlinear, predictive model. It consists of a Radial Basis Function Network and a least squares optimizer using QR decomposition. The optimized solution of a set of simultaneous equations in 81 unknowns is calculated in 150 (mu) S. The QR section emulates a triangular systolic array by the novel use of an array of 40 mature silicon DSP chips costing under DOL100 each. The DSP chips operate in synchronism at a 50 MHz clock rate passing data to each other through multi-port memories on a dead-letter box principle; there are no memory access conflicts and only two-port and three-port memories are required. The processor provides 1-GFlop of computing power per cubic-foot of electronics for a component cost of approximately DOL15,000.
Canonical forms for nonlinear systems
NASA Technical Reports Server (NTRS)
Su, R.; Hunt, L. R.; Meyer, G.
1983-01-01
Necessary and sufficient conditions for transforming a nonlinear system to a controllable linear system have been established, and this theory has been applied to the automatic flight control of aircraft. These transformations show that the nonlinearities in a system are often not intrinsic, but are the result of unfortunate choices of coordinates in both state and control variables. Given a nonlinear system (that may not be transformable to a linear system), we construct a canonical form in which much of the nonlinearity is removed from the system. If a system is not transformable to a linear one, then the obstructions to the transformation are obvious in canonical form. If the system can be transformed (it is called a linear equivalent), then the canonical form is a usual one for a controllable linear system. Thus our theory of canonical forms generalizes the earlier transformation (to linear systems) results. Our canonical form is not unique, except up to solutions of certain partial differential equations we discuss. In fact, the important aspect of this paper is the constructive procedure we introduce to reach the canonical form. As is the case in many areas of mathematics, it is often easier to work with the canonical form than in arbitrary coordinate variables.
A method for designing robust multivariable feedback systems
NASA Technical Reports Server (NTRS)
Milich, David A.; 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.
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.
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.
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
Steady state decoupling and design of linear multivariable systems
NASA Technical Reports Server (NTRS)
Huang, J. Y.; Thaler, G. J.
1974-01-01
A constructive criterion for decoupling the steady states of linear multivariable systems is developed. The criterion consists of n(n-1) inequalities with the type numbers of the compensator transfer functions as the unknowns. These unknowns can be chosen to satisfy the inequalities and hence achieve a steady state decoupling scheme. It turns out that pure integrators in the loops play an important role. An extended root locus design method is then developed to take care of the stability and transient response. The overall procedure is applied to the compensation design for STOL C-8A aircraft in the approach mode.
NASA Technical Reports Server (NTRS)
Bosworth, John T.; Burken, John J.
1997-01-01
Safety and productivity of the initial flight test phase of a new vehicle have been enhanced by developing the ability to measure the stability margins of the combined control system and vehicle in flight. One shortcoming of performing this analysis is the long duration of the excitation signal required to provide results over a wide frequency range. For flight regimes such as high angle of attack or hypersonic flight, the ability to maintain flight condition for this time duration is difficult. Significantly reducing the required duration of the excitation input is possible by tailoring the input to excite only the frequency range where the lowest stability margin is expected. For a multiple-input/multiple-output system, the inputs can be simultaneously applied to the control effectors by creating each excitation input with a unique set of frequency components. Chirp-Z transformation algorithms can be used to match the analysis of the results to the specific frequencies used in the excitation input. This report discusses the application of a tailored excitation input to a high-fidelity X-31A linear model and nonlinear simulation. Depending on the frequency range, the results indicate the potential to significantly reduce the time required for stability measurement.
Multivariable control of the Space Shuttle Remote Manipulator System
NASA Technical Reports Server (NTRS)
Adams, Neil J.; Appleby, Brent D.; Prakash, OM, II
1991-01-01
Linear controllers are designed to regulate the end effector of the Space Shuttle Remote Manipulator System (SRMS) operating in position hold mode. Design techniques used include H2 and H-infinity optimization. The nonlinear SRMS is linearized by modeling the effects of the significant nonlinearities as uncertain parameters. Each regulator design is evaluated for robust stability using both the small gain theorem with an H-infinity norm and the less conservative mu-analysis test. Regulator designs offer significant improvement over the current system for the nominal plant. Unfortunately, the SRMS model suffers from lightly damped poles with real parametric uncertainty. Under such conditions, the mu-analysis test, which allows for complex perturbations, cannot guarantee robust stability.
Modeling of Nonlinear Systems using Genetic Algorithm
NASA Astrophysics Data System (ADS)
Hayashi, Kayoko; Yamamoto, Toru; Kawada, Kazuo
In this paper, a newly modeling system by using Genetic Algorithm (GA) is proposed. The GA is an evolutionary computational method that simulates the mechanisms of heredity or evolution of living things, and it is utilized in optimization and in searching for optimized solutions. Most process systems have nonlinearities, so it is necessary to anticipate exactly such systems. However, it is difficult to make a suitable model for nonlinear systems, because most nonlinear systems have a complex structure. Therefore the newly proposed method of modeling for nonlinear systems uses GA. Then, according to the newly proposed scheme, the optimal structure and parameters of the nonlinear model are automatically generated.
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.
Multivariate optimization of production systems: The time dimension
Ravindran, N.; Horne, R.N.
1993-04-01
Traditional analysis of oil and gas production systems treats individual nodes one at a time. This only calculates a feasible solution which is not necessarily optimal. Multivariate optimization is able to determine the most profitable configuration, including all variables simultaneously. The optimization can also find the optimal recovery over a period of time, rather than just at a single instant as in traditional methods. This report describes the development of multivariate optimization for situations in which the decision variables may change as a function of time. For example, instead of estimating a tubing size which is optimal over the life of the project, this approach determines a series of optimal tubing sizes which may change from year to year. Examples show that under an optimal strategy, tubing size can be changed only infrequently while still increasing profitability of a project. The methods used in this work considered the special requirements of objectives which are not smooth functions of their decision variables. The physical problems considered included artificial lift production systems.
Multivariable control system installed at ARCO west Texas gas plant
Chou, K. ); Clay, R.M. ); Gamez, J.P. ); Berkowitz, P.N.; Papadopoulos, M.N. )
1992-11-16
This paper reports that a PC-based, multivariable process control (MVC) system was installed last year at an ARCO Oil and Gas Co. gas plant in West Texas. This gas-processing application was developed under sponsorship of the Gas Research Institute. The system was installed, tuned, and on-line within 2 weeks and fully verified in closed loop service by operations in 8 weeks. Four more gas processing installations are currently under way. The general and main objective of the MVC control system is to achieve continuous optimum operation of a process unit through on-line prediction and control of setpoints for the key process variables in the unit. specifically, the objective is to achieve this operation, especially under constantly changing conditions, with reliable solutions requiring minimal operator intervention, customization, or update effort upon each plant change. MVC was developed by continental Controls Inc. (CCI), Houston.
Theoretical constraints in the design of multivariable control systems
NASA Technical Reports Server (NTRS)
Rynaski, E. G.; Mook, D. J.
1993-01-01
The theoretical constraints inherent in the design of multivariable control systems were defined and investigated. These constraints are manifested by the system transmission zeros that limit or bound the areas in which closed loop poles and individual transfer function zeros may be placed. These constraints were investigated primarily in the context of system decoupling or non-interaction. It was proven that decoupling requires the placement of closed loop poles at the system transmission zeros. Therefore, the system transmission zeros must be minimum phase to guarantee a stable decoupled system. Once decoupling has been accomplished, the remaining part of the system exhibits transmission zeros at infinity, so nearly complete design freedom is possible in terms of placing both poles and zeros of individual closed loop transfer functions. A general, dynamic inversion model following system architecture was developed that encompasses both the implicit and explicit configuration. Robustness properties are developed along with other attributes of this type of system. Finally, a direct design is developed for the longitudinal-vertical degrees of freedom of aircraft motion to show how a direct lift flap can be used to improve the pitch-heave maneuvering coordination for enhanced flying qualities.
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.
Describing functions for nonlinear optical systems.
Ghosh, A K
1997-10-10
The concept of describing functions is useful for analyzing and designing nonlinear systems. A proposal for using the idea of describing functions for studying the behavior of a nonlinear optical processing system is given. The describing function can be used in the same way that a coherent transfer function or optical transfer function is used to characterize linear, shift-invariant optical processors. Two coherent optical systems for measuring the magnitude of the describing function of nonlinear optical processors are suggested. PMID:18264243
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.
Harinath, Eranda; Mann, George K I
2008-06-01
This paper describes a design and two-level tuning method for fuzzy proportional-integral derivative (FPID) controllers for a multivariable process where the fuzzy inference uses the inference of standard additive model. The proposed method can be used for any n x n multi-input-multi-output process and guarantees closed-loop stability. In the two-level tuning scheme, the tuning follows two steps: low-level tuning followed by high-level tuning. The low-level tuning adjusts apparent linear gains, whereas the high-level tuning changes the nonlinearity in the normalized fuzzy output. In this paper, two types of FPID configurations are considered, and their performances are evaluated by using a real-time multizone temperature control problem having a 3 x 3 process system. PMID:18558531
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.
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.
Steinhaeuser, Karsten J K; Ganguly, Auroop R; Chawla, Nitesh
2011-01-01
A systematic characterization of multivariate dependence at multiple spatio-temporal scales is critical to understanding climate system dynamics and improving predictive ability from models and data. However, dependence structures in climate are complex due to nonlinear dynamical generating processes, long-range spatial and long-memory temporal relationships, as well as low-frequency variability. Here we utilize complex networks to explore dependence in climate data. Specifically, networks constructed from reanalysis-based atmospheric variables over oceans and partitioned with community detection methods demonstrate the potential to capture regional and global dependence structures within and among climate variables. Proximity-based dependence as well as long-range spatial relationships are examined along with their evolution over time, yielding new insights on ocean meteorology. The tools are implicitly validated by confirming conceptual understanding about aggregate correlations and teleconnections. Our results also suggest a close similarity of observed dependence patterns in relative humidity and horizontal wind speed over oceans. In addition, updraft velocity, which relates to convective activity over the oceans, exhibits short spatiotemporal decorrelation scales but long-range dependence over time. The multivariate and multi-scale dependence patterns broadly persist over multiple time windows. Our findings motivate further investigations of dependence structures among observations, reanalysis and model-simulated data to enhance process understanding, assess model reliability and improve regional climate predictions.
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.
Berry phase in nonlinear systems
Liu, J.; Fu, L. B.
2010-05-15
The Berry phase acquired by an eigenstate that experienced a nonlinear adiabatic evolution is investigated thoroughly. The circuit integral of the Berry connection of the instantaneous eigenstate cannot account for the adiabatic geometric phase, while the Bogoliubov excitations around the eigenstates are found to be accumulated during the nonlinear adiabatic evolution and contribute a finite phase of geometric nature. A two-mode model is used to illustrate our theory. Our theory is applicable to Bose-Einstein condensate, nonlinear light propagation, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics.
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…
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.
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.
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.
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.
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.
Markovian master equation for nonlinear systems
NASA Astrophysics Data System (ADS)
de los Santos-Sánchez, O.; Récamier, J.; Jáuregui, R.
2015-06-01
Within the f-deformed oscillator formalism, we derive a Markovian master equation for the description of the damped dynamics of nonlinear systems that interact with their environment. The applicability of this treatment to the particular case of a Morse-like oscillator interacting with a thermal field is illustrated, and the decay of quantum coherence in such a system is analyzed in terms of the evolution on phase space of its nonlinear coherent states via the Wigner function.
Chaotic dynamics of weakly nonlinear systems
Vavriv, D.M.
1996-06-01
A review is given on the recent results in studying chaotic phenomena in weakly nonlinear systems. We are concerned with the class of chaotic states that can arise in physical systems with any degree of nonlinearity however small. The conditions for, and the mechanisms of, the transitions to chaos are discussed. These findings are illustrated by the results of the stability analysis of practical microwave and optical devices. {copyright} {ital 1996 American Institute of Physics.}
The effect of system nonlinearities on system noise statistics
NASA Technical Reports Server (NTRS)
Robinson, L. H., Jr.
1971-01-01
The effects are studied of nonlinearities in a baseline communications system on the system noise amplitude statistics. So that a meaningful identification of system nonlinearities can be made, the baseline system is assumed to transmit a single biphase-modulated signal through a relay satellite to the receiving equipment. The significant nonlinearities thus identified include square-law or product devices (e.g., in the carrier reference recovery loops in the receivers), bandpass limiters, and traveling wave tube amplifiers.
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.
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
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.
Impulsive synchronization of networked nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Jiang, Haibo; Bi, Qinsheng
2010-06-01
In this Letter, we investigate the problem of impulsive synchronization of networked multi-agent systems, where each agent can be modeled as an identical nonlinear dynamical system. Firstly, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the synchronization of the networked nonlinear dynamical system by using algebraic graph theory and impulsive control theory. Furthermore, how to select the discrete instants and impulsive constants is discussed. The case that the topologies of the networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.
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.
NASA Astrophysics Data System (ADS)
Athans, M.; Lee, W. H.; Lehtomaki, N. A.; Levy, B. C.; Ng, P. T. P.
1982-05-01
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 and new 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 of a single-input, single-output (SISO) 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 of linear-quadratic-Gaussian control systems are analyzed via this robustness theory and multiloop stability margins are presented; in particular, a new type of margin, a cross-feed margin, is introduced. Other frequency domain analysis and design techniques are also briefly discussed and their relation to the present robustness analysis is examined. In addition a linear-quadratic based design procedure that quarantees a prescribed degree of stability is developed, with special emphasis upon its robustness properties.
Decoupling in linear time-varying multivariable systems
NASA Technical Reports Server (NTRS)
Sankaran, V.
1973-01-01
The necessary and sufficient conditions for the decoupling of an m-input, m-output, linear time varying dynamical system by state variable feedback is described. The class of feedback matrices which decouple the system are illustrated. Systems which do not satisfy these results are described and systems with disturbances are considered. Some examples are illustrated to clarify the results.
Quadratic boundedness of uncertain nonlinear dynamic systems
NASA Astrophysics Data System (ADS)
Brockman, Mark Lawrence
Physical systems are often perturbed by unknown external disturbances or contain important system parameters which are difficult to model exactly. However, engineers are expected to design systems which perform well even in the presence of uncertainties. For example, an airplane designer can never know the precise direction or magnitude of wind gusts, or the exact mass distribution inside the aircraft, but passengers expect to arrive on time after a smooth ride. This thesis will first present the concept of quadratic boundedness of an uncertain nonlinear dynamic system, and then develop analysis techniques and control design methods for systems containing unknown disturbances and parameters. For a class of nonlinear systems, conditions for quadratic boundedness are given, and the relationship between quadratic boundedness and quadratic stability is explored. An important consequence of quadratic boundedness is the ability to calculate an upper bound on the system gain of an uncertain nonlinear system. For nominally linear systems, necessary and sufficient conditions for quadratic boundedness are given. The innovative use of linear matrix inequalities in an iterative algorithm provides a means to analyze the quadratic boundedness properties of systems containing parameter uncertainties. The analysis results establish a framework for the development of design methods which integrate performance specifications into the control design process for all the types of systems considered. Numerous examples illustrate the major results of the thesis.
Evolutionary quantitative genetics of nonlinear developmental systems.
Morrissey, Michael B
2015-08-01
In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium-term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time-steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances. PMID:26174586
Simple method of designing centralized PI controllers for multivariable systems based on SSGM.
Dhanya Ram, V; Chidambaram, M
2015-05-01
A method is given to design multivariable PI/PID controllers for stable and unstable multivariable systems. The method needs only the steady state gain matrix (SSGM). The method is based on the static decoupler design followed by SISO PI/PID controllers design and combining the resulted decoupler and the diagonal PI(D) controllers as the centralized controllers. The result of the present method is shown to be equivalent to the empirical method proposed by Davison EJ. Multivariable tuning regulators: the feed-forward and robust control of general servo-mechanism problem. IEEE Trans Autom Control 1976;21:35-41. Three simulation examples are given. The performance of the controllers is compared with that of the reported centralized controller based on the multivariable transfer function matrix. PMID:25530257
Stochastic Satbility and Performance Robustness of Linear Multivariable Systems
NASA Technical Reports Server (NTRS)
Ryan, Laurie E.; Stengel, Robert F.
1990-01-01
Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.
A new method for observing the running states of a single-variable nonlinear system.
Meng, Yu; Chen, Hong; Chen, Cheng
2015-03-01
In order to timely grasp a single variable nonlinear system running states, a new method called Scatter Point method is put forward in this paper. It can be used to observe or monitor the running states of a single variable nonlinear system in real-time. In this paper, the definition of the method is given at first, and then its working principle is expounded theoretically, after this, some physical experiments based on Chua's nonlinear system are conducted. At the same time, many scatter point graphs are measured by a general analog oscilloscope. The motion, number, and distribution of these scatter points shown on the oscilloscope screen can directly reflect the current states of the tested system. The experimental results further confirm that the method is effective and practical, in which the system running states are not easily lost. In addition, this method is not only suitable for single variable systems but also for multivariable systems. PMID:25833428
Squeezing spectra for nonlinear optical systems
NASA Technical Reports Server (NTRS)
Collett, M. J.; Walls, D. F.
1985-01-01
The squeezing spectra for the output fields of several intracavity nonlinear optical systems are obtained. It is shown that at critical points, e.g., the turning points for optical bistability, the threshold for parametric oscillation, and the self-pulsing instability in second-harmonic generation, perfect squeezing in the output field is, in principle, possible.
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.
Computer-Aided Decisions in Human Services: Expert Systems and Multivariate Models.
ERIC Educational Resources Information Center
Sicoly, Fiore
1989-01-01
This comparison of two approaches to the development of computerized supports for decision making--expert systems and multivariate models--focuses on computerized systems that assist professionals with tasks related to diagnosis or classification in human services. Validation of both expert systems and statistical models is emphasized. (39…
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 Astrophysics Data System (ADS)
Li, Heng; Ren, Changzhi; Song, Libin; Wu, Jun
2014-07-01
The direct drive tracking system of Telescope is one multivariable, nonlinear and strong coupling complex mechanical control system which is disturbed by some nonlinear disturbance such torque ripple, wind disturbance during the tracking process. the traditional PID control cannot fundamentally solved the contradiction between static and dynamic performance, tracking data and disturbance .This paper explores a kind of CMAC with nonlinear PID parallel composite control method for dual redundant telescope tracing servo system. The simulation result proves that combined algorithm based on CMAC and PID realizes the servo system without overshoot and accelerates the response of the system. What's more, CMAC feedforward control improves anti-disturbance ability and the control precision of the servo system.
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.
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.
Hypoglycemia Early Alarm Systems Based On Multivariable Models
Turksoy, Kamuran; Bayrak, Elif S; Quinn, Lauretta; Littlejohn, Elizabeth; Rollins, Derrick; Cinar, Ali
2013-01-01
Hypoglycemia is a major challenge of artificial pancreas systems and a source of concern for potential users and parents of young children with Type 1 diabetes (T1D). Early alarms to warn the potential of hypoglycemia are essential and should provide enough time to take action to avoid hypoglycemia. Many alarm systems proposed in the literature are based on interpretation of recent trends in glucose values. In the present study, subject-specific recursive linear time series models are introduced as a better alternative to capture glucose variations and predict future blood glucose concentrations. These models are then used in hypoglycemia early alarm systems that notify patients to take action to prevent hypoglycemia before it happens. The models developed and the hypoglycemia alarm system are tested retrospectively using T1D subject data. A Savitzky-Golay filter and a Kalman filter are used to reduce noise in patient data. The hypoglycemia alarm algorithm is developed by using predictions of future glucose concentrations from recursive models. The modeling algorithm enables the dynamic adaptation of models to inter-/intra-subject variation and glycemic disturbances and provides satisfactory glucose concentration prediction with relatively small error. The alarm systems demonstrate good performance in prediction of hypoglycemia and ultimately in prevention of its occurrence. PMID:24187436
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.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Stevens, P. K.
1981-01-01
This paper presents a generalization of the Nyquist stability criterion to include general multivariable linear stationary systems subject to linear static and dynamic feedback. At the same time, a unifying proof is given for all known versions of the Nyquist criterion for finite dimensional systems.
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.
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.
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.
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.
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.
Structural analysis and design of multivariable control systems: An algebraic approach
NASA Technical Reports Server (NTRS)
Tsay, Yih Tsong; Shieh, Leang-San; Barnett, Stephen
1988-01-01
The application of algebraic system theory to the design of controllers for multivariable (MV) systems is explored analytically using an approach based on state-space representations and matrix-fraction descriptions. Chapters are devoted to characteristic lambda matrices and canonical descriptions of MIMO systems; spectral analysis, divisors, and spectral factors of nonsingular lambda matrices; feedback control of MV systems; and structural decomposition theories and their application to MV control systems.
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. PMID:25433943
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.
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 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.
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.
Singularity perturbed zero dynamics of nonlinear systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.
1992-01-01
Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.
Explaining Student Success and Failure in a Distance Teaching System: A Multi-variate Approach.
ERIC Educational Resources Information Center
Woodley, Alan
A multivariate model to explain student success and failure at the Open University of the United Kingdom is outlined. The model is based on the results of an evaluation study that explored the suitability of this teaching system for young people under 21 years old. Twenty-three characteristics were designated as social and psychological problems,…
On the applicability of eigenvalue/eigenvector assignment in multivariable systems
NASA Technical Reports Server (NTRS)
Liberty, S. R.; Mielke, R. R.
1979-01-01
The technique of multivariable control-system design via assignment of the closed loop state matrix eigensystem is described. Features of this developing methodology include exact eigenvalue assignment, eigenvector assignment that approximates in a least squares sense a priori modal specifications, and an interactive design trade-off between the latter and desired eigensystem sensitivity with respect to plant parameters.
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
Linear pattern dynamics in nonlinear threshold systems
Rundle, John B.; Klein, W.; Tiampo, Kristy; Gross, Susanna
2000-03-01
Complex nonlinear threshold systems frequently show space-time behavior that is difficult to interpret. We describe a technique based upon a Karhunen-Loeve expansion that allows dynamical patterns to be understood as eigenstates of suitably constructed correlation operators. The evolution of space-time patterns can then be viewed in terms of a ''pattern dynamics'' that can be obtained directly from observable data. As an example, we apply our methods to a particular threshold system to forecast the evolution of patterns of observed activity. Finally, we perform statistical tests to measure the quality of the forecasts. (c) 2000 The American Physical Society.
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.
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 Tides in Close Binary Systems
NASA Astrophysics Data System (ADS)
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' >~ 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static "equilibrium" tidal distortion is, however, stable to parametric resonance except for solar binaries with P <~ 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 ≈ 103[P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the
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
Optimal and multivariable control of a turbogenerator
NASA Astrophysics Data System (ADS)
Lahoud, M. A.; Harley, R. G.; Secker, A.
The use of modern control methods to design multivariable controllers which improve the performance of a turbogenerator was investigated. The turbogenerator nonlinear mathematical model from which a linearized model is deduced is presented. The inverse Nyquist Array method and the theory of optimal control are both applied to the linearized model to generate two alternative control schemes. The schemes are implemented on the nonlinear simulation model to assess their dynamic performance. Results from modern multivariable control schemes are compared with the classical automatic voltage regulator and speed governor system.
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.
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.
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
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
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
Impulse position control algorithms for nonlinear systems
NASA Astrophysics Data System (ADS)
Sesekin, A. N.; Nepp, A. N.
2015-11-01
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.
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.
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.
Optimal uniform-damping ratio controller for sequential design of multivariable systems
NASA Technical Reports Server (NTRS)
Shieh, Leang G.; Liu, Zhen; Sunkel, John W.
1991-01-01
An optimal uniform-damping ratio controller is developed for the sequential design of a multivariable control system so that the designed closed-loop poles of the respective multivariable system and reduced-order observer are exactly placed on the negative real axis and/or the boundaries of desired sectors with constant-damping ratios. The functions in the quadratic performance index to be minimized are chosen as a combination of the weighted outputs, reduced states and inputs. Also, the optimal uniform-damping ratio controller is a combination of optimal output-feedback and optimal reduced-order state-feedback controllers. A numerical example is given to demonstrate the design procedure.
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.
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.
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.
Direct adaptive control for nonlinear uncertain dynamical systems
NASA Astrophysics Data System (ADS)
Hayakawa, Tomohisa
In light of the complex and highly uncertain nature of dynamical systems requiring controls, it is not surprising that reliable system models for many high performance engineering and life science applications are unavailable. In the face of such high levels of system uncertainty, robust controllers may unnecessarily sacrifice system performance whereas adaptive controllers are clearly appropriate since they can tolerate far greater system uncertainty levels to improve system performance. In this dissertation, we develop a Lyapunov-based direct adaptive and neural adaptive control framework that addresses parametric uncertainty, unstructured uncertainty, disturbance rejection, amplitude and rate saturation constraints, and digital implementation issues. Specifically, we consider the following research topics; direct adaptive control for nonlinear uncertain systems with exogenous disturbances; robust adaptive control for nonlinear uncertain systems; adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints; adaptive reduced-order dynamic compensation for nonlinear uncertain systems; direct adaptive control for nonlinear matrix second-order dynamical systems with state-dependent uncertainty; adaptive control for nonnegative and compartmental dynamical systems with applications to general anesthesia; direct adaptive control of nonnegative and compartmental dynamical systems with time delay; adaptive control for nonlinear nonnegative and compartmental dynamical systems with applications to clinical pharmacology; neural network adaptive control for nonlinear nonnegative dynamical systems; passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems; neural network adaptive dynamic output feedback control for nonlinear nonnegative systems using tapped delay memory units; Lyapunov-based adaptive control framework for discrete-time nonlinear systems with exogenous disturbances
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.
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
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
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.
Dagne, Getachew; Huang, Yangxin
2016-01-01
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
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
Nonlinear resonant phenomena in multilevel quantum systems
NASA Astrophysics Data System (ADS)
Hicke, Christian
We study nonlinear resonant phenomena in two-level and multilevel quantum systems. Our results are of importance for applications in the areas of quantum control, quantum computation, and quantum measurement. We present a method to perform fault-tolerant single-qubit gate operations using Landau-Zener tunneling. In a single Landau-Zoner pulse, the qubit transition frequency is varied in time so that it passes through the frequency of a radiation field. We show that a simple three-pulse sequence allows eliminating errors in the gate up to the third order in errors in the qubit energies or the radiation frequency. We study the nonlinear transverse response of a spin S > 1/2 with easy-axis anisotropy. The coherent transverse response displays sharp dips or peaks when the modulation frequency is adiabatically swept through multiphoton resonance. The effect is a consequence of a certain conformal property of the spin dynamics in a magnetic field for the anisotropy energy ∝ S2z . The occurrence of the dips or peaks is determined by the spin state. Their shape strongly depends on the modulation amplitude. Higher-order anisotropy breaks the symmetry, leading to sharp steps in the transverse response as function of frequency. The results bear on the dynamics of molecular magnets in a static magnetic field. We show that a modulated large-spin system has special symmetry. In the presence of dissipation it leads to characteristic nonlinear effects. They include abrupt switching between transverse magnetization branches with varying modulating field without hysteresis and a specific pattern of switching in the presence of multistability and hysteresis. Along with steady forced vibrations the transverse spin components can display transient vibrations at a combination of the Larmor frequency and a slower frequency determined by the anisotropy energy. The analysis is based on a microscopic theory that takes into account relaxation mechanisms important for single
Sivasamy, Aneetha Avalappampatty; 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 T(2) 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 T(2) 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
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.
Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings
Kadtke, J.B.; Bulsara, A.
1997-12-01
These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)
Experimental nonlinear laser systems: Bigger data for better science?
NASA Astrophysics Data System (ADS)
Kane, D. M.; Toomey, J. P.; McMahon, C.; Noblet, Y.; Argyris, A.; Syvridis, D.
2014-10-01
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.
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.
Nonlinear energy transfer in classical and quantum systems.
Manevitch, Leonid; Kovaleva, Agnessa
2013-02-01
In this paper we investigate the effect of slowly-varying parameters on the energy transfer in a weakly coupled system. For definiteness, we consider a system of two nonlinear oscillators, in which the directly excited first oscillator with constant parameter is attached to the oscillator with slowly time-varying frequency. It is proved that the equations of the slow passage through resonance in this system are identical to the equations of nonlinear Landau-Zener (LZ) tunneling. Three types of dynamical behavior are distinguished, namely, quasilinear, moderately nonlinear, and strongly nonlinear ones. Quasilinear systems exhibit a gradual energy transfer from the excited to the attached oscillator, while moderately nonlinear systems are characterized by an abrupt transition from the energy localization on the excited oscillator to the localization on the attached oscillator. In strongly nonlinear systems, the transition from the energy localization to strong energy exchange between the oscillators is revealed. Explicit approximate solutions describing the transient processes in moderately and strongly nonlinear systems are suggested. Correctness of the constructed approximations is confirmed by numerical results. The results presented in this paper, in addition to providing an analytical framework for understanding the transient dynamics, suggest an approximate procedure for solving the nonlinear LZ problem with arbitrary initial conditions over a finite time-interval. PMID:23496588
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.
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.
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.
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.
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.
Sakhanenko, Nikita A.; Skupin, Alexander; Ignac, Tomasz
2014-01-01
Abstract Context dependence is central to the description of complexity. Keying on the pairwise definition of “set complexity,” we use an information theory approach to formulate general measures of systems complexity. We examine the properties of multivariable dependency starting with the concept of interaction information. We then present a new measure for unbiased detection of multivariable dependency, “differential interaction information.” This quantity for two variables reduces to the pairwise “set complexity” previously proposed as a context-dependent measure of information in biological systems. We generalize it here to an arbitrary number of variables. Critical limiting properties of the “differential interaction information” are key to the generalization. This measure extends previous ideas about biological information and provides a more sophisticated basis for the study of complexity. The properties of “differential interaction information” also suggest new approaches to data analysis. Given a data set of system measurements, differential interaction information can provide a measure of collective dependence, which can be represented in hypergraphs describing complex system interaction patterns. We investigate this kind of analysis using simulated data sets. The conjoining of a generalized set complexity measure, multivariable dependency analysis, and hypergraphs is our central result. While our focus is on complex biological systems, our results are applicable to any complex system. PMID:24377753
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.
NASA Astrophysics Data System (ADS)
Usui, Norihisa; Ishizaki, Shiro; Fujii, Yosuke; Tsujino, Hiroyuki; Yasuda, Tamaki; Kamachi, Masafumi
The Meteorological Research Institute multivariate ocean variational estimation (MOVE) System has been developed as the next-generation ocean data assimilation system in Japan Meteorological Agency. A multivariate three-dimensional variational (3DVAR) analysis scheme with vertical coupled temperature salinity empirical orthogonal function modes is adopted. The MOVE system has two varieties, the global (MOVE-G) and North Pacific (MOVE-NP) systems. The equatorial Pacific and western North Pacific are analyzed with assimilation experiments using MOVE-G and -NP, respectively. In each system, the salinity and velocity fields are well reproduced, even in cases without salinity data. Changes in surface and subsurface zonal currents during the 1997/98 El Niño event are captured well, and their transports are reasonably consistent with in situ observations. For example, the eastward transport in the upper layer around the equator has 70 Sv in spring 1997 and weakens in spring 1998. With MOVE-NP, the Kuroshio transport has 25 Sv in the East China Sea, and 40 Sv crossing the ASUKA (Affiliated Surveys of the Kuroshio off Cape Ashizuri) line south of Japan. The variations in the Kuroshio transports crossing the ASUKA line agree well with observations. The Ryukyu Current System has a transport ranging from 6 Sv east of Taiwan to 17 Sv east of Amami. The Oyashio transport crossing the OICE (Oyashio Intensive observation line off Cape Erimo) line south of Hokkaido has 14 Sv southwestward (near shore) and 11 Sv northeastward (offshore). In the Kuroshio Oyashio transition area east of Japan, the eastward transport has 41 Sv (32 36°N) and 12 Sv (36 39°N) crossing the 145°E line.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
Nonlinear normal modes in electrodynamic systems: A nonperturbative approach
NASA Astrophysics Data System (ADS)
Kudrin, A. V.; Kudrina, O. A.; Petrov, E. Yu.
2016-06-01
We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributed conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known to hold only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.
Nonlinear Optics in Novel Polymer Systems.
NASA Astrophysics Data System (ADS)
Li, Lian
Polymeric nonlinear optical (NLO) materials have recently attracted considerable attention and been the subject of intensive investigations. Polymeric NLO materials possessing large second and third order NLO properties, ultrafast response times, high optical damage threshold, transparency over a broad wavelength range, and capability to be easily processed into good optical quality thin films, offer significant advantages over the traditional inorganic materials for applications in fabricating integrated optical devices, such as waveguide electro-optic (EO) modulators and optical frequency doublers, and optical signal processing devices. This dissertation presents the experimental investigations on novel NLO polymers synthesized in the Laboratory of Electronic and Photonic Materials at University of Massachusetts Lowell. Progress made for the past few years on polymeric NLO materials is reviewed, especially with regard to the second order NLO properties of the polymeric materials. Two novel stable second order NLO polymer systems, an interpenetrating polymer network (IPN) formed via thermal crosslinking and a sol-gel process, and a photocrosslinkable conducting polymer, upon poling and crosslinking, exhibited large and stable second order NLO properties measured for these polymers by using the second harmonic generation (SHG) technique. For the IPN system, the SHG measurements as a function of time at several elevated temperatures indicate the superb stability of the second order NLO properties. For the conducting NLO polymer, the NLO property of the poled and photocrosslinked polymer film is stable at room temperature. The wavelength shifting of a Q-switched Nd:YAG laser by stimulated Raman scattering is also described. Measurements were made on the third order NLO properties of a dye doped photocrosslinkable guest-host polymer system at different dye concentrations with a modified Michelson interferometer. By functionalizing the dye to make it more compatible to
Energy harvesting in the nonlinear electromagnetic system
NASA Astrophysics Data System (ADS)
Kucab, K.; Górski, G.; Mizia, J.
2015-11-01
We examine the electrical response of electromagnetic device working both in the linear and nonlinear domain. The harvester is consisted of small magnet moving in isolating tube surrounded by the coil attached to the electrical circuit. In the nonlinear case the magnet vibrates in between two fixed magnets attached to the both ends of the tube. Additionally we use two springs which limit the movement of the small magnet. The linear case is when the moving magnet is attached to the repelling springs, and the static magnets have been replaced by the non-magnetic material. The potentials and forces were calculated using both the analytical expressions and the finite elements method. We compare the results for energy harvesting obtained in these two cases. The generated output power in the linear case reaches the peak value 80 mW near the resonance frequency ω0 for maximum base acceleration considered by us, whereas in the non-linear case the corresponding outpot power has the peak value 95 mW and additionally relatively high values in the excitation frequencies range up to ω = 1.2ω0. The numerical results also show that the power efficiency in the nonlinear case exceeds the corresponding efficiency in the linear case at relatively high values of base accelerations greater than 5 g. The results show the increase of harvested energy in the broad band of excitation frequencies in the nonlinear case.
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.
Nonlinear dynamics in tunable graphene nanoelectromechanical systems
NASA Astrophysics Data System (ADS)
Guan, Fen; Kumaravadivel, Piranavan; Averin, Dmitri; Du, Xu
2015-03-01
We report the fabrication and characterization of graphene nanoelectromechanical resonators (GNEMR) on flexible substrates. The intrinsic stain in graphene is tuned by bending the substrate, during which a transition from hardening to softening resonance behavior and a minimum resonance frequency are observed. To explain these observations, a resonator model taking into account the intrinsic strain and electrostatic force is developed. Including higher-order nonlinear terms, a minimum frequency is obtained analytically from the model and matches with experimental data. Results from numerical simulation demonstrate also the transition in the nonlinear behavior. Additionally, the model-based fittings determine the intrinsic strain and mass of graphene samples accurately. Our devices allow thorough exploration of the nonlinear dynamics in GNEMR and may help further study of the intrinsic electrical properties of the materials under strain.
NASA Technical Reports Server (NTRS)
Beattie, E. C.
1980-01-01
An inlet/engine/nozzle integrated control mode for the propulsion system of an advanced supersonic commercial aircraft was studied. Results show that integration of these control functions can result in both operational and performance benefits for the propulsion system. For example, this integrated control mode may make it possible to minimize the use of inlet bypass doors for shock position control. This may be of benefit to the aircraft as a result of minimizing: (1) bypass bleed drag effects; (2) perturbations to the aircraft resulting from the side thrust effect of the bypass bleeds; and (3) potential unstarts of the inlet. A conceptual integrated control mode was developed which makes use of many cross coupling paths between inlet and engine control variables and inlet and engine sensed variables. A multivariable control design technique based upon linear quadratic regulator theory was applied to designing the feedback gains for this control to allow a simulation evaluation of the benefits of the integrated control mode.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Devineni, N.; Lall, U.; Perveen, S.
2012-12-01
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 etc. 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. Non parametric bootstrap resampling methods and Hierarchical Bayesian methods that can easily handle the high dimensionality of such problems will 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 Columbia Water Center's pilot project in Punjab region of India.
An experimental study of nonlinear dynamic system identification
NASA Technical Reports Server (NTRS)
Stry, Greselda I.; Mook, D. Joseph
1990-01-01
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.
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°).
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°).
Computational studies of nonlinear dispersive plasma systems
NASA Astrophysics Data System (ADS)
Qian, Xin
Plasma systems with dispersive waves are ubiquitous. Dispersive waves have the property that their wave velocity depends on the wave number of the wave. These waves show up in weakly as well as strongly coupled plasmas, and play a significant role in the underlying plasma dynamics. Dispersive waves bring new challenges to the computer simulation of nonlinear phenomena. The goal of this thesis is to discuss two computational studies of plasma phenomena, one drawn from strongly coupled complex or dusty plasmas, and the other from weakly coupled hydrogen plasmas. In the realm of dusty plasmas, we focus on the problem of three-dimensional (3D) Mach cones which we study by means of Molecular Dynamics (MD) simulations, assuming that the dust particles interact via a Yukawa potential. While laboratory and MD simulations have explored thoroughly the properties of Mach cones in 2D, elucidating the important role of dispersive waves in the formation of multiple cones, the simulations presented in this thesis represent the first 3D MD studies of Mach cones in strongly coupled dusty plasmas. These results have qualitative similarities with experimental observations on 3D Mach cones from the PK-3 plus project, which studies complex plasmas under microgravity conditions aboard the International Space station. In the realm of weakly coupled plasmas, we present results on the application of non-oscillatory central schemes to Hall MHD reconnection problems, in which the presence of dispersive whistler waves presents a formidable challenge for numerical algorithms that rely on explicit time-stepping schemes. In particular, we focus on the semi-discrete central formulation of Kurganov and Tadmor (2000), which has the advantage that it allow for larger time steps, and with significantly smaller numerical viscosity, than fully discrete schemes. We implement the Hall MHD equations through the CentPACK software package that implements the Kurganov-Tadmor formulation for a wide range of
An experimental study of nonlinear dynamic system identification
NASA Technical Reports Server (NTRS)
Stry, Greselda I.; Mook, D, Joseph
1991-01-01
A technique based on the Minimum Model Error optimal estimation approach is employed for robust identification of a nonlinear dynamic system. A simple harmonic oscillator with quadratic position feedback was simulated on an analog computer. With the aid of analog measurements and an assumed linear model, the Minimum Model Error Algorithm accurately identifies the quadratic nonlinearity. The tests demonstrate that the method is robust with respect to prior ignorance of the nonlinear system model and with respect to measurement record length, regardless of initial conditions.
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.
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.
On-line robust nonlinear state estimators for nonlinear bioprocess systems
NASA Astrophysics Data System (ADS)
Iratni, A.; Katebi, R.; Mostefai, M.
2012-04-01
This paper presents the design of a new robust nonlinear estimator for estimation of states of nonlinear systems. Two approaches are considered based on the state-dependent Riccati equation formulation and the technique of H-infinity control design. The proposed method differs from other well-known state estimators, because not only nonlinear dynamics but also the robustness is taken into account. The proposed method is implemented and tested on a biological wastewater system. The simulation study compares the Extended Kalman Estimator ( EKE), the State-Dependent Riccati Estimator ( SDRE), and the Extended H-infinity Estimator ( EHE) with a new proposed State Dependent H-infinity Estimator ( SDHE). The results are compared for different weather conditions, i.e. dry, rain and storm, showing a superior performance of the proposed method.
Nonlinear dynamic phenomena in the space shuttle thermal protection system
NASA Technical Reports Server (NTRS)
Housner, J. M.; Edighoffer, H. H.; Park, K. C.
1981-01-01
The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.
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
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.
Impact of nonlinear and polarization effects in coherent systems.
Xie, Chongjin
2011-12-12
Coherent detection with digital signal processing (DSP) significantly changes the ways impairments are managed in optical communication systems. In this paper, we review the recent advances in understanding the impact of fiber nonlinearities, polarization-mode dispersion (PMD), and polarization-dependent loss (PDL) in coherent optical communication systems. We first discuss nonlinear transmission performance of three coherent optical communication systems, homogeneous polarization-division-multiplexed (PDM) quadrature-phase-shift-keying (QPSK), hybrid PDM-QPSK and on/off keying (OOK), and PDM 16-ary quadrature-amplitude modulation (QAM) systems. We show that while the dominant nonlinear effects in coherent optical communication systems without optical dispersion compensators (ODCs) are intra-channel nonlinearities, the dominant nonlinear effects in dispersion-managed (DM) systems with inline dispersion compensation fiber (DCF) are different when different modulation formats are used. In DM coherent optical communication systems using modulation formats of constant amplitude, the dominant nonlinear effect is nonlinear polarization scattering induced by cross-polarization modulation (XPolM), whereas when modulation formats of non-constant amplitude are used, the impact of inter-channel cross-phase modulation (XPM) is much larger than XPolM. We then describe the effects of PMD and PDL in coherent systems. We show that although in principle PMD can be completely compensated in a coherent optical receiver, a real coherent receiver has limited tolerance to PMD due to hardware limitations. Two PDL models used to evaluate PDL impairments are discussed. We find that a simple lumped model significantly over-estimates PDL impairments and show that a distributed model has to be used in order to accurately evaluate PDL impairments. Finally, we apply system outage considerations to coherent systems, taking into account the statistics of polarization effects in fiber. PMID
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
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.
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.
Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems
Lü, Xin-You; Zhang, Wei-Min; Ashhab, Sahel; Wu, Ying; Nori, Franco
2013-01-01
We investigate a hybrid electro-optomechanical system that allows us to realize controllable strong Kerr nonlinearities even in the weak-coupling regime. We show that when the controllable electromechanical subsystem is close to its quantum critical point, strong photon-photon interactions can be generated by adjusting the intensity (or frequency) of the microwave driving field. Nonlinear optical phenomena, such as the appearance of the photon blockade and the generation of nonclassical states (e.g., Schrödinger cat states), are demonstrated in the weak-coupling regime, making the observation of strong Kerr nonlinearities feasible with currently available optomechanical technology. PMID:24126279
Code System for Solving Nonlinear Systems of Equations via the Gauss-Newton Method.
Energy Science and Technology Software Center (ESTSC)
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.
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.
Applications of nonlinear system identification to structural health monitoring.
Farrar, C. R.; Sohn, H.; Robertson, A. N.
2004-01-01
The process of implementing a damage detection strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM). In many cases damage causes a structure that initially behaves in a predominantly linear manner to exhibit nonlinear response when subject to its operating environment. The formation of cracks that subsequently open and close under operating loads is an example of such damage. The damage detection process can be significantly enhanced if one takes advantage of these nonlinear effects when extracting damage-sensitive features from measured data. This paper will provide an overview of nonlinear system identification techniques that are used for the feature extraction process. Specifically, three general approaches that apply nonlinear system identification techniques to the damage detection process are discussed. The first two approaches attempt to quantify the deviation of the system from its initial linear characteristics that is a direct result of damage. The third approach is to extract features from the data that are directly related to the specific nonlinearity associated with the damaged condition. To conclude this discussion, a summary of outstanding issues associated with the application of nonlinear system identification techniques to the SHM problem is presented.
Damage detection in nonlinear systems using multiple system augmentations and matrix updating
NASA Astrophysics Data System (ADS)
D'Souza, Kiran; Epureanu, Bogdan I.
2006-03-01
Recently, a damage detection method for nonlinear systems using model updating has been developed by the authors. The method uses an augmented linear model of the system, which is determined from the functional form of the nonlinearities and a nonlinear discrete model of the system. The modal properties of the augmented system after the onset of damage are extracted from the system using a modal analysis technique that uses known but not prescribed forcing. Minimum Rank Perturbation Theory was generalized so that damage location and extent could be determined using the augmented modal properties. The method was demonstrated previously for cubic springs and Coulomb friction nonlinearities. In this work, the methodology is extended to handle large systems where only the first few of the augmented eigenvectors are known. The methodology capitalizes on the ability to create multiple augmentations for a single nonlinear system. Cubic spring nonlinearities are explored within a nonlinear 3-bay truss structure for various damage scenarios simulated numerically.
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.
Simulation program of nonlinearities applied to telecommunication systems
NASA Technical Reports Server (NTRS)
Thomas, C.
1979-01-01
In any satellite communication system, the problems of distorsion created by nonlinear devices or systems must be considered. The subject of this paper is the use of the Fast Fourier Transform (F.F.T.) in the prediction of the intermodulation performance of amplifiers, mixers, filters. A nonlinear memory-less model is chosen to simulate amplitude and phase nonlinearities of the device in the simulation program written in FORTRAN 4. The experimentally observed nonlinearity parameters of a low noise 3.7-4.2 GHz amplifier are related to the gain and phase coefficients of Fourier Service Series. The measured results are compared with those calculated from the simulation in the cases where the input signal is composed of two, three carriers and noise power density.
Aeroelasticity of Nonlinear Tail / Rudder Systems with Freeplay
NASA Astrophysics Data System (ADS)
Rishel, Evan
This thesis details the development of a linear/nonlinear three degree of freedom aeroelastic system designed and manufactured at the University of Washington (UW). Describing function analysis was carried out in the frequency domain. Time domain simulations were carried out to account for all types of motion. Nonlinear aeroelastic behavior may lead to limit cycles which can be captured in the frequency domain using describing function approximation and numerically using Runga-Kutta integration. Linear and nonlinear aeroelastic tests were conducted in the UW 3x3 low-speed wind tunnel to determine the linear flutter speed and frequency of the system as well as its nonlinear behavior when freeplay is introduced. The test data is presented along with the results of the MATLAB-based simulations. The correlation between test and numerical results is very high.
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
Energy Science and Technology Software Center (ESTSC)
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
Chaotic and hyperchaotic attractors of a complex nonlinear system
NASA Astrophysics Data System (ADS)
Mahmoud, Gamal M.; Al-Kashif, M. A.; Farghaly, A. A.
2008-02-01
In this paper, we introduce a complex nonlinear hyperchaotic system which is a five-dimensional system of nonlinear autonomous differential equations. This system exhibits both chaotic and hyperchaotic behavior and its dynamics is very rich. Based on the Lyapunov exponents, the parameter values at which this system has chaotic, hyperchaotic attractors, periodic and quasi-periodic solutions and solutions that approach fixed points are calculated. The stability analysis of these fixed points is carried out. The fractional Lyapunov dimension of both chaotic and hyperchaotic attractors is calculated. Some figures are presented to show our results. Hyperchaos synchronization is studied analytically as well as numerically, and excellent agreement is found.
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
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. PMID:26285223
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.
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
NASA Astrophysics Data System (ADS)
Fan, Wei; Liu, Jin-Yang
2013-09-01
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.
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
A nonlinear complementarity approach for the national energy modeling system
Gabriel, S.A.; Kydes, A.S.
1995-03-08
The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach. The authors describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, they show that the NCP format is equally valid for a more general form of NEMS. They also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP.
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.
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.
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
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.
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.
Energy transfer in systems with random forcing and nonlinear dissipation
NASA Astrophysics Data System (ADS)
Pignol, Ricardo Jorge
The purpose of this thesis is to study energy transfer in nonlinear systems. In the first part, I focus on a model of two nonlinearly coupled (complex) oscillators subject to stochastic forcing and nonlinear dissipation. This model arises from isolating an individual resonant quartet in a general dispersive system, and reducing it further by exploiting some of the system's symmetries. It turns out that the reduced model exhibits a rich and complex behavior encountered in far larger systems, with two qualitatively distinct regimes arising as one varies the system's single non-dimensional parameter: one that can be characterized as a perturbation of thermal equilibrium, and another highly constrained state, with phase and amplitude locking , and singular invariant measures. The relative simplicity of the reduced model allows a thorough numerical and theoretical treatment (including a closed expression for the system's invariant measures) that furnishes valuable insight on the energy transfer process in systems with much higher dimensionality. In the second part, the damped oscillator is replaced by an individual mode of the inviscid Burgers equation. Here, the dissipation occurs through shocks. Despite the complexity resulting from the inclusion of a nonlinear partial differential equation, I show that much of this system's behavior can be inferred precisely from a reduction to one of the cases studied in the first part.
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.
Applications of equivalent linearization approaches to nonlinear piping systems
Park, Y.; Hofmayer, C.; Chokshi, N.
1997-04-01
The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA`s are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations.
Dynamic analysis of nonlinear rotor-housing systems
NASA Technical Reports Server (NTRS)
Noah, Sherif T.
1988-01-01
Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.
Nonlinear control structures based on embedded neural system models.
Lightbody, G; Irwin, G W
1997-01-01
This paper investigates in detail the possible application of neural networks to the modeling and adaptive control of nonlinear systems. Nonlinear neural-network-based plant modeling is first discussed, based on the approximation capabilities of the multilayer perceptron. A structure is then proposed to utilize feedforward networks within a direct model reference adaptive control strategy. The difficulties involved in training this network, embedded within the closed-loop are discussed and a novel neural-network-based sensitivity modeling approach proposed to allow for the backpropagation of errors through the plant to the neural controller. Finally, a novel nonlinear internal model control (IMC) strategy is suggested, that utilizes a nonlinear neural model of the plant to generate parameter estimates over the nonlinear operating region for an adaptive linear internal model, without the problems associated with recursive parameter identification algorithms. Unlike other neural IMC approaches the linear control law can then be readily designed. A continuous stirred tank reactor was chosen as a realistic nonlinear case study for the techniques discussed in the paper. PMID:18255659
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.
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.
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.
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
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.
Perturbation analysis of a clearance-type nonlinear system
NASA Astrophysics Data System (ADS)
Zhu, Farong; Parker, Robert G.
2006-05-01
This study applies the method of multiple scales to obtain periodic solutions of a two-pulley belt system with clearance-type nonlinearity. The purpose is to explain the published numerical results and clarify how design parameters affect the system dynamics. The validity of the perturbation method for such strong nonlinearity is evaluated. The closed-form frequency-response relation is determined at the first order, and an implicit expression is obtained for the second-order approximation. The preload applied to the accessory determines the softening level of the nonlinearity. Larger preload leads to less disengagement and less softening. For a considerable range of practical parameter values, the analytical solutions well approximate the numerical results from harmonic balance.
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
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.
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.
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.
Multivariate dynamical systems models for estimating causal interactions in fMRI
Ryali, Srikanth; Supekar, Kaustubh; Chen, Tianwen; Menon, Vinod
2010-01-01
Analysis of dynamical interactions between distributed brain areas is of fundamental importance for understanding cognitive information processing. However, estimating dynamic causal interactions between brain regions using functional magnetic resonance imaging (fMRI) poses several unique challenges. For one, fMRI measures Blood Oxygenation Level Dependent (BOLD) signals, rather than the underlying latent neuronal activity. Second, regional variations in the hemodynamic response function (HRF) can significantly influence estimation of casual interactions between them. Third, causal interactions between brain regions can change with experimental context over time. To overcome these problems, we developed a novel state-space Multivariate Dynamical Systems (MDS) model to estimate intrinsic and experimentally-induced modulatory causal interactions between multiple brain regions. A probabilistic graphical framework is then used to estimate the parameters of MDS as applied to fMRI data. We show that MDS accurately takes into account regional variations in the HRF and estimates dynamic causal interactions at the level of latent signals. We develop and compare two estimation procedures using maximum likelihood estimation (MLE) and variational Bayesian (VB) approaches for inferring model parameters. Using extensive computer simulations, we demonstrate that, compared to Granger causal analysis (GCA), MDS exhibits superior performance for a wide range of signal to noise ratios (SNRs), sample length and network size. Our simulations also suggest that GCA fails to uncover causal interactions when there is a conflict between the direction of intrinsic and modulatory influences. Furthermore, we show that MDS estimation using VB methods is more robust and performs significantly better at low SNRs and shorter time series than MDS with MLE. Our study suggests that VB estimation of MDS provides a robust method for estimating and interpreting causal network interactions in fMRI data
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.
Terminal Sliding Modes In Nonlinear Control Systems
NASA Technical Reports Server (NTRS)
Venkataraman, Subramanian T.; Gulati, Sandeep
1993-01-01
Control systems of proposed type called "terminal controllers" offers increased precision and stability of robotic operations in presence of unknown and/or changing parameters. Systems include special computer hardware and software implementing novel control laws involving terminal sliding modes of motion: closed-loop combination of robot and terminal controller converge, in finite time, to point of stable equilibrium in abstract space of velocity and/or position coordinates applicable to particular control problem.
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
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.
Application of dynamical systems theory to nonlinear aircraft dynamics
NASA Technical Reports Server (NTRS)
Culick, Fred E. C.; Jahnke, Craig C.
1988-01-01
Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.
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.
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
Nonlinearity as a resource for nonclassicality in anharmonic systems
NASA Astrophysics Data System (ADS)
Albarelli, Francesco; Ferraro, Alessandro; Paternostro, Mauro; Paris, Matteo G. A.
2016-03-01
Nonclassicality is a key ingredient for quantum enhanced technologies and experiments involving macroscopic quantum coherence. Considering various exactly solvable quantum-oscillator systems, we address the role played by the anharmonicity of their potential in the establishment of nonclassical features. Specifically, we show that a monotonic relation exists between the entropic nonlinearity of the considered potentials and their ground-state nonclassicality, as quantified by the negativity of the Wigner function. In addition, in order to clarify the role of squeezing, which is not captured by the negativity of the Wigner function, we focus on the Glauber-Sudarshan P function and address the nonclassicality-nonlinearity relation using the entanglement potential. Finally, we consider the case of a generic sixth-order potential confirming the idea that nonlinearity is a resource for the generation of nonclassicality and may serve as a guideline for the engineering of quantum oscillators.
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.
Synchronised output regulation of nonlinear multi-agent systems
NASA Astrophysics Data System (ADS)
Xiang, Ji; Li, Yanjun; Wei, Wei
2015-01-01
This paper considers a synchronised output regulation (SOR) problem of nonlinear multi-agent systems with switching graph. The SOR means that all agents have their outputs synchronised but also ultimately evolve on a manifold determined by a predefined exosystem. Each agent constructs its local copy of the predefined exosystem and exchanges the state information of the local exosystem to realise the synchronisation of local exosystem. A controller based on the nonlinear output regulation theory is then presented to force the agent's output track the output of local exosystem. It is shown that the SOR is solvable under the assumptions same as that for nonlinear output regulation of a single agent, if the switching graph satisfies the bounded interconnectivity times condition. Both state feedback and output feedback are addressed. A numerical simulation is made to show the efficacy of the analytic results.
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
A nonlinear model for gas chromatograph systems
NASA Technical Reports Server (NTRS)
Feinberg, M. P.
1975-01-01
Fundamental engineering design techniques and concepts were studied for the optimization of a gas chromatograph-mass spectrometer chemical analysis system suitable for use on an unmanned, Martian roving vehicle. Previously developed mathematical models of the gas chromatograph are found to be inadequate for predicting peak heights and spreading for some experimental conditions and chemical systems. A modification to the existing equilibrium adsorption model is required; the Langmuir isotherm replaces the linear isotherm. The numerical technique of Crank-Nicolson was studied for use with the linear isotherm to determine the utility of the method. Modifications are made to the method eliminate unnecessary calculations which result in an overall reduction of the computation time of about 42 percent. The Langmuir isotherm is considered which takes into account the composition-dependent effects on the thermodynamic parameter, mRo.
NASA Astrophysics Data System (ADS)
Aerts, Johan R. M.; de Greef, Daniël; Peacock, John; Dirckx, Joris J. J.
2011-08-01
Recently, a new signal analysis method was developed to detect small non-linear distortions in weakly non-linear systems using specially designed broadband excitation signals, i.e. odd random phase multisines. The method allows the detection and quantification of the system response, noise level and both odd and even degree nonlinear distortions over an extensive frequency range from one single short-term measurement. Here, this method is implemented in an opto-acoustical set-up to detect small non-linearities in the response of vibrating structures. Because of the highly linear response achievable with heterodyne vibrometry, it is possible to detect non-linearities in the system under test with extremely high sensitivity. Non-linear behaviour is very common in biomechanical systems, but their dynamics and thus response might change over time. This leads to measurement artifacts that cause an overestimation of the noise level. A correction algorithm can be applied to remove the effect of these time variations, so that heterodyne vibrometry also allows the detection and quantification of non-linearities in unstable biomechanical systems. In this paper the technique is demonstrated with a measurement of the non-linear distortions in the vibration of the gerbil middle ear, where the use of a non-contact optical detection method is essential to not disturb the tiny vibrating structures.