New results on robust exponential stability of integral delay systems
NASA Astrophysics Data System (ADS)
Melchor-Aguilar, Daniel
2016-06-01
The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov-Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.
NASA Astrophysics Data System (ADS)
Mao, Yanbing; Zhang, Hongbin
2014-05-01
This paper deals with stability and robust H∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov-Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.
On the Stability of Exponential Backoff
Song, Nah-Oak; Kwak, Byung-Jae; Miller, Leonard E.
2003-01-01
Random access schemes for packet networks featuring distributed control require algorithms and protocols for resolving packet collisions that occur as the uncoordinated terminals contend for the channel. A widely used collision resolution protocol is the exponential backoff (EB). New analytical results for the stability of the (binary) EB are given. Previous studies on the stability of the (binary) EB have produced contradictory results instead of a consensus: some proved instability, others showed stability under certain conditions. In these studies, simplified and/or modified models of the backoff algorithm were used. In this paper, care is taken to use a model that reflects the actual behavior of backoff algorithms. We show that EB is stable under a throughput definition of stability; the throughput of the network converges to a non-zero constant as the offered load N goes to infinity. We also obtain the analytical expressions for the saturation throughput for a given number of nodes, N. The analysis considers the general case of EB with backoff factor r, where BEB is the special case with r = 2. We show that r = 1/(1 − e−1) is the optimum backoff factor that maximizes the throughput. The accuracy of the analysis is checked against simulation results.
Circuit design and exponential stabilization of memristive neural networks.
Wen, Shiping; Huang, Tingwen; Zeng, Zhigang; Chen, Yiran; Li, Peng
2015-03-01
This paper addresses the problem of circuit design and global exponential stabilization of memristive neural networks with time-varying delays and general activation functions. Based on the Lyapunov-Krasovskii functional method and free weighting matrix technique, a delay-dependent criteria for the global exponential stability and stabilization of memristive neural networks are derived in form of linear matrix inequalities (LMIs). Two numerical examples are elaborated to illustrate the characteristics of the results. It is noteworthy that the traditional assumptions on the boundness of the derivative of the time-varying delays are removed. PMID:25481670
Cauchy Problem and Exponential Stability for the Inhomogeneous Landau Equation
NASA Astrophysics Data System (ADS)
Carrapatoso, Kleber; Tristani, Isabelle; Wu, Kung-Chien
2016-07-01
This work deals with the inhomogeneous Landau equation on the torus in the cases of hard, Maxwellian and moderately soft potentials. We first investigate the linearized equation and we prove exponential decay estimates for the associated semigroup. We then turn to the nonlinear equation and we use the linearized semigroup decay in order to construct solutions in a close-to-equilibrium setting. Finally, we prove an exponential stability for such a solution, with a rate as close as we want to the optimal rate given by the semigroup decay.
On exponential stability of gravity driven viscoelastic flows
NASA Astrophysics Data System (ADS)
Jiang, Fei; Wu, Guochun; Zhong, Xin
2016-05-01
We investigate stability of an equilibrium state to a nonhomogeneous incompressible viscoelastic fluid driven by gravity in a bounded domain Ω ⊂R3 of class C3. First, we establish a critical number κC, which depends on the equilibrium density and the gravitational constant, and is a threshold of the elasticity coefficient κ for instability and stability of the linearized perturbation problem around the equilibrium state. Then we prove that the equilibrium state is exponential stability provided that κ >κC and the initial disturbance quantities around the equilibrium state satisfy some relations. In particular, if the equilibrium density ρ bar is a Rayleigh-Taylor (RT) type and ρbar‧ is a constant, our result strictly shows that the sufficiently large elasticity coefficient can prevent the RT instability from occurrence.
NASA Astrophysics Data System (ADS)
Chen, Huabin; Zhao, Yang
2015-10-01
This paper is mainly concerned with the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic neural networks with interval time-varying delay. With an appropriate augmented Lyapunov-Krasovskii functional (LKF) formulated, the convex combination method is utilised to estimate the derivative of the LKF. Some new delay-dependent exponential stability criteria for such systems are obtained in terms of linear matrix inequalities, which involve fewer matrix variables and have less conservatism. Finally, two illustrative numerical examples are given to show the effectiveness of our obtained results.
NASA Astrophysics Data System (ADS)
Chen, Zhaohui; Huang, Qi
2016-01-01
This paper focuses on the problems of globally exponential stability and stabilization with H∞ performance for a class of interconnected Markovian jump system with mode-dependent delays in interconnection. By constructing a Lyapunov-Krasovskii functional, delay-range-dependent globally mean-square exponential stability conditions are established in terms of linear matrix inequalities. Based on the obtained conditions, state feedback control utilizing global state information and state feedback control utilizing global state information of decentralised observers are developed to render the closed-loop interconnected Markovian jump time-delay system globally exponential stable with H∞ performance. Numerical simulation of a power system, composed of three coupled machines, is used to illustrate the effectiveness of the obtained results.
Zhang, Yunong; Wang, Jun
2002-01-01
Global exponential stability is the most desirable stability property of recurrent neural networks. The paper presents new results for recurrent neural networks applied to online computation of feedback gains of linear time-invariant multivariable systems via pole assignment. The theoretical analysis focuses on the global exponential stability, convergence rates, and selection of design parameters. The theoretical results are further substantiated by simulation results conducted for synthesizing linear feedback control systems with different specifications and design requirements. PMID:18244461
Robust Stabilization Control for an Electric Bicycle
NASA Astrophysics Data System (ADS)
Kawamura, Takuro; Murakami, Toshiyuki
Recently, bicycles have gained immense popularity because they have high mobility and are an environment-friendly means of transport. However, many people tend to avoid riding a bicycle because it is unstable. In order to solve this problem, stabilization control for a bicycle has been researched. The aim of this study is improvement of the robustness in stabilization control. To achieve this goal, control systems that use a camber angle disturbance observer (CADO) are proposed. Two kinds of CADOs are proposed in this paper, and the performances of these two observers are compared. The proposed control systems provide higher robustness than does the conventional method. The validity of the proposed methods is confirmed by the experimental results.
NASA Astrophysics Data System (ADS)
Mohamad, Sannay
2008-05-01
This paper demonstrates that there is a discrete-time analogue which does not require any restriction on the size of the time-step in order to preserve the exponential stability of an artificial neural network with distributed delays. The analysis exploits an appropriate Lyapunov sequence and a discrete-time system of Halanay inequalities, and also either a Young inequality or a geometric-arithmetic mean inequality, to derive several sufficient conditions on the network parameters for the exponential stability of the analogue. The sufficiency conditions are independent of the time-step, and they correspond to those that establish the exponential stability of the continuous-time network.
Numerical robust stability estimation in milling process
NASA Astrophysics Data System (ADS)
Zhang, Xiaoming; Zhu, Limin; Ding, Han; Xiong, Youlun
2012-09-01
The conventional prediction of milling stability has been extensively studied based on the assumptions that the milling process dynamics is time invariant. However, nominal cutting parameters cannot guarantee the stability of milling process at the shop floor level since there exists many uncertain factors in a practical manufacturing environment. This paper proposes a novel numerical method to estimate the upper and lower bounds of Lobe diagram, which is used to predict the milling stability in a robust way by taking into account the uncertain parameters of milling system. Time finite element method, a milling stability theory is adopted as the conventional deterministic model. The uncertain dynamics parameters are dealt with by the non-probabilistic model in which the parameters with uncertainties are assumed to be bounded and there is no need for probabilistic distribution densities functions. By doing so, interval instead of deterministic stability Lobe is obtained, which guarantees the stability of milling process in an uncertain milling environment. In the simulations, the upper and lower bounds of Lobe diagram obtained by the changes of modal parameters of spindle-tool system and cutting coefficients are given, respectively. The simulation results show that the proposed method is effective and can obtain satisfying bounds of Lobe diagrams. The proposed method is helpful for researchers at shop floor to making decision on machining parameters selection.
Adaptive control: Stability, convergence, and robustness
NASA Technical Reports Server (NTRS)
Sastry, Shankar; Bodson, Marc
1989-01-01
The deterministic theory of adaptive control (AC) is presented in an introduction for graduate students and practicing engineers. Chapters are devoted to basic AC approaches, notation and fundamental theorems, the identification problem, model-reference AC, parameter convergence using averaging techniques, and AC robustness. Consideration is given to the use of prior information, the global stability of indirect AC schemes, multivariable AC, linearizing AC for a class of nonlinear systems, AC of linearizable minimum-phase systems, and MIMO systems decouplable by static state feedback.
Stability, complexity and robustness in population dynamics.
Demongeot, J; Hazgui, H; Ben Amor, H; Waku, J
2014-09-01
The problem of stability in population dynamics concerns many domains of application in demography, biology, mechanics and mathematics. The problem is highly generic and independent of the population considered (human, animals, molecules,…). We give in this paper some examples of population dynamics concerning nucleic acids interacting through direct nucleic binding with small or cyclic RNAs acting on mRNAs or tRNAs as translation factors or through protein complexes expressed by genes and linked to DNA as transcription factors. The networks made of these interactions between nucleic acids (considered respectively as edges and nodes of their interaction graph) are complex, but exhibit simple emergent asymptotic behaviours, when time tends to infinity, called attractors. We show that the quantity called attractor entropy plays a crucial role in the study of the stability and robustness of such genetic networks. PMID:25107273
Exponential Stability for Stochastic Neural Networks of Neutral Type with Impulsive Effects
NASA Astrophysics Data System (ADS)
Sakthivel, Rathinasamy; Samidurai, R.; Anthoni, S. Marshal
This paper is concerned with the exponential stability of stochastic neural networks of neutral type with impulsive effects. By employing the Lyapunov functional and stochastic analysis, a new stability criterion for the stochastic neural network is derived in terms of linear matrix inequality. A numerical example is provided to show the effectiveness and applicability of the obtained result.
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.
1995-01-01
It has been shown recently how virtual passive controllers can be designed for second-order dynamic systems to achieve robust stability. The virtual controllers were visualized as systems made up of spring, mass and damping elements. In this paper, a new approach emphasizing on the notion of positive realness to the same second-order dynamic systems is used. Necessary and sufficient conditions for positive realness are presented for scalar spring-mass-dashpot systems. For multi-input multi-output systems, we show how a mass-spring-dashpot system can be made positive real by properly choosing its output variables. In particular, sufficient conditions are shown for the system without output velocity. Furthermore, if velocity cannot be measured then the system parameters must be precise to keep the system positive real. In practice, system parameters are not always constant and cannot be measured precisely. Therefore, in order to be useful positive real systems must be robust to some degrees. This can be achieved with the design presented in this paper.
On exponential stability of linear Levin-Nohel integro-differential equations
NASA Astrophysics Data System (ADS)
Tien Dung, Nguyen
2015-02-01
The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].
Exponential stability of an elastic string with local Kelvin-Voigt damping
NASA Astrophysics Data System (ADS)
Zhang, Qiong
2010-12-01
This paper is devoted to analyzing an elastic string with local Kelvin-Voigt damping. We prove the exponential stability of the system when the material coefficient function near the interface is smooth enough. Our method is based on the frequency method and semigroup theory.
NASA Astrophysics Data System (ADS)
Devianto, Dodi
2016-02-01
It is constructed convolution of generated random variable from independent and identically exponential distribution with stabilizer constant. The characteristic function of this distribution is obtained by using Laplace-Stieltjes transform. The uniform continuity property of characteristic function from this convolution is obtained by using analytical methods as basic properties.
Chen, Huabin; Shi, Peng; Lim, Cheng-Chew; Hu, Peng
2016-06-01
In this paper, the exponential stability in p th( p > 1 )-moment for neutral stochastic Markov systems with time-varying delay is studied. The derived stability conditions comprise two forms: 1) the delay-independent stability criteria which are obtained by establishing an integral inequality and 2) the delay-dependent stability criteria which are captured by using the theory of the functional differential equations. As its applications, the obtained stability results are used to investigate the exponential stability in p th( p > 1 )-moment for the neutral stochastic neural networks with time-varying delay and Markov switching, and the globally exponential adaptive synchronization for the neutral stochastic complex dynamical systems with time-varying delay and Markov switching, respectively. On the delay-independent criteria, sufficient conditions are given in terms of M -matrix and thus are easy to check. The delay-dependent criteria are presented in the forms of the algebraic inequalities, and the least upper bound of the time-varying delay is also provided. The primary advantages of these obtained results over some recent and similar works are that the differentiability or continuity of the delay function is not required, and that the difficulty stemming from the presence of the neutral item and the Markov switching is overcome. Three numerical examples are provided to examine the effectiveness and potential of the theoretic results obtained. PMID:27187938
Robust three-axis attitude stabilization for inertial pointing spacecraft using magnetorquers
NASA Astrophysics Data System (ADS)
Celani, Fabio
2015-02-01
In this work feedback control laws are designed for achieving three-axis attitude stabilization of inertial pointing spacecraft using only magnetic torquers. The designs are based on an almost periodic model of geomagnetic field along the spacecraft's orbit. Both attitude plus attitude rate feedback and attitude only feedback are proposed. Both feedback laws achieve local exponential stability robustly with respect to large uncertainties in the spacecraft's inertia matrix. The latter properties are proved using general averaging and Lyapunov stability. Simulations are included to validate the effectiveness of the proposed control algorithms.
Computation of robustly stabilizing PID controllers for interval systems.
Matušů, Radek; Prokop, Roman
2016-01-01
The paper is focused on the computation of all possible robustly stabilizing Proportional-Integral-Derivative (PID) controllers for plants with interval uncertainty. The main idea of the proposed method is based on Tan's (et al.) technique for calculation of (nominally) stabilizing PI and PID controllers or robustly stabilizing PI controllers by means of plotting the stability boundary locus in either P-I plane or P-I-D space. Refinement of the existing method by consideration of 16 segment plants instead of 16 Kharitonov plants provides an elegant and efficient tool for finding all robustly stabilizing PID controllers for an interval system. The validity and relatively effortless application of presented theoretical concepts are demonstrated through a computation and simulation example in which the uncertain mathematical model of an experimental oblique wing aircraft is robustly stabilized. PMID:27350931
Global exponential stability for switched memristive neural networks with time-varying delays.
Xin, Youming; Li, Yuxia; Cheng, Zunshui; Huang, Xia
2016-08-01
This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov-Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples. PMID:27164266
Wavelet Filtering to Reduce Conservatism in Aeroservoelastic Robust Stability Margins
NASA Technical Reports Server (NTRS)
Brenner, Marty; Lind, Rick
1998-01-01
Wavelet analysis for filtering and system identification was used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins was reduced with parametric and nonparametric time-frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data was used to reduce the effects of external desirableness and unmodeled dynamics. Parametric estimates of modal stability were also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. F-18 high Alpha Research Vehicle aeroservoelastic flight test data demonstrated improved robust stability prediction by extension of the stability boundary beyond the flight regime.
On-Line Robust Modal Stability Prediction using Wavelet Processing
NASA Technical Reports Server (NTRS)
Brenner, Martin J.; Lind, Rick
1998-01-01
Wavelet analysis for filtering and system identification has been used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins is reduced with parametric and nonparametric time- frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data is used to reduce the effects of external disturbances and unmodeled dynamics. Parametric estimates of modal stability are also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. The F-18 High Alpha Research Vehicle aeroservoelastic flight test data demonstrates improved robust stability prediction by extension of the stability boundary beyond the flight regime. Guidelines and computation times are presented to show the efficiency and practical aspects of these procedures for on-line implementation. Feasibility of the method is shown for processing flight data from time- varying nonstationary test points.
Yang, Shiju; Li, Chuandong; Huang, Tingwen
2016-03-01
The problem of exponential stabilization and synchronization for fuzzy model of memristive neural networks (MNNs) is investigated by using periodically intermittent control in this paper. Based on the knowledge of memristor and recurrent neural network, the model of MNNs is formulated. Some novel and useful stabilization criteria and synchronization conditions are then derived by using the Lyapunov functional and differential inequality techniques. It is worth noting that the methods used in this paper are also applied to fuzzy model for complex networks and general neural networks. Numerical simulations are also provided to verify the effectiveness of theoretical results. PMID:26797471
Stagnation-point flow and heat transfer over an exponentially shrinking sheet: A stability analysis
NASA Astrophysics Data System (ADS)
Ismail, Nurul Syuhada; Arifin, Norihan Md.; Bachok, Norfifah; Mahiddin, Norhasimah
2016-06-01
Numerical solutions for the stagnation-point flow and heat transfer over an exponentially shrinking sheet have been investigated. The governing boundary layer equations are transformed into an ordinary differential equation using a non-similar transformation. By using the bvp4c solver in MATLAB, the results of the equations can be solved numerically. Numerical results indicate that in certain parameter, the non-unique solutions for the velocity and the temperature do exist. A linear stability analysis shows that only one solution is linearly stable otherwise is unstable. Then, the stability analysis is performed to identify which solution is stable between the two non-unique solutions.
The Role of a Steepness Parameter in the Exponential Stability of a Model Problem. Numerical Aspects
NASA Astrophysics Data System (ADS)
Todorovic, N.
2011-06-01
The Nekhoroshev theorem considers quasi integrable Hamiltonians providing stability of actions in exponentially long times. One of the hypothesis required by the theorem is a mathematical condition called steepness. Nekhoroshev conjectured that different steepness properties should imply numerically observable differences in the stability times. After a recent study on this problem (Guzzo et al. 2011, Todorovic et al. 2011) we show some additional numerical results on the change of resonances and the diffusion laws produced by the increasing effect of steepness. The experiments are performed on a 4-dimensional steep symplectic map designed in a way that a parameter smoothly regulates the steepness properties in the model.
Song, Qiankun; Yan, Huan; Zhao, Zhenjiang; Liu, Yurong
2016-07-01
In this paper, the global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and using matrix inequality technique, several sufficient conditions in complex-valued linear matrix inequality form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the considered neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literatures, which is demonstrated via two examples with simulations. PMID:27136664
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.
1994-01-01
This progress report gives current progress of the research in nonlinear robust control using positive real concept. The progress is documented in a draft paper. In the paper, the manipulator dynamics is reformulated differently from the existing equations of motion for free base robots. This new formulation gives a compact form of the dynamic equations for easy computation. The nonlinear terms are now considered. The results show that for an additional nonlinear friction term, the feedback controller designed using passivity concept works quite well. Although design of such a controller requires simulation of the dynamics for the example shown in the following draft, this design procedure is feasible.
Yielding Elastic Tethers Stabilize Robust Cell Adhesion
Whitfield, Matt J.; Luo, Jonathon P.; Thomas, Wendy E.
2014-01-01
Many bacteria and eukaryotic cells express adhesive proteins at the end of tethers that elongate reversibly at constant or near constant force, which we refer to as yielding elasticity. Here we address the function of yielding elastic adhesive tethers with Escherichia coli bacteria as a model for cell adhesion, using a combination of experiments and simulations. The adhesive bond kinetics and tether elasticity was modeled in the simulations with realistic biophysical models that were fit to new and previously published single molecule force spectroscopy data. The simulations were validated by comparison to experiments measuring the adhesive behavior of E. coli in flowing fluid. Analysis of the simulations demonstrated that yielding elasticity is required for the bacteria to remain bound in high and variable flow conditions, because it allows the force to be distributed evenly between multiple bonds. In contrast, strain-hardening and linear elastic tethers concentrate force on the most vulnerable bonds, which leads to failure of the entire adhesive contact. Load distribution is especially important to noncovalent receptor-ligand bonds, because they become exponentially shorter lived at higher force above a critical force, even if they form catch bonds. The advantage of yielding is likely to extend to any blood cells or pathogens adhering in flow, or to any situation where bonds are stretched unequally due to surface roughness, unequal native bond lengths, or conditions that act to unzip the bonds. PMID:25473833
Generic super-exponential stability of elliptic equilibrium positions for symplectic vector fields
NASA Astrophysics Data System (ADS)
Niederman, Laurent
2013-11-01
In this article, we consider linearly stable elliptic fixed points (equilibrium) for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. We will focus on the neighborhood of elliptic fixed points but the case of linearly stable isotropic reducible invariant tori in a Hamiltonian system should be similar. More specifically, Morbidelli and Giorgilli have proved a result of stability over superexponentially long times if one considers an analytic Lagrangian torus, invariant for an analytic Hamiltonian system, with a diophantine translation vector which admits a sign-definite torsion. Then, the solutions of the system move very little over times which are super-exponentially long with respect to the inverse of the distance to the invariant torus. The proof proceeds in two steps: first one constructs a high-order Birkhoff normal form, then one applies the Nekhoroshev theory. Bounemoura has shown that the second step of this construction remains valid if the Birkhoff normal form linked to the invariant torus or the elliptic fixed point belongs to a generic set among the formal series. This is not sufficient to prove this kind of super-exponential stability results in a general setting. We should also establish that the most strongly non resonant elliptic fixed point or invariant torus in a Hamiltonian system admits Birkhoff normal forms fitted for the application of the Nekhoroshev theory. Actually, the set introduced by Bounemoura is already very large but not big enough to ensure that a typical Birkhoff normal form falls into this class. We show here that this property is satisfied generically in the sense of the measure (prevalence) through infinite-dimensional probe spaces (that is, an infinite number of parameters chosen at random) with methods similar to those developed in a paper of Gorodetski, Kaloshin and Hunt in another setting.
Robust stability of positive switched systems with dwell time
NASA Astrophysics Data System (ADS)
Liu, Jinjin; Zhang, Kanjian; Wei, Haikun
2016-08-01
This paper studies robust stability of positive switched systems (PSSs) with polytopic uncertainties in both discrete-time and continuous-time contexts. By using multiple linear copositive Lyapunov functions, a sufficient condition for stability of PSSs with dwell time is addressed. Being different from time-invariant multiple linear copositive Lyapunov functions, the Lyapunov functions constructed in this paper are time-varying during the dwell time and time-invariant afterwards. Then, robust stability of PSSs with polytopic uncertainties is solved. All conditions are solvable via linear programming. Finally, illustrative examples are given to demonstrate the validity of the proposed results.
NASA Astrophysics Data System (ADS)
Grobbelaar-Van Dalsen, Marié
2015-08-01
This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function , that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.
NASA Astrophysics Data System (ADS)
Wu, Ailong; Zeng, Zhigang
2015-03-01
Modeling and related characterization of memristive neurodynamic systems becomes a critical pathway towards neuromorphic system designs. This paper presents a general class of memristive neural networks with time-varying delays. Some improved algebraic criteria for global exponential stability of memristive neural networks are obtained. The criteria improve some previous results and are easy to be verified with the physical parameters of system itself. The proposed framework for theoretical analysis of memristive neurodynamic systems may be useful in developing nanoscale memristor device as synapse in neuromorphic computing architectures.
Robust stability of stochastic delayed additive neural networks with Markovian switching.
Huang, He; Ho, Daniel W C; Qu, Yuzhong
2007-09-01
This paper is concerned with the problem of robust stability for stochastic interval delayed additive neural networks (SIDANN) with Markovian switching. The time delay is assumed to be time-varying. In such neural networks, the features of stochastic systems, interval systems, time-varying delay systems and Markovian switching are taken into account. The mathematical model of this kind of neural networks is first proposed. Secondly, the global exponential stability in the mean square is studied for the SIDANN with Markovian switching. Based on the Lyapunov method, several stability conditions are presented, which can be expressed in terms of linear matrix inequalities. As a subsequent result, the stochastic interval additive neural networks with time-varying delay are also discussed. A sufficient condition is given to determine its stability. Finally, two simulation examples are provided to illustrate the effectiveness of the results developed. PMID:17714914
Exponential stability analysis of linear systems with multiple successive delay components
NASA Astrophysics Data System (ADS)
Lin, Chun-Pi; Fong, I.-Kong
2013-06-01
A general class of linear systems with multiple successive delay components is considered in this article. The delays are assumed to vary in intervals, and delay-dependent exponential stability conditions are derived in terms of linear matrix inequalities. To reduce conservativeness, a new Lyapunov-Krasovskii functional is designed to contain more complete state information, so that a derivation procedure with time-varying delays treated as uncertain parameters can be adopted. Usage of slack variables and inequalities are refrained as much as possible when bounds on the Lyapunov derivative are sought. The stability criteria are tested by two popular numerical examples, with less conservative results obtained in all the checked cases. Besides, a practical application of the derived conditions is illustrated.
Robust local stability of multilayer recurrent neural networks.
Suykens, J K; De Moor, B; Vandewalle, J
2000-01-01
In this paper we derive a condition for robust local stability of multilayer recurrent neural networks with two hidden layers. The stability condition follows from linking theory about linearization, robustness analysis of linear systems under nonlinear perturbation and matrix inequalities. A characterization of the basin of attraction of the origin is given in terms of the level set of a quadratic Lyapunov function. In a similar way like for NL theory, local stability is imposed around the origin and the apparent basin of attraction is made large by applying the criterion, while the proven basin of attraction is relatively small due to conservatism of the criterion. Modifying dynamic backpropagation by the new stability condition is discussed and illustrated by simulation examples. PMID:18249754
Use of a genetic algorithm to analyze robust stability problems
Murdock, T.M.; Schmitendorf, W.E.; Forrest, S.
1990-01-01
This note resents a genetic algorithm technique for testing the stability of a characteristic polynomial whose coefficients are functions of unknown but bounded parameters. This technique is fast and can handle a large number of parametric uncertainties. We also use this method to determine robust stability margins for uncertain polynomials. Several benchmark examples are included to illustrate the two uses of the algorithm. 27 refs., 4 figs.
High-Spin Organic Diradical with Robust Stability.
Gallagher, Nolan M; Bauer, Jackson J; Pink, Maren; Rajca, Suchada; Rajca, Andrzej
2016-08-01
Triplet ground-state organic molecules are interesting with respect to several emerging technologies but typically exhibit limited stability. We report two organic diradicals, one of which possesses a triplet ground state (2J/kB = 234 ± 36 K) and robust stability at elevated temperatures. We are able to sublime this high-spin diradical under high vacuum at 140 °C with no significant decomposition. PMID:27430499
Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts
NASA Technical Reports Server (NTRS)
Gupta, Sandeep
1996-01-01
Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.
Song, Qiankun; Yan, Huan; Zhao, Zhenjiang; Liu, Yurong
2016-09-01
This paper investigates the stability problem for a class of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. By employing the idea of vector Lyapunov function, M-matrix theory and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of equilibrium point. When the impulsive effects are not considered, several sufficient conditions are also given to guarantee the existence, uniqueness and global exponential stability of equilibrium point. Two examples are given to illustrate the effectiveness and lower level of conservatism of the proposed criteria in comparison with some existing results. PMID:27239891
Robustness for slope stability modelling under deep uncertainty
NASA Astrophysics Data System (ADS)
Almeida, Susana; Holcombe, Liz; Pianosi, Francesca; Wagener, Thorsten
2015-04-01
Landslides can have large negative societal and economic impacts, such as loss of life and damage to infrastructure. However, the ability of slope stability assessment to guide management is limited by high levels of uncertainty in model predictions. Many of these uncertainties cannot be easily quantified, such as those linked to climate change and other future socio-economic conditions, restricting the usefulness of traditional decision analysis tools. Deep uncertainty can be managed more effectively by developing robust, but not necessarily optimal, policies that are expected to perform adequately under a wide range of future conditions. Robust strategies are particularly valuable when the consequences of taking a wrong decision are high as is often the case of when managing natural hazard risks such as landslides. In our work a physically based numerical model of hydrologically induced slope instability (the Combined Hydrology and Stability Model - CHASM) is applied together with robust decision making to evaluate the most important uncertainties (storm events, groundwater conditions, surface cover, slope geometry, material strata and geotechnical properties) affecting slope stability. Specifically, impacts of climate change on long-term slope stability are incorporated, accounting for the deep uncertainty in future climate projections. Our findings highlight the potential of robust decision making to aid decision support for landslide hazard reduction and risk management under conditions of deep uncertainty.
Sun, Xi-Ming; Wang, Xue-Fang; Tan, Ying; Wang, Xiao-Liang; Wang, Wei
2016-06-01
This paper provides a design strategy for temperature control of the gas chromatograph. Usually gas chromatograph is modeled by a simple first order system with a time-delay, and a proportion integration (PI) controller is widely used to regulate the output of the gas chromatograph to the desired temperature. As the characteristics of the gas chromatograph varies at the different temperature range, the single-model based PI controller cannot work well when output temperature varies from one range to another. Moreover, the presence of various disturbance will further deteriorate the performance. In order to improve the accuracy of the temperature control, multiple models are used at the different temperature ranges. With a PI controller designed for each model accordingly, a delay-dependent switching control scheme using the dwell time technique is proposed to ensure the absolute exponential stability of the closed loop. Experiment results demonstrate the effectiveness of the proposed switching technique. PMID:26316283
Li, Yongkun; Li, Bing
2016-01-01
In this paper, we first give a new definition of almost periodic time scales, two new definitions of almost periodic functions on time scales and investigate some basic properties of them. Then, as an application, by using a fixed point theorem in Banach space and the time scale calculus theory, we obtain some sufficient conditions for the existence and exponential stability of positive almost periodic solutions for a class of Nicholson's blowflies models on time scales. Finally, we present an illustrative example to show the effectiveness of obtained results. Our results show that under a simple condition the continuous-time Nicholson's blowflies model and its discrete-time analogue have the same dynamical behaviors. PMID:27468397
NASA Astrophysics Data System (ADS)
Wehbe, Ali; Youssef, Wael
2010-10-01
In this paper, we study the energy decay rate for the elastic Bresse system in one-dimensional bounded domain. The physical system consists of three wave equations. The two wave equations about the rotation angle and the longitudinal displacement are damped by two locally distributed feedbacks at the neighborhood of the boundary. Then indirect damping is applied to the equation for the transverse displacement of the beam through the coupling terms. We will establish the exponential stability for this system in the case of the same speed of propagation in the equation for the vertical displacement and the equation for the rotation angle of the system. When the wave speeds are different, nonexponential decay rate is proved and a polynomial-type decay rate is obtained. The frequency domain method and the multiplier technique are applied.
Wehbe, Ali; Youssef, Wael
2010-10-15
In this paper, we study the energy decay rate for the elastic Bresse system in one-dimensional bounded domain. The physical system consists of three wave equations. The two wave equations about the rotation angle and the longitudinal displacement are damped by two locally distributed feedbacks at the neighborhood of the boundary. Then indirect damping is applied to the equation for the transverse displacement of the beam through the coupling terms. We will establish the exponential stability for this system in the case of the same speed of propagation in the equation for the vertical displacement and the equation for the rotation angle of the system. When the wave speeds are different, nonexponential decay rate is proved and a polynomial-type decay rate is obtained. The frequency domain method and the multiplier technique are applied.
Decentralized adaptive control of robot manipulators with robust stabilization design
NASA Technical Reports Server (NTRS)
Yuan, Bau-San; Book, Wayne J.
1988-01-01
Due to geometric nonlinearities and complex dynamics, a decentralized technique for adaptive control for multilink robot arms is attractive. Lyapunov-function theory for stability analysis provides an approach to robust stabilization. Each joint of the arm is treated as a component subsystem. The adaptive controller is made locally stable with servo signals including proportional and integral gains. This results in the bound on the dynamical interactions with other subsystems. A nonlinear controller which stabilizes the system with uniform boundedness is used to improve the robustness properties of the overall system. As a result, the robot tracks the reference trajectories with convergence. This strategy makes computation simple and therefore facilitates real-time implementation.
Robust stability of diamond families of polynomials with complex coefficients
NASA Technical Reports Server (NTRS)
Xu, Zhong Ling
1993-01-01
Like the interval model of Kharitonov, the diamond model proves to be an alternative powerful device for taking into account the variation of parameters in prescribed ranges. The robust stability of some kinds of diamond polynomial families with complex coefficients are discussed. By exploiting the geometric characterizations of their value sets, we show that, for the family of polynomials with complex coefficients and both their real and imaginary parts lying in a diamond, the stability of eight specially selected extreme point polynomials is necessary as well as sufficient for the stability of the whole family. For the so-called simplex family of polynomials, four extreme point and four exposed edge polynomials of this family need to be checked for the stability of the entire family. The relations between the stability of various diamonds are also discussed.
Zhang, Guodong; Shen, Yi
2015-07-01
This paper is concerned with the global exponential stabilization of memristor-based chaotic neural networks with both time-varying delays and general activation functions. Here, we adopt nonsmooth analysis and control theory to handle memristor-based chaotic neural networks with discontinuous right-hand side. In particular, several new sufficient conditions ensuring exponential stabilization of memristor-based chaotic neural networks are obtained via periodically intermittent control. In addition, the proposed results here are easy to verify and they also extend the earlier publications. Finally, numerical simulations illustrate the effectiveness of the obtained results. PMID:25148672
NASA Astrophysics Data System (ADS)
Sun, Jianhua; Wan, Li
2005-08-01
Convergence dynamics of Cohen-Grossberg neural networks (CGNNs) with continuously distributed delays are discussed. Without assuming the differentiability and monotonicity of activation functions, the differentiability of amplification functions and the symmetry of synaptic interconnection weights, by skilfully constructing suitable Lyapunov functionals and employing inequality technique, three sets of easily verifiable delay independent criteria to guarantee the global exponential stability of a unique equilibrium point are given, and moreover, by constructing Poincaré mapping, other three sets of easily verifiable delay independent criteria to assure the existence and globally exponential stability of periodic solutions are obtained. Six examples are given to illustrate the theoretical results.
Does a crouched leg posture enhance running stability and robustness?
Blum, Yvonne; Birn-Jeffery, Aleksandra; Daley, Monica A; Seyfarth, Andre
2011-07-21
Humans and birds both walk and run bipedally on compliant legs. However, differences in leg architecture may result in species-specific leg control strategies as indicated by the observed gait patterns. In this work, control strategies for stable running are derived based on a conceptual model and compared with experimental data on running humans and pheasants (Phasianus colchicus). From a model perspective, running with compliant legs can be represented by the planar spring mass model and stabilized by applying swing leg control. Here, linear adaptations of the three leg parameters, leg angle, leg length and leg stiffness during late swing phase are assumed. Experimentally observed kinematic control parameters (leg rotation and leg length change) of human and avian running are compared, and interpreted within the context of this model, with specific focus on stability and robustness characteristics. The results suggest differences in stability characteristics and applied control strategies of human and avian running, which may relate to differences in leg posture (straight leg posture in humans, and crouched leg posture in birds). It has been suggested that crouched leg postures may improve stability. However, as the system of control strategies is overdetermined, our model findings suggest that a crouched leg posture does not necessarily enhance running stability. The model also predicts different leg stiffness adaptation rates for human and avian running, and suggests that a crouched avian leg posture, which is capable of both leg shortening and lengthening, allows for stable running without adjusting leg stiffness. In contrast, in straight-legged human running, the preparation of the ground contact seems to be more critical, requiring leg stiffness adjustment to remain stable. Finally, analysis of a simple robustness measure, the normalized maximum drop, suggests that the crouched leg posture may provide greater robustness to changes in terrain height. PMID
An approximation theorem for entire functions of exponential type and stability of zero sequences
NASA Astrophysics Data System (ADS)
Khabibullin, B. N.
2004-02-01
Let L be an entire function of exponential type in \\mathbb C with indicator function h_L; let \\Lambda=\\{\\lambda_n\\}, n=1,2,\\dots, be a subsequence of zeros of the entire function of exponential type L\
Xi, Qiang
2016-01-01
In this letter, we consider a model of Cohen-Grossberg neural networks with piecewise constant argument of generalized type and impulses. Sufficient conditions ensuring the existence and uniqueness of solutions are obtained. Based on constructing a new differential inequality with piecewise constant argument and impulse and using the Lyapunov function method, we derive sufficient conditions ensuring the global exponential stability of equilibrium point, with approximate exponential convergence rate. An example is given to illustrate the validity and advantage of the theoretical results. PMID:26599709
Impossibility of unconditional stability and robustness of diffusive acceleration schemes
Azmy, Y.Y.
1998-01-01
The authors construct a problem for which exists no preconditioner with a cell-centered diffusion coupling stencil that is unconditionally stable and robust. In particular they consider an asymptotic limit of the Periodic Horizontal Interface (PHI) configuration wherein the cell height in both layers approaches zero like {sigma}{sup 2} while the total cross section varies like a in one layer and like 1/{sigma} in the other layer. In such case they show that the conditions for stability and robustness of the flat eigenmodes of the iteration residual imply instability of the modes flat in the y-dimension and rapidly varying in the x-dimension. This paper is important for radiation transport studies.
Determination of robust stability margin for second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.; Kau, C.-T.; Juang, Jer-Nan
1992-01-01
Robust stabilization of uncertain systems has been extensively investigated and the stability test for the whole set of uncertain parameters has been reduced to a finite number of test points, four points for the characteristic polynomial with independent coefficients. As a result the robust stability margin can be determined using a reasonable amount of computation. It is impossible to apply the results of the test to a practical system as the coefficients of the characteristic polynomial for a physical system are usually functions of uncertain parameters. However, many physical systems may be represented by a second-order mass-spring-damper system with a special multilinear form in its characteristic polynomial. This paper investigates second-order mass-spring-damper systems and the reduction of the number of test points. It is shown that such a system with arbritrary compensators always has a multilinear characteristic polynomial. It is also shown that a line in the two-dimensional parameter space forms the boundary after the mapping of a multilinear characteristic polynomial and this interior extreme line forms a conic curve in the complex plane. The boundary of uncertain domain for a multilinear polynomial with two uncertainty parameters can be determined analytically using this curve, and the four sides image of a square of the uncertain parameter. Therefore, the stability margin may be determined by checking the intersections of the boundary with the zero point. A similar procedure can be used for second-order systems with more than two uncertainty parameters when parameter optimization is used in determining the boundary.
NASA Astrophysics Data System (ADS)
Bao, Haibo; Cao, Jinde
2011-09-01
This paper investigates the problem of the global exponential stability for neutral-type impulsive neural networks with mixed delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays and the jumping parameters are generated from a continuous time discrete state homogenous Markov process. Based on the Lyapunov functional, a sufficient criterion is derived in terms of linear matrix equality (LMI).
Exponential stability preservation in semi-discretisations of BAM networks with nonlinear impulses
NASA Astrophysics Data System (ADS)
Mohamad, Sannay; Gopalsamy, K.
2009-01-01
This paper demonstrates the reliability of a discrete-time analogue in preserving the exponential convergence of a bidirectional associative memory (BAM) network that is subject to nonlinear impulses. The analogue derived from a semi-discretisation technique with the value of the time-step fixed is treated as a discrete-time dynamical system while its exponential convergence towards an equilibrium state is studied. Thereby, a family of sufficiency conditions governing the network parameters and the impulse magnitude and frequency is obtained for the convergence. As special cases, one can obtain from our results, those corresponding to the non-impulsive discrete-time BAM networks and also those corresponding to continuous-time (impulsive and non-impulsive) systems. A relation between the Lyapunov exponent of the non-impulsive system and that of the impulsive system involving the size of the impulses and the inter-impulse intervals is obtained.
Lack of exponential stability to Timoshenko system with viscoelastic Kelvin-Voigt type
NASA Astrophysics Data System (ADS)
Malacarne, Andréia; Muñoz Rivera, Jaime Edilberto
2016-06-01
We study the Timoshenko systems with a viscoelastic dissipative mechanism of Kelvin-Voigt type. We prove that the model is analytical if and only if the viscoelastic damping is present in both the shear stress and the bending moment. Otherwise, the corresponding semigroup is not exponentially stable no matter the choice of the coefficients. This result is different to all others related to Timoshenko model with partial dissipation, which establish that the system is exponentially stable if and only if the wave speeds are equal. Finally, we show that the solution decays polynomially to zero as {t^{-1/2}} , no matter where the viscoelastic mechanism is effective and that the rate is optimal whenever the initial data are taken on the domain of the infinitesimal operator.
NASA Astrophysics Data System (ADS)
Liao, Xiaofeng; Wong, Kwok-Wo
2003-04-01
In this paper, the dynamical characteristics of hybrid bidirectional associative memory neural networks with constant transmission delays are investigated. Without assuming symmetry of synaptic connection weights and monotonicity and differentiability of activation functions, Halanay-type inequalities (which are different from the approach of constructing Lyapunov functionals) are employed to derive the delay-independent sufficient conditions under which the networks converge exponentially to the equilibria associated with temporally uniform external inputs. Our results are less conservative and restrictive than previously known results.
NASA Astrophysics Data System (ADS)
Liu, Wenjun
2014-11-01
In this paper, we consider a wave equation with space variable coefficients. Due to physical considerations, a distributed delay damping is acted on the part of the boundary. Under suitable assumptions, we prove the exponential stability of the energy based on the use of Riemannian geometry method, the perturbed energy argument, and some observability inequalities. From the applications point of view, our results may provide some qualitative analysis and intuition for the researchers in fields such as engineering, biophysics, and mechanics. And the method is rather general and can be adapted to other evolution systems with variable coefficients (e. g. elasticity plates) as well.
NASA Astrophysics Data System (ADS)
Mohamad, Sannay
2001-11-01
Convergence dynamics of continuous-time bidirectional neural networks with constant transmission delays are studied. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, Lyapunov functionals and Halanay-type inequalities are constructed and employed to derive delay independent sufficient conditions under which the continuous-time networks converge exponentially to the equilibria associated with temporally uniform external inputs to the networks. Discrete-time analogues of the continuous-time networks are formulated and we study their dynamical characteristics. It is shown that the convergence dynamics of the continuous-time networks are preserved by the discrete-time analogues without any restriction on the discretization step-size. Several examples are given to illustrate the advantages of the discrete-time analogues in numerically simulating the continuous-time networks.
Robustness of fuzzy logic power system stabilizers applied to multimachine power system
Hiyama, Takashi . Dept. of Electrical Engineering and Computer Science)
1994-09-01
This paper investigates the robustness of fuzzy logic stabilizers using the information of speed and acceleration states of a study unit. The input signals are the real power output and/or the speed of the study unit. Non-linear simulations show the robustness of the fuzzy logic power system stabilizers. Experiments are also performed by using a micro-machine system. The results show the feasibility of proposed fuzzy logic stabilizer.
Li, Hongfei; Jiang, Haijun; Hu, Cheng
2016-03-01
In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results. PMID:26752438
Apalara, Tijani A.; Messaoudi, Salim A.
2015-06-15
In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo’s law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715–2733, 2012), using a method different from that of Santos et al. (J Diff Eqs 253:2715–2733, 2012). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715–2733, 2012) using the multiplier method in the case of absence of delay. The polynomial decay issue in the presence of a small delay is an open question.
NASA Astrophysics Data System (ADS)
Ivashchuk, V. D.
2016-08-01
A (n+1)-dimensional gravitational model with Gauss-Bonnet term and a cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with an exponential dependence of the scale factors, a_i ˜ exp { ( v^i t) }, i =1, dots , n , are analyzed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. if K(v) = sum _{k = 1}n v^k ≠ 0. We prove that under a certain restriction R imposed solutions with K(v) > 0 are stable, while solutions with K(v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v^1 = v^2 =v^3 = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed.
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
NASA Technical Reports Server (NTRS)
Ryan, R.
1993-01-01
Robustness is a buzz word common to all newly proposed space systems design as well as many new commercial products. The image that one conjures up when the word appears is a 'Paul Bunyon' (lumberjack design), strong and hearty; healthy with margins in all aspects of the design. In actuality, robustness is much broader in scope than margins, including such factors as simplicity, redundancy, desensitization to parameter variations, control of parameter variations (environments flucation), and operational approaches. These must be traded with concepts, materials, and fabrication approaches against the criteria of performance, cost, and reliability. This includes manufacturing, assembly, processing, checkout, and operations. The design engineer or project chief is faced with finding ways and means to inculcate robustness into an operational design. First, however, be sure he understands the definition and goals of robustness. This paper will deal with these issues as well as the need for the requirement for robustness.
Robustness, stability and efficiency of phage lambda genetic switch: dynamical structure analysis.
Zhu, X-M; Yin, L; Hood, L; Ao, P
2004-12-01
Based on the dynamical structure theory for complex networks recently developed by one of us and on the physical-chemical models for gene regulation, developed by Shea and Ackers in the 1980's, we formulate a direct and concise mathematical framework for the genetic switch controlling phage lambda life cycles, which naturally includes the stochastic effect. The dynamical structure theory states that the dynamics of a complex network is determined by its four elementary components: The dissipation (analogous to degradation), the stochastic force, the driving force determined by a potential, and the transverse force. The potential may be interpreted as a landscape for the phage development in terms of attractive basins, saddle points, peaks and valleys. The dissipation gives rise to the adaptivity of the phage in the landscape defined by the potential: The phage always has the tendency to approach the bottom of the nearby attractive basin. The transverse force tends to keep the network on the equal-potential contour of the landscape. The stochastic fluctuation gives the phage the ability to search around the potential landscape by passing through saddle points. With molecular parameters in our model fixed primarily by the experimental data on wild-type phage and supplemented by data on one mutant, our calculated results on mutants agree quantitatively with the available experimental observations on other mutants for protein number, lysogenization frequency, and a lysis frequency in lysogen culture. The calculation reproduces the observed robustness of the phage lambda genetic switch. This is the first mathematical description that successfully represents such a wide variety of major experimental phenomena. Specifically, we find: (1) The explanation for both the stability and the efficiency of phage lambda genetic switch is the exponential dependence of saddle point crossing rate on potential barrier height, a result of the stochastic motion in a landscape; and (2
BenAbdallah, Abdallah; Hammami, Mohamed Ali; Kallel, Jalel
2009-03-05
In this paper we present some sufficient conditions for the robust stability and stabilization of time invariant uncertain piecewise linear system using homogenous piecewise polynomial Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities which can be numerically solved. An application of the obtained result is given. It consists in resolving the stabilization of piecewise uncertain linear control systems by using a state piecewise linear feedback.
NASA Astrophysics Data System (ADS)
Pan, Li-Xin; Jin, Hong-Zhang; Wang, Lin-Lin
2011-06-01
In the case of Autonomous Underwater Vehicle (AUV) navigating with low speed near water surface, a new method for design of roll motion controller is proposed in order to restrain wave disturbance effectively and improve roll stabilizing performance. Robust control is applied, which is based on uncertain nonlinear horizontal motion model of AUV and the principle of zero speed fin stabilizer. Feedback linearization approach is used to transform the complex nonlinear system into a comparatively simple linear system. For parameter uncertainty of motion model, the controller is designed with mixed-sensitivity method based on H-infinity robust control theory. Simulation results show better robustness improved by this control method for roll stabilizing of AUV navigating near water surface.
Liu, Yanbin; Liu, Mengying; Sun, Peihua
2014-01-01
A typical model of hypersonic vehicle has the complicated dynamics such as the unstable states, the nonminimum phases, and the strong coupling input-output relations. As a result, designing a robust stabilization controller is essential to implement the anticipated tasks. This paper presents a robust stabilization controller based on the guardian maps theory for hypersonic vehicle. First, the guardian maps theories are provided to explain the constraint relations between the open subsets of complex plane and the eigenvalues of the state matrix of closed-loop control system. Then, a general control structure in relation to the guardian maps theories is proposed to achieve the respected design demands. Furthermore, the robust stabilization control law depending on the given general control structure is designed for the longitudinal model of hypersonic vehicle. Finally, a simulation example is provided to verify the effectiveness of the proposed methods. PMID:24795535
Liu, Mengying; Sun, Peihua
2014-01-01
A typical model of hypersonic vehicle has the complicated dynamics such as the unstable states, the nonminimum phases, and the strong coupling input-output relations. As a result, designing a robust stabilization controller is essential to implement the anticipated tasks. This paper presents a robust stabilization controller based on the guardian maps theory for hypersonic vehicle. First, the guardian maps theories are provided to explain the constraint relations between the open subsets of complex plane and the eigenvalues of the state matrix of closed-loop control system. Then, a general control structure in relation to the guardian maps theories is proposed to achieve the respected design demands. Furthermore, the robust stabilization control law depending on the given general control structure is designed for the longitudinal model of hypersonic vehicle. Finally, a simulation example is provided to verify the effectiveness of the proposed methods. PMID:24795535
Robust stabilization of the Space Station in the presence of inertia matrix uncertainty
NASA Technical Reports Server (NTRS)
Wie, Bong; Liu, Qiang; Sunkel, John
1993-01-01
This paper presents a robust H-infinity full-state feedback control synthesis method for uncertain systems with D11 not equal to 0. The method is applied to the robust stabilization problem of the Space Station in the face of inertia matrix uncertainty. The control design objective is to find a robust controller that yields the largest stable hypercube in uncertain parameter space, while satisfying the nominal performance requirements. The significance of employing an uncertain plant model with D11 not equal 0 is demonstrated.
Robust control design with real parameter uncertainty using absolute stability theory. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
How, Jonathan P.; Hall, Steven R.
1993-01-01
The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds.
Robust Stability of Scaled-Four-Channel Teleoperation with Internet Time-Varying Delays
Delgado, Emma; Barreiro, Antonio; Falcón, Pablo; Díaz-Cacho, Miguel
2016-01-01
We describe the application of a generic stability framework for a teleoperation system under time-varying delay conditions, as addressed in a previous work, to a scaled-four-channel (γ-4C) control scheme. Described is how varying delays are dealt with by means of dynamic encapsulation, giving rise to mu-test conditions for robust stability and offering an appealing frequency technique to deal with the stability robustness of the architecture. We discuss ideal transparency problems and we adapt classical solutions so that controllers are proper, without single or double differentiators, and thus avoid the negative effects of noise. The control scheme was fine-tuned and tested for complete stability to zero of the whole state, while seeking a practical solution to the trade-off between stability and transparency in the Internet-based teleoperation. These ideas were tested on an Internet-based application with two Omni devices at remote laboratory locations via simulations and real remote experiments that achieved robust stability, while performing well in terms of position synchronization and force transparency. PMID:27128914
Robust Stability of Scaled-Four-Channel Teleoperation with Internet Time-Varying Delays.
Delgado, Emma; Barreiro, Antonio; Falcón, Pablo; Díaz-Cacho, Miguel
2016-01-01
We describe the application of a generic stability framework for a teleoperation system under time-varying delay conditions, as addressed in a previous work, to a scaled-four-channel (γ-4C) control scheme. Described is how varying delays are dealt with by means of dynamic encapsulation, giving rise to mu-test conditions for robust stability and offering an appealing frequency technique to deal with the stability robustness of the architecture. We discuss ideal transparency problems and we adapt classical solutions so that controllers are proper, without single or double differentiators, and thus avoid the negative effects of noise. The control scheme was fine-tuned and tested for complete stability to zero of the whole state, while seeking a practical solution to the trade-off between stability and transparency in the Internet-based teleoperation. These ideas were tested on an Internet-based application with two Omni devices at remote laboratory locations via simulations and real remote experiments that achieved robust stability, while performing well in terms of position synchronization and force transparency. PMID:27128914
Karra, Udayarka; Huang, Guoxian; Umaz, Ridvan; Tenaglier, Christopher; Wang, Lei; Li, Baikun
2013-09-01
A novel and robust distributed benthic microbial fuel cell (DBMFC) was developed to address the energy supply issues for oceanographic sensor network applications, especially under scouring and bioturbation by aquatic life. Multi-anode/cathode configuration was employed in the DBMFC system for enhanced robustness and stability in the harsh ocean environment. The results showed that the DBMFC system achieved peak power and current densities of 190mW/m(2) and 125mA/m(2) respectively. Stability characterization tests indicated the DBMFC with multiple anodes achieved higher power generation over the systems with single anode. A computational model that integrated physical, electrochemical and biological factors of MFCs was developed to validate the overall performance of the DBMFC system. The model simulation well corresponded with the experimental results, and confirmed the hypothesis that using a multi anode/cathode MFC configuration results in reliable and robust power generation. PMID:23890975
Robust H∞ stabilization of a hard disk drive system with a single-stage actuator
NASA Astrophysics Data System (ADS)
Harno, Hendra G.; Kiin Woon, Raymond Song
2015-04-01
This paper considers a robust H∞ control problem for a hard disk drive system with a single stage actuator. The hard disk drive system is modeled as a linear time-invariant uncertain system where its uncertain parameters and high-order dynamics are considered as uncertainties satisfying integral quadratic constraints. The robust H∞ control problem is transformed into a nonlinear optimization problem with a pair of parameterized algebraic Riccati equations as nonconvex constraints. The nonlinear optimization problem is then solved using a differential evolution algorithm to find stabilizing solutions to the Riccati equations. These solutions are used for synthesizing an output feedback robust H∞ controller to stabilize the hard disk drive system with a specified disturbance attenuation level.
Control design for robust stability in linear regulators: Application to aerospace flight control
NASA Technical Reports Server (NTRS)
Yedavalli, R. K.
1986-01-01
Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.
Fernández de Cañete, J; Barreiro, A; García-Cerezo, A; García-Moral, I
2001-01-01
A stabilization method based on the input-output conicity criterion is presented. Conventional learning algorithms are applied to adjust the controller dynamics, and robust stability of the closed-loop system is guaranteed by modifying the training patterns which yield unstable behavior. The methodology developed expands the class of nonlinear systems to be controlled using neural control schemes, so that the stabilization of a broad class of neural-network-based control systems, even with unknown dynamics, is assured. Straightforwardness in the application of this method is evident in contrast to the Lyapunov function approach. PMID:18249978
Robust Stability Analysis of the Space Launch System Control Design: A Singular Value Approach
NASA Technical Reports Server (NTRS)
Pei, Jing; Newsome, Jerry R.
2015-01-01
Classical stability analysis consists of breaking the feedback loops one at a time and determining separately how much gain or phase variations would destabilize the stable nominal feedback system. For typical launch vehicle control design, classical control techniques are generally employed. In addition to stability margins, frequency domain Monte Carlo methods are used to evaluate the robustness of the design. However, such techniques were developed for Single-Input-Single-Output (SISO) systems and do not take into consideration the off-diagonal terms in the transfer function matrix of Multi-Input-Multi-Output (MIMO) systems. Robust stability analysis techniques such as H(sub infinity) and mu are applicable to MIMO systems but have not been adopted as standard practices within the launch vehicle controls community. This paper took advantage of a simple singular-value-based MIMO stability margin evaluation method based on work done by Mukhopadhyay and Newsom and applied it to the SLS high-fidelity dynamics model. The method computes a simultaneous multi-loop gain and phase margin that could be related back to classical margins. The results presented in this paper suggest that for the SLS system, traditional SISO stability margins are similar to the MIMO margins. This additional level of verification provides confidence in the robustness of the control design.
Flight control application of new stability robustness bounds for linear uncertain systems
NASA Technical Reports Server (NTRS)
Yedavalli, Rama K.
1993-01-01
This paper addresses the issue of obtaining bounds on the real parameter perturbations of a linear state-space model for robust stability. Based on Kronecker algebra, new, easily computable sufficient bounds are derived that are much less conservative than the existing bounds since the technique is meant for only real parameter perturbations (in contrast to specializing complex variation case to real parameter case). The proposed theory is illustrated with application to several flight control examples.
Koh, Yeong Jun; Lee, Chulwoo; Kim, Chang-Su
2015-12-01
We propose a video stabilization algorithm, which extracts a guaranteed number of reliable feature trajectories for robust mesh grid warping. We first estimate feature trajectories through a video sequence and transform the feature positions into rolling-free smoothed positions. When the number of the estimated trajectories is insufficient, we generate virtual trajectories by augmenting incomplete trajectories using a low-rank matrix completion scheme. Next, we detect feature points on a large moving object and exclude them so as to stabilize camera movements, rather than object movements. With the selected feature points, we set a mesh grid on each frame and warp each grid cell by moving the original feature positions to the smoothed ones. For robust warping, we formulate a cost function based on the reliability weights of each feature point and each grid cell. The cost function consists of a data term, a structure-preserving term, and a regularization term. By minimizing the cost function, we determine the robust mesh grid warping and achieve the stabilization. Experimental results demonstrate that the proposed algorithm reconstructs videos more stably than the conventional algorithms. PMID:26394425
Wang, Leimin; Shen, Yi; Sheng, Yin
2016-04-01
This paper is concerned with the finite-time robust stabilization of delayed neural networks (DNNs) in the presence of discontinuous activations and parameter uncertainties. By using the nonsmooth analysis and control theory, a delayed controller is designed to realize the finite-time robust stabilization of DNNs with discontinuous activations and parameter uncertainties, and the upper bound of the settling time functional for stabilization is estimated. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results. PMID:26878721
Xu, Lijun; Jiang, Qi; Gu, Guodong
2016-01-01
A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results. PMID:27190502
High-throughput thermal scanning for protein stability: making a good technique more robust.
Seabrook, Shane A; Newman, Janet
2013-08-12
We present a high-throughput approach to help define experimental formulations that enhance protein stability, which is based on differential scanning fluorimetry (DSF). The method involves defining the thermal stability of a protein against a screen of 13 buffer systems, systematically sampling pH from 5.0 to 9.0 at high and low salt concentrations, using both redundancy and extensive controls to make the method robust. The screen allows rapid determination of a suitable base formulation for protein samples, and is particularly useful for difficult samples: those that are rapidly degraded or cannot be sufficiently concentrated for downstream analyses. Data obtained from three samples in this assay illustrate the vastly different values for thermal stability that can be obtained from different formulations. This approach is simple to interpret and reliable enough that it has been implemented as a service through the Collaborative Crystallisation Centre (C3). PMID:23710551
Robust adaptive spin-axis stabilization of a symmetric spacecraft using two bounded torques
NASA Astrophysics Data System (ADS)
Gui, Haichao; Vukovich, George
2015-12-01
The spin-axis stabilization of an axisymmetric spacecraft by two control torques perpendicular to the symmetry axis is addressed. Two control laws are designed to align the symmetry axis along a desired inertial direction despite the revolution around the symmetry axis. The first controller takes a saturated proportional-derivative form and can stabilize the spin-axis to the desired direction with a priori bounded torques in the absence of modeling uncertainties. In order to achieve better robustness, an adaptive controller is then designed to account for the inertia uncertainties and disturbances, in addition to actuator saturation. Numerical examples are presented to demonstrate the advantageous features of the proposed algorithm compared with conventional spin-axis stabilization methods.
Redi, M.H.; Diallo, A.; Cooper, W.A.; Fu, G.Y.
2000-01-27
Concerns about the flexibility and robustness of a compact quasiaxial stellarator design are addressed by studying the effects of varied pressure and rotational transform profiles on expected performance. For thirty, related, fully three-dimensional configurations the global, ideal magnetohydrodynamic stability is evaluated as well as energetic particle transport. It is found that tokamak intuition is relevant to understanding the magnetohydrodynamic stability, with pressure gradient driving terms and shear stabilization controlling both the periodicity preserving, N=0, and the non-periodicity preserving, N=1, unstable kink modes. Global kink modes are generated by steeply peaked pressure profiles near the half radius and edge localized kink modes are found for plasmas with steep pressure profiles at the edge as well as with edge rotational transform above 0.5. Energetic particle transport is not strongly dependent on these changes of pressure and current (or rotational transform) profiles, although a weak inverse dependence on pressure peaking through the corresponding Shafranov shift is found. While good transport and MHD stability are not anticorrelated in these equilibria, stability only results from a delicate balance of the pressure and shear stabilization forces. A range of interesting MHD behaviors is found for this large set of equilibria, exhibiting similar particle transport properties.
On the control of elastic vehicles - Model simplification and stability robustness
NASA Technical Reports Server (NTRS)
Schmidt, David K.; Newman, Brett
1989-01-01
Quantitative criteria are presented for model simplification, or order reduction, such that the reduced order model may be used to synthesize and evaluate a control law, and the stability and stability robustness obtained using the reduced-order model will be preserved when controlling the full-order system. The error introduced due to model simplification is treated as modeling uncertainty, and some of the results from multivariable robustness theory are brought to bear on the model simplification problem. A numerical procedure developed previously is shown to lead to results that meet the necessary criteria. The procedure is applied to reduce the model of a flexible aircraft. Also, the importance of the control law itself, in meeting the modeling criteria, is underscored. An example is included that demonstrates that an apparently robust control law actually amplifies modest modeling errors in the critical frequency region, and leads to undesirable results. The cause of this problem is identified to be associated with the canceling of lightly-damped transmission zeroes in the plant.
A Robust Method of Vehicle Stability Accurate Measurement Using GPS and INS
NASA Astrophysics Data System (ADS)
Miao, Zhibin; Zhang, Hongtian; Zhang, Jinzhu
2015-12-01
With the development of the vehicle industry, controlling stability has become more and more important. Techniques of evaluating vehicle stability are in high demand. Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) is a very practical method to get high-precision measurement data. Usually, the Kalman filter is used to fuse the data from GPS and INS. In this paper, a robust method is used to measure vehicle sideslip angle and yaw rate, which are two important parameters for vehicle stability. First, a four-wheel vehicle dynamic model is introduced, based on sideslip angle and yaw rate. Second, a double level Kalman filter is established to fuse the data from Global Positioning System and Inertial Navigation System. Then, this method is simulated on a sample vehicle, using Carsim software to test the sideslip angle and yaw rate. Finally, a real experiment is made to verify the advantage of this approach. The experimental results showed the merits of this method of measurement and estimation, and the approach can meet the design requirements of the vehicle stability controller.
Wang, Jin; Li, Chunhe; Wang, Erkang
2010-05-01
Studying the cell cycle process is crucial for understanding cell growth, proliferation, development, and death. We uncovered some key factors in determining the global robustness and function of the budding yeast cell cycle by exploring the underlying landscape and flux of this nonequilibrium network. The dynamics of the system is determined by both the landscape which attracts the system down to the oscillation orbit and the curl flux which drives the periodic motion on the ring. This global structure of landscape is crucial for the coherent cell cycle dynamics and function. The topography of the underlying landscape, specifically the barrier height separating basins of attractions, characterizes the capability of changing from one part of the system to another. This quantifies the stability and robustness of the system. We studied how barrier height is influenced by environmental fluctuations and perturbations on specific wirings of the cell cycle network. When the fluctuations increase, the barrier height decreases and the period and amplitude of cell cycle oscillation is more dispersed and less coherent. The corresponding dissipation of the system quantitatively measured by the entropy production rate increases. This implies that the system is less stable under fluctuations. We identified some key structural elements for wirings of the cell cycle network responsible for the change of the barrier height and therefore the global stability of the system through the sensitivity analysis. The results are in agreement with recent experiments and also provide new predictions. PMID:20393126
A novel predictive control algorithm and robust stability criteria for integrating processes.
Zhang, Bin; Yang, Weimin; Zong, Hongyuan; Wu, Zhiyong; Zhang, Weidong
2011-07-01
This paper introduces a novel predictive controller for single-input/single-output (SISO) integrating systems, which can be directly applied without pre-stabilizing the process. The control algorithm is designed on the basis of the tested step response model. To produce a bounded system response along the finite predictive horizon, the effect of the integrating mode must be zeroed while unmeasured disturbances exist. Here, a novel predictive feedback error compensation method is proposed to eliminate the permanent offset between the setpoint and the process output while the integrating system is affected by load disturbance. Also, a rotator factor is introduced in the performance index, which is contributed to the improvement robustness of the closed-loop system. Then on the basis of Jury's dominant coefficient criterion, a robust stability condition of the resulted closed loop system is given. There are only two parameters which need to be tuned for the controller, and each has a clear physical meaning, which is convenient for implementation of the control algorithm. Lastly, simulations are given to illustrate that the proposed algorithm can provide excellent closed loop performance compared with some reported methods. PMID:21353217
Robust flow stability: Theory, computations and experiments in near wall turbulence
NASA Astrophysics Data System (ADS)
Bobba, Kumar Manoj
Helmholtz established the field of hydrodynamic stability with his pioneering work in 1868. From then on, hydrodynamic stability became an important tool in understanding various fundamental fluid flow phenomena in engineering (mechanical, aeronautics, chemical, materials, civil, etc.) and science (astrophysics, geophysics, biophysics, etc.), and turbulence in particular. However, there are many discrepancies between classical hydrodynamic stability theory and experiments. In this thesis, the limitations of traditional hydrodynamic stability theory are shown and a framework for robust flow stability theory is formulated. A host of new techniques like gramians, singular values, operator norms, etc. are introduced to understand the role of various kinds of uncertainty. An interesting feature of this framework is the close interplay between theory and computations. It is shown that a subset of Navier-Stokes equations are globally, non-nonlinearly stable for all Reynolds number. Yet, invoking this new theory, it is shown that these equations produce structures (vortices and streaks) as seen in the experiments. The experiments are done in zero pressure gradient transiting boundary layer on a flat plate in free surface tunnel. Digital particle image velocimetry, and MEMS based laser Doppler velocimeter and shear stress sensors have been used to make quantitative measurements of the flow. Various theoretical and computational predictions are in excellent agreement with the experimental data. A closely related topic of modeling, simulation and complexity reduction of large mechanics problems with multiple spatial and temporal scales is also studied. A nice method that rigorously quantifies the important scales and automatically gives models of the problem to various levels of accuracy is introduced. Computations done using spectral methods are presented.
Anderson, Ericka L; Li, Weizhong; Klitgord, Niels; Highlander, Sarah K; Dayrit, Mark; Seguritan, Victor; Yooseph, Shibu; Biggs, William; Venter, J Craig; Nelson, Karen E; Jones, Marcus B
2016-01-01
As reports on possible associations between microbes and the host increase in number, more meaningful interpretations of this information require an ability to compare data sets across studies. This is dependent upon standardization of workflows to ensure comparability both within and between studies. Here we propose the standard use of an alternate collection and stabilization method that would facilitate such comparisons. The DNA Genotek OMNIgene∙Gut Stool Microbiome Kit was compared to the currently accepted community standard of freezing to store human stool samples prior to whole genome sequencing (WGS) for microbiome studies. This stabilization and collection device allows for ambient temperature storage, automation, and ease of shipping/transfer of samples. The device permitted the same data reproducibility as with frozen samples, and yielded higher recovery of nucleic acids. Collection and stabilization of stool microbiome samples with the DNA Genotek collection device, combined with our extraction and WGS, provides a robust, reproducible workflow that enables standardized global collection, storage, and analysis of stool for microbiome studies. PMID:27558918
Anderson, Ericka L.; Li, Weizhong; Klitgord, Niels; Highlander, Sarah K.; Dayrit, Mark; Seguritan, Victor; Yooseph, Shibu; Biggs, William; Venter, J. Craig; Nelson, Karen E.; Jones, Marcus B.
2016-01-01
As reports on possible associations between microbes and the host increase in number, more meaningful interpretations of this information require an ability to compare data sets across studies. This is dependent upon standardization of workflows to ensure comparability both within and between studies. Here we propose the standard use of an alternate collection and stabilization method that would facilitate such comparisons. The DNA Genotek OMNIgene∙Gut Stool Microbiome Kit was compared to the currently accepted community standard of freezing to store human stool samples prior to whole genome sequencing (WGS) for microbiome studies. This stabilization and collection device allows for ambient temperature storage, automation, and ease of shipping/transfer of samples. The device permitted the same data reproducibility as with frozen samples, and yielded higher recovery of nucleic acids. Collection and stabilization of stool microbiome samples with the DNA Genotek collection device, combined with our extraction and WGS, provides a robust, reproducible workflow that enables standardized global collection, storage, and analysis of stool for microbiome studies. PMID:27558918
Chen, Bor-Sen; Chang, Yu-Te; Wang, Yu-Chao
2008-02-01
Molecular noises in gene networks come from intrinsic fluctuations, transmitted noise from upstream genes, and the global noise affecting all genes. Knowledge of molecular noise filtering in gene networks is crucial to understand the signal processing in gene networks and to design noise-tolerant gene circuits for synthetic biology. A nonlinear stochastic dynamic model is proposed in describing a gene network under intrinsic molecular fluctuations and extrinsic molecular noises. The stochastic molecular-noise-processing scheme of gene regulatory networks for attenuating these molecular noises is investigated from the nonlinear robust stabilization and filtering perspective. In order to improve the robust stability and noise filtering, a robust gene circuit design for gene networks is proposed based on the nonlinear robust H infinity stochastic stabilization and filtering scheme, which needs to solve a nonlinear Hamilton-Jacobi inequality. However, in order to avoid solving these complicated nonlinear stabilization and filtering problems, a fuzzy approximation method is employed to interpolate several linear stochastic gene networks at different operation points via fuzzy bases to approximate the nonlinear stochastic gene network. In this situation, the method of linear matrix inequality technique could be employed to simplify the gene circuit design problems to improve robust stability and molecular-noise-filtering ability of gene networks to overcome intrinsic molecular fluctuations and extrinsic molecular noises. PMID:18270080
NASA Technical Reports Server (NTRS)
Garg, Sanjay
1989-01-01
A methodology to improve the stability robustness of feedback control systems designed using direct eigenspace assignment techniques is presented. The method consists of considering the sensitivity of the minimum singular value of the return difference transfer matrix at the plant input to small changes in the desired closed-loop eigenvalues and the specified elements of the desired closed-loop eigenvectors. Closed-form expressions for the gradient of the minimum return difference singular value with respect to desired closed-loop eigenvalue and eigenvector parameters are derived. Closed-form expressions for the gradients of the control feedback gains with respect to the specified eigenspace parameters are obtained as an intermediate step. The use of the gradient information to improve the guaranteed gain and phase margins in eigenspace assignment based designs is demonstrated by application to an advanced fighter aircraft.
Li, Ning; Cao, Jinde; Hayat, Tasawar
2014-08-01
This paper is concerned with a class of nonlinear uncertain switched networks with discrete time-varying delays . Based on the strictly complete property of the matrices system and the delay-decomposing approach, exploiting a new Lyapunov-Krasovskii functional decomposing the delays in integral terms, the switching rule depending on the state of the network is designed. Moreover, by piecewise delay method, discussing the Lyapunov functional in every different subintervals, some new delay-dependent robust stability criteria are derived in terms of linear matrix inequalities, which lead to much less conservative results than those in the existing references and improve previous results. Finally, an illustrative example is given to demonstrate the validity of the theoretical results. PMID:25009673
Buffered Qualitative Stability explains the robustness and evolvability of transcriptional networks
Albergante, Luca; Blow, J Julian; Newman, Timothy J
2014-01-01
The gene regulatory network (GRN) is the central decision‐making module of the cell. We have developed a theory called Buffered Qualitative Stability (BQS) based on the hypothesis that GRNs are organised so that they remain robust in the face of unpredictable environmental and evolutionary changes. BQS makes strong and diverse predictions about the network features that allow stable responses under arbitrary perturbations, including the random addition of new connections. We show that the GRNs of E. coli, M. tuberculosis, P. aeruginosa, yeast, mouse, and human all verify the predictions of BQS. BQS explains many of the small- and large‐scale properties of GRNs, provides conditions for evolvable robustness, and highlights general features of transcriptional response. BQS is severely compromised in a human cancer cell line, suggesting that loss of BQS might underlie the phenotypic plasticity of cancer cells, and highlighting a possible sequence of GRN alterations concomitant with cancer initiation. DOI: http://dx.doi.org/10.7554/eLife.02863.001 PMID:25182846
NASA Astrophysics Data System (ADS)
Nguyen, Quan M.; Peleg, Avner; Tran, Thinh P.
2015-01-01
We develop a method for transmission stabilization and robust dynamic switching for colliding optical soliton sequences in broadband waveguide systems with nonlinear gain and loss. The method is based on employing hybrid waveguides, consisting of spans with linear gain and cubic loss, and spans with linear loss, cubic gain, and quintic loss. We show that the amplitude dynamics is described by a hybrid Lotka-Volterra (LV) model, and use the model to determine the physical parameter values required for enhanced transmission stabilization and switching. Numerical simulations with coupled nonlinear Schrödinger equations confirm the predictions of the LV model, and show complete suppression of radiative instability and pulse distortion. This enables stable transmission over distances larger by an order of magnitude compared with uniform waveguides with linear gain and cubic loss. Moreover, multiple on-off and off-on dynamic switching events are demonstrated over a wide range of soliton amplitudes, showing the superiority of hybrid waveguides compared with static switching in uniform waveguides.
NASA Astrophysics Data System (ADS)
Ratschbacher, Lothar; Gallego, Jose; Ghosh, Sutapa; Alavi, Seyed; Alt, Wolfgang; Martinez-Dorantes, Miguel; Meschede, Dieter
2016-04-01
Fiber Fabry-Perot cavities, formed by micro-machined mirrors on the end-facets of optical fibers, are used in an increasing number of technical and scientific applications. Some of the most promising areas of application of these optical micro-resonators with high finesse and small mode volume are in the field of quantum communication and information. The resonator-enhanced light-matter interaction, for instance, provide basis for the realization of efficient optical interfaces between stationary matter-based quantum nodes and flying single-photon qubits. To date fiber Fabry-Perot cavities have been successfully applied in experiments interfacing single photons with a wide range of quantum systems, including cold atoms, ions and solid state emitters as well as quantum optomechanical experiments. Here we address some important practical questions that arise during the experimental implementation of high finesse fiber Fabry-Perot cavities: How can optimal fiber cavity alignment be achieved and how can the efficiency of coupling light from the optical fibers to the cavity mode and vice versa be characterized? How should optical fiber cavities be constructed and stabilized to fulfill their potential for miniaturization and integration into robust scientific and technological devices that can operate outside of dedicated laboratory environments in the future? The first two questions we answer with an analytic mode matching calculation that relates the alignment dependent fiber-to-cavity mode-matching efficiency to the easily measurable dip in the reflected light power at the cavity resonance. Our general analysis provides a simple recipe for the optimal alignment of fiber Fabry-Perot cavities and moreover for the first time explains the asymmetry in their reflective line shapes. The latter question we explore by investigating a novel, intrinsically rigid fiber cavity design that makes use of the high passive stability of a monolithic cavity spacer and employs thermal
ERIC Educational Resources Information Center
Ishigami, Yoko; Klein, Raymond M.
2015-01-01
The current study examined the robustness, stability, reliability, and isolability of the attention network scores (alerting, orienting, and executive control) when young children experienced repeated administrations of the child version of the Attention Network Test (ANT; Rueda et al., 2004). Ten test sessions of the ANT were administered to 12…
Robust motion filtering as an enabler to video stabilization for a tele-operated mobile robot
NASA Astrophysics Data System (ADS)
Chereau, Romain; Breckon, Toby P.
2013-10-01
An increasing number of inspection and hazardous environment tasks use mobile robotic vehicles manually tele-operated via a live video feed from an on-board camera. The resulting video imagery frequently suffers from vibration artefacts compromising the accuracy and security of operation in addition to the viable duration for human tele-operation. Here we aim to automatically remove these unwanted visual effects using a novel real-time video stabilization approach. Prior work for hand-held and vehicle mounted cameras is ill-suited to the high-frequency, large magnitude (10-15% of image size) vibration encountered on the short wheelbase, non-suspended robotic platforms typically deployed for such tasks. Without prior knowledge of the robot ego-motion (or vibration characteristics) we develop a novel four stage filtering approach to identify robust Local Motion Vectors (LMV) for Global Motion Vector (GMV) estimation in successive video frames whilst preserving the required real-time responsiveness for tele-operation. Experimental results over a range of tele-operation scenarios show that the method provides both significant qualitative visual improvement and a quantitative reduction in measurable video image displacement (caused by vibration).
NASA Astrophysics Data System (ADS)
Ngamroo, Issarachai
2010-12-01
It is well known that the superconducting magnetic energy storage (SMES) is able to quickly exchange active and reactive power with the power system. The SMES is expected to be the smart storage device for power system stabilization. Although the stabilizing effect of SMES is significant, the SMES is quite costly. Particularly, the superconducting magnetic coil size which is the essence of the SMES, must be carefully selected. On the other hand, various generation and load changes, unpredictable network structure, etc., cause system uncertainties. The power controller of SMES which is designed without considering such uncertainties, may not tolerate and loses stabilizing effect. To overcome these problems, this paper proposes the new design of robust SMES controller taking coil size and system uncertainties into account. The structure of the active and reactive power controllers is the 1st-order lead-lag compensator. No need for the exact mathematical representation, system uncertainties are modeled by the inverse input multiplicative perturbation. Without the difficulty of the trade-off of damping performance and robustness, the optimization problem of control parameters is formulated. The particle swarm optimization is used for solving the optimal parameters at each coil size automatically. Based on the normalized integral square error index and the consideration of coil current constraint, the robust SMES with the smallest coil size which still provides the satisfactory stabilizing effect, can be achieved. Simulation studies in the two-area four-machine interconnected power system show the superior robustness of the proposed robust SMES with the smallest coil size under various operating conditions over the non-robust SMES with large coil size.
Theory, computation, and application of exponential splines
NASA Technical Reports Server (NTRS)
Mccartin, B. J.
1981-01-01
A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
Im, Hyeon-Gyun; Jin, Jungho; Ko, Ji-Hoon; Lee, Jaemin; Lee, Jung-Yong; Bae, Byeong-Soo
2014-01-21
We report on the performance of an all-in-one flexible hybrid conducting film employing a monolithically embedded AgNW transparent electrode and a high-performance glass-fabric reinforced composite substrate (AgNW-GFRHybrimer film). Specifically, we perform in-depth investigations on the stability of the AgNW-GFRHybrimer film against heat, thermal oxidation, and wet chemicals to demonstrate the potential of the hybrid conducting film as a robust electrode platform for thin-film optoelectronic devices. With the ease of large-area processability, smooth surface topography, and robust performance stability, the AgNW-GFRHybrimer film can be a promising platform for high-performance optoelectronic devices. PMID:24284890
Jin, Q B; Liu, Q; Huang, B
2016-03-01
This paper considers the problem of determining all the robust PID (proportional-integral-derivative) controllers in terms of the gain and phase margins (GPM) for open-loop unstable first order plus time delay (UFOPTD) processes. It is the first time that the feasible ranges of the GPM specifications provided by a PID controller are given for UFOPTD processes. A gain and phase margin tester is used to modify the original model, and the ranges of the margin specifications are derived such that the modified model can be stabilized by a stabilizing PID controller based on Hermite-Biehlers Theorem. Furthermore, we obtain all the controllers satisfying a given margin specification. Simulation studies show how to use the results to design a robust PID controller. PMID:26708658
NASA Astrophysics Data System (ADS)
Ripamonti, Francesco; Resta, Ferruccio; Vivani, Andrea
2015-04-01
The aim of this paper is to present two control logics and an attitude estimator for UAV stabilization and remote piloting, that are as robust as possible to physical parameters variation and to other external disturbances. Moreover, they need to be implemented on low-cost micro-controllers, in order to be attractive for commercial drones. As an example, possible applications of the two switching control logics could be area surveillance and facial recognition by means of a camera mounted on the drone: the high computational speed logic is used to reach the target, when the high-stability one is activated, in order to complete the recognition tasks.
Jaballi, Ahmed; Sakly, Anis; Hajjaji, Ahmed El
2016-07-01
This paper provides novel sufficient conditions on robust asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy with time-varying delays. The attention is focused on developing new algebraic criteria to break with classical criteria in terms of Linear Matrix Inequalities (LMIs). Firstly, based on the M-matrix proprieties and through l1,∞ induced norms notion, new delay-dependent sufficient conditions are derived to ensure the asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy systems with time-varying delay. Secondly, these results are extended for a class of uncertain discrete-time switched fuzzy systems with time delays, modeled by difference equations. Finally, two numerical examples and practical example (a robot arm) are provided to demonstrate the advantage and the effectiveness of our results. PMID:26996925
NASA Astrophysics Data System (ADS)
Im, Hyeon-Gyun; Jin, Jungho; Ko, Ji-Hoon; Lee, Jaemin; Lee, Jung-Yong; Bae, Byeong-Soo
2013-12-01
We report on the performance of an all-in-one flexible hybrid conducting film employing a monolithically embedded AgNW transparent electrode and a high-performance glass-fabric reinforced composite substrate (AgNW-GFRHybrimer film). Specifically, we perform in-depth investigations on the stability of the AgNW-GFRHybrimer film against heat, thermal oxidation, and wet chemicals to demonstrate the potential of the hybrid conducting film as a robust electrode platform for thin-film optoelectronic devices. With the ease of large-area processability, smooth surface topography, and robust performance stability, the AgNW-GFRHybrimer film can be a promising platform for high-performance optoelectronic devices.We report on the performance of an all-in-one flexible hybrid conducting film employing a monolithically embedded AgNW transparent electrode and a high-performance glass-fabric reinforced composite substrate (AgNW-GFRHybrimer film). Specifically, we perform in-depth investigations on the stability of the AgNW-GFRHybrimer film against heat, thermal oxidation, and wet chemicals to demonstrate the potential of the hybrid conducting film as a robust electrode platform for thin-film optoelectronic devices. With the ease of large-area processability, smooth surface topography, and robust performance stability, the AgNW-GFRHybrimer film can be a promising platform for high-performance optoelectronic devices. Electronic supplementary information (ESI) available: Further characteristics of AgNW-GFRHybrimer films and thermal oxidation of AgNW on glass. See DOI: 10.1039/c3nr05348b
Precup, Radu-Emil; David, Radu-Codrut; Petriu, Emil M; Radac, Mircea-Bogdan; Preitl, Stefan
2014-11-01
This paper suggests a new generation of optimal PI controllers for a class of servo systems characterized by saturation and dead zone static nonlinearities and second-order models with an integral component. The objective functions are expressed as the integral of time multiplied by absolute error plus the weighted sum of the integrals of output sensitivity functions of the state sensitivity models with respect to two process parametric variations. The PI controller tuning conditions applied to a simplified linear process model involve a single design parameter specific to the extended symmetrical optimum (ESO) method which offers the desired tradeoff to several control system performance indices. An original back-calculation and tracking anti-windup scheme is proposed in order to prevent the integrator wind-up and to compensate for the dead zone nonlinearity of the process. The minimization of the objective functions is carried out in the framework of optimization problems with inequality constraints which guarantee the robust stability with respect to the process parametric variations and the controller robustness. An adaptive gravitational search algorithm (GSA) solves the optimization problems focused on the optimal tuning of the design parameter specific to the ESO method and of the anti-windup tracking gain. A tuning method for PI controllers is proposed as an efficient approach to the design of resilient control systems. The tuning method and the PI controllers are experimentally validated by the adaptive GSA-based tuning of PI controllers for the angular position control of a laboratory servo system. PMID:25330468
Robust reliable control design for networked control system with sampling communication
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Santra, Srimanta; Mathiyalagan, K.; Su, Hongye
2015-12-01
In this article, the problem of robust exponential stability and reliable stabilisation for a class of continuous-time networked control systems (NCSs) with a sample-data controller and unknown time-varying sampling rate is considered. The analysis is based on average dwell-time, Lyapunov-Krasovskii functional and linear matrix inequality (LMI) technique. The delay-dependent criteria are developed for ensuring the robust exponential stability of the considered NCSs. The obtained conditions are formulated in terms of LMIs that can easily be solved by using standard software packages. Furthermore, the result is extended to study the robust stabilisation for NCS with parameter uncertainties. A state feedback controller is constructed in terms of the solution to a set of LMIs, which guarantee the robust exponential stabilisation of NCS and the controller. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.
Stabilization and robustness of non-linear unity-feedback system - Factorization approach
NASA Technical Reports Server (NTRS)
Desoer, C. A.; Kabuli, M. G.
1988-01-01
The paper is a self-contained discussion of a right factorization approach in the stability analysis of the nonlinear continuous-time or discrete-time, time-invariant or time-varying, well-posed unity-feedback system S1(P, C). It is shown that a well-posed stable feedback system S1(P, C) implies that P and C have right factorizations. In the case where C is stable, P has a normalized right-coprime factorization. The factorization approach is used in stabilization and simultaneous stabilization results.
ERIC Educational Resources Information Center
Huynh, Huynh; Rawls, Anita
2011-01-01
There are at least two procedures to assess item difficulty stability in the Rasch model: robust z procedure and "0.3 Logit Difference" procedure. The robust z procedure is a variation of the z statistic that reduces dependency on outliers. The "0.3 Logit Difference" procedure is based on experiences in Rasch linking for tests developed by…
Meyer-Baese, A; Theis, F; Emmett, M R
2010-01-01
The tryptophan system present in Escherichia coli represents an important regulatory unit described by multiple feedback loops. The role of these feedback loops is crucial for the analysis of the dynamical behavior of the tryptophan synthesis. We analyze the robust stability of this system which models the dynamics of both fast state, such as transcription and synthesis of free operator, and slow state, such as translation and tryptophan synthesis under consideration of nonlinear uncertainties. In addition, we analyze the role of these feedback loops as key design components of this regulatory unit responsible for its physiological performance. The range of allowed parameter perturbations and the conditions that ensure the existence of asymptotically stable equilibria of the perturbed system are determined. We also analyze two important alternate regulatory designs for the tryptophan synthesis pathway and derive the stability conditions. PMID:20865501
An Exceptional Exponential Function
ERIC Educational Resources Information Center
Curgus, Branko
2006-01-01
We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base "e." A similar link is established for families of functions obtained by composing…
Surface Coordination of Black Phosphorus for Robust Air and Water Stability.
Zhao, Yuetao; Wang, Huaiyu; Huang, Hao; Xiao, Quanlan; Xu, Yanhua; Guo, Zhinan; Xie, Hanhan; Shao, Jundong; Sun, Zhengbo; Han, Weijia; Yu, Xue-Feng; Li, Penghui; Chu, Paul K
2016-04-11
A titanium sulfonate ligand is synthesized for surface coordination of black phosphorus (BP). In contrast to serious degradation observed from the bare BP, the BP after surface coordination exhibits excellent stability during dispersion in water and exposure to air for a long period of time, thereby significantly extending the lifetime and spurring broader application of BP. PMID:26968443
NASA Astrophysics Data System (ADS)
Hossain, Jahangir; Mahmud, Apel; Roy, Naruttam K.; Pota, Hemanshu R.
2013-10-01
In stressed power systems with large induction machine component, there exist undamped electromechanical modes and unstable monotonic voltage modes. This article proposes a sequential design of an excitation controller and a power system stabiliser (PSS) to stabilise the system. The operating region, with induction machines in stressed power systems, is often not captured using a linearisation around an operating point, and to alleviate this situation a robust controller is designed which guarantees stable operation in a large region of operation. A minimax linear quadratic Gaussian design is used for the design of the supplementary control to automatic voltage regulators, and a classical PSS structure is used to damp electromechanical oscillations. The novelty of this work is in proposing a method to capture the unmodelled nonlinear dynamics as uncertainty in the design of the robust controller. Tight bounds on the uncertainty are obtained using this method which enables high-performance controllers. An IEEE benchmark test system has been used to demonstrate the performance of the designed controller.
NASA Astrophysics Data System (ADS)
Schaefer, Bradley E.; Dyson, Samuel E.
1996-08-01
A common Gamma-Ray Burst-light curve shape is the ``FRED'' or ``fast-rise exponential-decay.'' But how exponential is the tail? Are they merely decaying with some smoothly decreasing decline rate, or is the functional form an exponential to within the uncertainties? If the shape really is an exponential, then it would be reasonable to assign some physically significant time scale to the burst. That is, there would have to be some specific mechanism that produces the characteristic decay profile. So if an exponential is found, then we will know that the decay light curve profile is governed by one mechanism (at least for simple FREDs) instead of by complex/multiple mechanisms. As such, a specific number amenable to theory can be derived for each FRED. We report on the fitting of exponentials (and two other shapes) to the tails of ten bright BATSE bursts. The BATSE trigger numbers are 105, 257, 451, 907, 1406, 1578, 1883, 1885, 1989, and 2193. Our technique was to perform a least square fit to the tail from some time after peak until the light curve approaches background. We find that most FREDs are not exponentials, although a few come close. But since the other candidate shapes come close just as often, we conclude that the FREDs are misnamed.
Robust torque control of an elastic robotic arm based on invertibility and feedback stabilization
NASA Technical Reports Server (NTRS)
Singh, S. N.; Schy, A. A.
1985-01-01
An approach to the control of elastic robotic systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law, u sub d, is derived such that in the closed loop system, independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law, u sub s, is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that, in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u sub d + u sub s.
Reichert, Malinda D; Lin, Chia-Cheng; Vela, Javier
2014-07-08
Anisotropic II–VI semiconductor nanostructures are important photoactive materials for various energy conversion and optical applications. However, aside from the many available surface chemistry studies and from their ubiquitous photodegradation under continuous illumination, the general chemical reactivity and thermal stability (phase and shape transformations) of these materials are poorly understood. Using CdSe and CdS nanorods as model systems, we have investigated the behavior of II–VI semiconductor nanorods against various conditions of extreme chemical and physical stress (acids, bases, oxidants, reductants, and heat). CdSe nanorods react rapidly with acids, becoming oxidized to Se or SeO2. In contrast, CdSe nanorods remain mostly unreactive when treated with bases or strong oxidants, although bases do partially etch the tips of the nanorods (along their axis). Roasting (heating in air) of CdSe nanorods results in rock-salt CdO, but neither CdSe nor CdO is easily reduced by hydrogen (H2). Another reductant, n-BuLi, reduces CdSe nanorods to metallic Cd. Variable temperature X-ray diffraction experiments show that axial annealing and selective axial melting of the nanorods precede particle coalescence. Furthermore, thermal analysis shows that the axial melting of II–VI nanorods is a ligand-dependent process. In agreement with chemical reactivity and thermal stability observations, silica-coating experiments show that the sharpest (most curved) II–VI surfaces are most active against heterogeneous nucleation of a silica shell. These results provide valuable insights into the fate and possible ways to enhance the stability and improve the use of II–VI semiconductor nanostructures in the fields of optics, magnetism, and energy conversion.
ERIC Educational Resources Information Center
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Collaborative Research: Robust Climate Projections and Stochastic Stability of Dynamical Systems
Ghil, Michael; McWilliams, James; Neelin, J. David; Zaliapin, Ilya; Chekroun, Mickael; Kondrashov, Dmitri; Simonnet, Eric
2011-10-13
The project was completed along the lines of the original proposal, with additional elements arising as new results were obtained. The originally proposed three thrusts were expanded to include an additional, fourth one. (i) The e ffects of stochastic perturbations on climate models have been examined at the fundamental level by using the theory of deterministic and random dynamical systems, in both nite and in nite dimensions. (ii) The theoretical results have been implemented first on a delay-diff erential equation (DDE) model of the El-Nino/Southern-Oscillation (ENSO) phenomenon. (iii) More detailed, physical aspects of model robustness have been considered, as proposed, within the stripped-down ICTP-AGCM (formerly SPEEDY) climate model. This aspect of the research has been complemented by both observational and intermediate-model aspects of mid-latitude and tropical climate. (iv) An additional thrust of the research relied on new and unexpected results of (i) and involved reduced-modeling strategies and associated prediction aspects have been tested within the team's empirical model reduction (EMR) framework. Finally, more detailed, physical aspects have been considered within the stripped-down SPEEDY climate model. The results of each of these four complementary e fforts are presented in the next four sections, organized by topic and by the team members concentrating on the topic under discussion.
NASA Astrophysics Data System (ADS)
Requejo, Rubén J.; Camacho, Juan; Cuesta, José A.; Arenas, Alex
2012-08-01
The emergence and promotion of cooperation are two of the main issues in evolutionary game theory, as cooperation is amenable to exploitation by defectors, which take advantage of cooperative individuals at no cost, dooming them to extinction. It has been recently shown that the existence of purely destructive agents (termed jokers) acting on the common enterprises (public goods games) can induce stable limit cycles among cooperation, defection, and destruction when infinite populations are considered. These cycles allow for time lapses in which cooperators represent a relevant fraction of the population, providing a mechanism for the emergence of cooperative states in nature and human societies. Here we study analytically and through agent-based simulations the dynamics generated by jokers in finite populations for several selection rules. Cycles appear in all cases studied, thus showing that the joker dynamics generically yields a robust cyclic behavior not restricted to infinite populations. We also compute the average time in which the population consists mostly of just one strategy and compare the results with numerical simulations.
Design, stability and robustness analyses of neural networks in control systems
NASA Astrophysics Data System (ADS)
Shen, Jie
1998-12-01
Artificial Neural Network (ANN), also known as connectionist learning and parallel distributed processing, is finding its applications in diverse fields: many branches of engineering, health sciences, cognitive science, archaeology, finance, etc. This research tries to make some efforts to emphasize "design" methodology in ANN, and to explore the structures by which ANN can solve difficult problems by identifying proper ANN architecture. Two classes of ANN--multi-layer neural networks and recurrent networks--are investigated in the context of control of systems and estimation of unknown parameters. The multi-layer neural networks converge to optimal solutions by satisfying mathematical formulations associated with the Hamilton approach and the dynamic programming approach. A benchmark aerospace application is used for illustration. A variant of the Hopfield network, called the Modified Hopfield Neural Network (MHNN), is proposed to show the design approach to the determination of weights in recurrent networks. It is shown how the equilibrium point of this network helps with inversion operations arising in optimal gain determination. Control of dynamic systems using recurrent neural networks are presented. The robustness of the recurrent networks to parameter variation is considered in the context of weights. Analyses are carried out in the frequency domain and the time domain.
Robust design of polyrhythmic neural circuits
NASA Astrophysics Data System (ADS)
Schwabedal, Justus T. C.; Neiman, Alexander B.; Shilnikov, Andrey L.
2014-08-01
Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus indicating an increased robustness. Conversely, after adding noise we find that noise-induced rhythm switching intensifies if the coupling strength is increased beyond a critical value, indicating a decreased robustness. We analyze this stochastic arrhythmia and develop a generic description of its dynamic mechanism. Based on our mechanistic insight, we show how physiological parameters of neuronal dynamics and network coupling can be balanced to enhance rhythm robustness against noise. Our findings are applicable to a broad class of relaxation-oscillator networks, including Fitzhugh-Nagumo and other Hodgkin-Huxley-type networks.
A robust method to screen detergents for membrane protein stabilization, revisited.
Champeil, Philippe; Orlowski, Stéphane; Babin, Simon; Lund, Sten; le Maire, Marc; Møller, Jesper; Lenoir, Guillaume; Montigny, Cédric
2016-10-15
This report is a follow up of our previous paper (Lund, Orlowski, de Foresta, Champeil, le Maire and Møller (1989), J Biol Chem 264:4907-4915) showing that solubilization in detergent of a membrane protein may interfere with its long-term stability, and proposing a protocol to reveal the kinetics of such irreversible inactivation. We here clarify the fact that when various detergents are tested for their effects, special attention has of course to be paid to their critical micelle concentration. We also investigate the effects of a few more detergents, some of which have been recently advertised in the literature, and emphasize the role of lipids together with detergents. Among these detergents, lauryl maltose neopentyl glycol (LMNG) exerts a remarkable ability, even higher than that of β-dodecylmaltoside (DDM), to protect our test enzyme, the paradigmatic P-type ATPase SERCA1a from sarcoplasmic reticulum. Performing such experiments for one's favourite protein probably remains useful in pre-screening assays testing various detergents. PMID:27443956
NASA Astrophysics Data System (ADS)
Vachirasricirikul, Sitthidet; Ngamroo, Issarachai; Kaitwanidvilai, Somyot
It is well known that the power system controller designed by H∞ control is complicated, high order and impractical. In power system applications, practical structures such as proportional integral derivative (PID) etc., are widely used, because of their simple structure, less number of tuning parameters and low-order. However, tuning of controller parameters to achieve a good performance and robustness is based on designer's experiences. To overcome this problem, this paper proposes a fixed structure robust H∞ loop shaping control to design Static Var Compensator (SVC) and Automatic Voltage Regulator (AVR) for robust stabilization of voltage fluctuation in an isolated wind-diesel hybrid power system. The structure of the robust controller of SVC and AVR is specified by a PID controller. In the system modeling, a normalized coprime factorization is applied to represent possible unstructured uncertainties in the power system such as variation of system parameters, generating and loading conditions etc. Based on the H∞ loop shaping, the performance and robust stability conditions are formulated as the optimization problem. The particle swarm optimization is applied to solve for PID control parameters of SVC and AVR simultaneously. Simulation studies confirm the control effect and robustness of the proposed control.
Li, XS; Narayanan, S; Michaelis, VK; Ong, TC; Keeler, EG; Kim, H; Mckay, IS; Griffin, RG; Wang, EN
2015-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg2+ ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg, Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the lab-scale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N-2 sorption, Al-27/Si-29 MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick's 2nd law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N-2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications. (C) 2014 Elsevier Inc. All rights reserved.
Leng, Yan; Wang, Zhifei; Tsai, Li-Kai; Leeds, Peter; Fessler, Emily Bame; Wang, Junyu; Chuang, De-Maw
2013-01-01
Fibroblast growth factor-21 (FGF-21) is a new member of the FGF super-family and an important endogenous regulator of glucose and lipid metabolism. It has been proposed as a therapeutic target for diabetes and obesity. Its function in the central nervous system (CNS) remains unknown. Previous studies from our laboratory demonstrated that aging primary neurons are more vulnerable to glutamate-induced excitotoxicity, and that co-treatment with the mood stabilizers lithium and valproic acid (VPA) induces synergistic neuroprotective effects. This study sought to identify molecule(s) involved in these synergistic effects. We found that FGF-21 mRNA was selectively and dramatically elevated by co-treatment with lithium and VPA in primary rat brain neurons. FGF-21 protein levels were also robustly increased in neuronal lysates and culture medium following lithium-VPA co-treatment. Combining glycogen synthase kinase-3 (GSK-3) inhibitors with VPA or histone deacetylase (HDAC) inhibitors with lithium synergistically increased FGF-21 mRNA levels, supporting that synergistic effects of lithium and VPA are mediated via GSK-3 and HDAC inhibition, respectively. Exogenous FGF-21 protein completely protected aging neurons from glutamate challenge. This neuroprotection was associated with enhanced Akt-1 activation and GSK-3 inhibition. Lithium-VPA co-treatment dramatically prolonged lithium-induced Akt-1 activation and augmented GSK-3 inhibition. Akt-1 knockdown markedly decreased FGF-21 mRNA levels, and reduced the neuroprotection induced by FGF-21 or lithium-VPA co-treatment. In addition, FGF-21 knockdown reduced lithium-VPA co-treatment-induced Akt-1 activation and neuroprotection against excitotoxicity. Together, our novel results suggest that FGF-21 is a key mediator of the effects of these mood stabilizers, and a potential new therapeutic target for CNS disorders. PMID:24468826
Li, Xiansen; Narayanan, Shankar; Michaelis, Vladimir K.; Ong, Ta-Chung; Keeler, Eric G.; Kim, Hyunho; McKay, Ian S.; Griffin, Robert G.; Wang, Evelyn N.
2014-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg2+ ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg,Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the labscale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N2 sorption, 27Al/29Si MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick’s 2nd law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications. PMID:25395877
Li, Xiansen; Narayanan, Shankar; Michaelis, Vladimir K; Ong, Ta-Chung; Keeler, Eric G; Kim, Hyunho; McKay, Ian S; Griffin, Robert G; Wang, Evelyn N
2015-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg(2+) ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg,Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the labscale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N2 sorption, (27)Al/(29)Si MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick's 2(nd) law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications. PMID:25395877
Exponentiated power Lindley distribution
Ashour, Samir K.; Eltehiwy, Mahmoud A.
2014-01-01
A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data. PMID:26644927
Exponentiated power Lindley distribution.
Ashour, Samir K; Eltehiwy, Mahmoud A
2015-11-01
A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data. PMID:26644927
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Wright, Charles; Henry, Jon; Burov, Stas; Lin, Yihan; Crosson, Sean; Dinner, Aaron; Scherer, Norbert
2013-03-01
The interplay between growth and division of cells is has been studied in the context of exponential growth of bacterial cells (in suitable conditions) for decades. However, bulk culture studies obscure phenomena that manifest in single cells over many generations. We introduce a unique technology combining microfluidics, single-cell imaging, and quantitative analysis. This enables us to track the growth of single Caulobacter crescentus stalked cells over hundreds of generations. The statistics that we extract indicate a size thresholding mechanism for cell division and a non-trivial scaling collapse of division time distributions at different temperatures. In this talk I shall discuss these observations and a stochastic model of growth and division that captures all our observations with no free parameters.
The petroleum exponential (again)
NASA Astrophysics Data System (ADS)
Bell, Peter M.
The U.S. production and reserves of liquid and gaseous petroleum have declined since 1960, at least in the lower 48 states. This decline stems from decreased discovery rates, as predicted by M. King Hubbert in the mid-1950's. Hubbert's once unpopular views were based on statistical analysis of the production history of the petroleum industry, and now, even with inclusion of the statistical perturbation caused by the Prudhoe Bay-North Alaskan Slope discovery (the largest oil field ever found in the United States), it seems clear again that production is following the exponential curve to depletion of the resource—to the end of the ultimate yield of petroleum from wells in the United States.In a recent report, C. Hall and C. Cleveland of Cornell University show that large atypical discoveries, such as the Prudhoe Bay find, are but minor influences on what now appears to be the crucial intersection of two exponentials [Science, 211, 576-579, 1981]: the production-per-drilled-foot curve of Hubbert, which crosses zero production no later than the year 2005; the other, a curve that plots the energy cost of drilling and extraction with time; that is, the cost-time rate of how much oil is used to drill and extract oil from the ground. The intersection, if no other discoveries the size of the Prudhoe Bay field are made, could be as early as 1990, the end of the present decade. The inclusion of each Prudhoe-Bay-size find extends the year of intersection by only about 6 years. Beyond that point, more than one barrel of petroleum would be expended for each barrel extracted from the ground. The oil exploration-extraction and refining industry is currently the second most energy-intensive industry in the U.S., and the message seems clear. Either more efficient drilling and production techniques are discovered, or domestic production will cease well before the end of this century if the Hubbert analysis modified by Hall and Cleveland is correct.
OPINION: Safe exponential manufacturing
NASA Astrophysics Data System (ADS)
Phoenix, Chris; Drexler, Eric
2004-08-01
In 1959, Richard Feynman pointed out that nanometre-scale machines could be built and operated, and that the precision inherent in molecular construction would make it easy to build multiple identical copies. This raised the possibility of exponential manufacturing, in which production systems could rapidly and cheaply increase their productive capacity, which in turn suggested the possibility of destructive runaway self-replication. Early proposals for artificial nanomachinery focused on small self-replicating machines, discussing their potential productivity and their potential destructiveness if abused. In the light of controversy regarding scenarios based on runaway replication (so-called 'grey goo'), a review of current thinking regarding nanotechnology-based manufacturing is in order. Nanotechnology-based fabrication can be thoroughly non-biological and inherently safe: such systems need have no ability to move about, use natural resources, or undergo incremental mutation. Moreover, self-replication is unnecessary: the development and use of highly productive systems of nanomachinery (nanofactories) need not involve the construction of autonomous self-replicating nanomachines. Accordingly, the construction of anything resembling a dangerous self-replicating nanomachine can and should be prohibited. Although advanced nanotechnologies could (with great difficulty and little incentive) be used to build such devices, other concerns present greater problems. Since weapon systems will be both easier to build and more likely to draw investment, the potential for dangerous systems is best considered in the context of military competition and arms control.
Vaseem, Mohammad; McKerricher, Garret; Shamim, Atif
2016-01-13
Currently, silver-nanoparticle-based inkjet ink is commercially available. This type of ink has several serious problems such as a complex synthesis protocol, high cost, high sintering temperatures (∼200 °C), particle aggregation, nozzle clogging, poor shelf life, and jetting instability. For the emerging field of printed electronics, these shortcomings in conductive inks are barriers for their widespread use in practical applications. Formulating particle-free silver inks has potential to solve these issues and requires careful design of the silver complexation. The ink complex must meet various requirements, such as in situ reduction, optimum viscosity, storage and jetting stability, smooth uniform sintered films, excellent adhesion, and high conductivity. This study presents a robust formulation of silver-organo-complex (SOC) ink, where complexing molecules act as reducing agents. The 17 wt % silver loaded ink was printed and sintered on a wide range of substrates with uniform surface morphology and excellent adhesion. The jetting stability was monitored for 5 months to confirm that the ink was robust and highly stable with consistent jetting performance. Radio frequency inductors, which are highly sensitive to metal quality, were demonstrated as a proof of concept on flexible PEN substrate. This is a major step toward producing high-quality electronic components with a robust inkjet printing process. PMID:26713357
NASA Astrophysics Data System (ADS)
Wang, Yonggang; Wen, Ting; Park, Changyong; Kenney-Benson, Curtis; Pravica, Michael; Yang, Wenge; Zhao, Yusheng
2016-01-01
The structure stability under high pressure and thermal expansion behavior of Na3OBr and Na4OI2, two prototypes of alkali-metal-rich antiperovskites, were investigated by in situ synchrotron X-ray diffraction techniques under high pressure and low temperature. Both are soft materials with bulk modulus of 58.6 GPa and 52.0 GPa for Na3OBr and Na4OI2, respectively. The cubic Na3OBr structure and tetragonal Na4OI2 with intergrowth K2NiF4 structure are stable under high pressure up to 23 GPa. Although being a characteristic layered structure, Na4OI2 exhibits nearly isotropic compressibility. Negative thermal expansion was observed at low temperature range (20-80 K) in both transition-metal-free antiperovskites for the first time. The robust high pressure structure stability was examined and confirmed by first-principles calculations among various possible polymorphisms qualitatively. The results provide in-depth understanding of the negative thermal expansion and robust crystal structure stability of these antiperovskite systems and their potential applications.
On the Matrix Exponential Function
ERIC Educational Resources Information Center
Hou, Shui-Hung; Hou, Edwin; Pang, Wan-Kai
2006-01-01
A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.
NASA Astrophysics Data System (ADS)
Faure, Guilhem; Koonin, Eugene V.
2015-05-01
Robustness to destabilizing effects of mutations is thought of as a key factor of protein evolution. The connections between two measures of robustness, the relative core size and the computationally estimated effect of mutations on protein stability (ΔΔG), protein abundance and the selection pressure on protein-coding genes (dN/dS) were analyzed for the organisms with a large number of available protein structures including four eukaryotes, two bacteria and one archaeon. The distribution of the effects of mutations in the core on protein stability is universal and indistinguishable in eukaryotes and bacteria, centered at slightly destabilizing amino acid replacements, and with a heavy tail of more strongly destabilizing replacements. The distribution of mutational effects in the hyperthermophilic archaeon Thermococcus gammatolerans is significantly shifted toward strongly destabilizing replacements which is indicative of stronger constraints that are imposed on proteins in hyperthermophiles. The median effect of mutations is strongly, positively correlated with the relative core size, in evidence of the congruence between the two measures of protein robustness. However, both measures show only limited correlations to the expression level and selection pressure on protein-coding genes. Thus, the degree of robustness reflected in the universal distribution of mutational effects appears to be a fundamental, ancient feature of globular protein folds whereas the observed variations are largely neutral and uncoupled from short term protein evolution. A weak anticorrelation between protein core size and selection pressure is observed only for surface residues in prokaryotes but a stronger anticorrelation is observed for all residues in eukaryotic proteins. This substantial difference between proteins of prokaryotes and eukaryotes is likely to stem from the demonstrable higher compactness of prokaryotic proteins.
NASA Astrophysics Data System (ADS)
Ho, D.; Salmonson, J.; Haan, S.; Clark, D.; Lindl, J.; Meezan, N.; Thomas, C.
2015-11-01
We present six ignition designs using W-doped HDC ablators with, respectively, 2, 3, and 4-step increases in Tr. Fuel adiabat α ranges between 1.5 and 4. The 4-step design has the lowest α of 1.5 but has the highest ablation front Rayleigh-Taylor (RT) growth. Consequently, the overall robustness of the 4-step design is inferior to the intermediate- α 3-step design, assuming typical currently measured surface roughness spectrum. As the foot level is increased further and the shocks merge inside the fuel, the fuel adiabat is raised to 4. The RT growth and mix are reduced but the 1D margin is decreased making it overall more susceptible to surface roughness. The 2-step α = 2.5 design turns out to be the most robust against surface roughness and still can deliver very high 1D yield of 14.5 MJ. Systematic evaluation of the robustness of these capsules with respect to low-mode radiation asymmetries, will also be discussed. Different paths to achieve low-convergence-ratio implosions (i.e. high velocity and high α as one option versus low velocity and low α as another option), while still giving respectable neutron yield will be presented. Finally, we discuss how the performance of these doped capsules changes; if the Au wall of the hohlraum is replaced by U. Work performed under auspices of U.S. DOE by LLNL under DE-AC52-07NA27344.
Pandya, Darpan N; Bhatt, Nikunj; An, Gwang Il; Ha, Yeong Su; Soni, Nisarg; Lee, Hochun; Lee, Yong Jin; Kim, Jung Young; Lee, Woonghee; Ahn, Heesu; Yoo, Jeongsoo
2014-09-11
The first macrocyclic bifunctional chelator incorporating propylene cross-bridge was efficiently synthesized from cyclam in seven steps. After the introduction of an extra functional group for facile conjugation onto the propylene cross-bridge, the two carboxylic acid pendants could contribute to strong coordination of Cu(II) ions, leading to a robust Cu complex. The cyclic RGD peptide conjugate of PCB-TE2A-NCS was prepared and successfully radiolabeled with (64)Cu ion. The radiolabeled peptide conjugate was evaluated in vivo through a biodistribution study and animal PET imaging to demonstrate high tumor uptake with low background. PMID:25137619
Exponential approximations in optimal design
NASA Technical Reports Server (NTRS)
Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.
1990-01-01
One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth. PMID:25062238
Universality in Stochastic Exponential Growth
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.
2014-07-01
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Jiang, Yanjun; Liu, Xinlong; Chen, Yafei; Zhou, Liya; He, Ying; Ma, Li; Gao, Jing
2014-02-01
A novel catalytic system of Pickering emulsion stabilized by lipase-containing periodic mesoporous organosilica was constructed (named LP@PE) and used as biocatalyst for biodiesel production. The reaction parameters were optimized and the optimum conditions were as follows: the water fraction 0.65%, molar ratio of ethanol to oleic acid 2:1, immobilized lipase particles 150mg, phosphate buffer pH 7.0 and temperature 30°C. Under these conditions, the maximum biodiesel yield obtained via esterification of oleic acid with ethanol could reach 95.8%. The biodiesel yield could maintain 88.6% after LP@PE was used 15times. The LP@PE was also used in the synthesis of biodiesel from Jatropha curcas oil. The highest yield could reach 87.1% and the yield was 73.0% after 10 cycles. All these results demonstrated that Pickering emulsion system stabilized by immobilized enzyme may possess much potential in many enzymatic industrial applications. PMID:24368276
Sneppen, Kim; Dodd, Ian B
2015-01-01
How alternative chromatin-based regulatory states can be made stable and heritable in order to provide robust epigenetic memory is poorly understood. Here, we develop a stochastic model of the silencing system in Saccharomyces cerevisiae that incorporates cooperative binding of the repressive SIR complex and antisilencing histone modifications, in addition to positive feedback in Sir2 recruitment. The model was able to reproduce key features of SIR regulation of an HM locus, including heritable bistability, dependence on the silencer elements, and sensitivity to SIR dosage. We found that antisilencing methylation of H3K79 by Dot1 was not needed to generate these features, but acted to reduce spreading of SIR binding, consistent with its proposed role in containment of silencing. In contrast, cooperative inter-nucleosome interactions mediated by the SIR complex were critical for concentrating SIR binding around the silencers in the absence of barriers, and for providing bistability in SIR binding. SIR-SIR interactions magnify the cooperativity in the Sir2-histone deacetylation positive feedback reaction and complete a double-negative feedback circuit involving antisilencing modifications. Thus, our modeling underscores the potential importance of cooperative interactions between nucleosome-bound complexes both in the SIR system and in other chromatin-based complexes in epigenetic regulation. PMID:25830651
Sneppen, Kim; Dodd, Ian B
2015-01-01
How alternative chromatin-based regulatory states can be made stable and heritable in order to provide robust epigenetic memory is poorly understood. Here, we develop a stochastic model of the silencing system in Saccharomyces cerevisiae that incorporates cooperative binding of the repressive SIR complex and antisilencing histone modifications, in addition to positive feedback in Sir2 recruitment. The model was able to reproduce key features of SIR regulation of an HM locus, including heritable bistability, dependence on the silencer elements, and sensitivity to SIR dosage. We found that antisilencing methylation of H3K79 by Dot1 was not needed to generate these features, but acted to reduce spreading of SIR binding, consistent with its proposed role in containment of silencing. In contrast, cooperative inter-nucleosome interactions mediated by the SIR complex were critical for concentrating SIR binding around the silencers in the absence of barriers, and for providing bistability in SIR binding. SIR-SIR interactions magnify the cooperativity in the Sir2-histone deacetylation positive feedback reaction and complete a double-negative feedback circuit involving antisilencing modifications. Thus, our modeling underscores the potential importance of cooperative interactions between nucleosome-bound complexes both in the SIR system and in other chromatin-based complexes in epigenetic regulation. PMID:25830651
Barth, Aline Bergesch; de Oliveira, Gabriela Bolfe; Malesuik, Marcelo Donadel; Paim, Clésio Soldatelli; Volpato, Nadia Maria
2011-08-01
A stability-indicating liquid chromatography method for the determination of the antifungal agent butenafine hydrochloride (BTF) in a cream was developed and validated using the Plackett-Burman experimental design for robustness evaluation. Also, the drug photodegradation kinetics was determined. The analytical column was operated with acetonitrile, methanol and a solution of triethylamine 0.3% adjusted to pH 4.0 (6:3:1) at a flow rate of 1 mL/min and detection at 283 nm. BTF extraction from the cream was done with n-butyl alcohol and methanol in ultrasonic bath. The performed degradation conditions were: acid and basic media with HCl 1M and NaOH 1M, respectively, oxidation with H(2)O(2) 10%, and the exposure to UV-C light. No interference in the BTF elution was verified. Linearity was assessed (r(2) = 0.9999) and ANOVA showed non-significative linearity deviation (p > 0.05). Adequate results were obtained for repeatability, intra-day precision, and accuracy. Critical factors were selected to examine the method robustness with the two-level Plackett-Burman experimental design and no significant factors were detected (p > 0.05). The BTF photodegradation kinetics was determined for the standard and for the cream, both in methanolic solution, under UV light at 254 nm. The degradation process can be described by first-order kinetics in both cases. PMID:21801482
Real-Time Exponential Curve Fits Using Discrete Calculus
NASA Technical Reports Server (NTRS)
Rowe, Geoffrey
2010-01-01
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
Punctuated evolution and robustness in morphogenesis
Grigoriev, D.; Reinitz, J.; Vakulenko, S.; Weber, A.
2014-01-01
This paper presents an analytic approach to the pattern stability and evolution problem in morphogenesis. The approach used here is based on the ideas from the gene and neural network theory. We assume that gene networks contain a number of small groups of genes (called hubs) controlling morphogenesis process. Hub genes represent an important element of gene network architecture and their existence is empirically confirmed. We show that hubs can stabilize morphogenetic pattern and accelerate the morphogenesis. The hub activity exhibits an abrupt change depending on the mutation frequency. When the mutation frequency is small, these hubs suppress all mutations and gene product concentrations do not change, thus, the pattern is stable. When the environmental pressure increases and the population needs new genotypes, the genetic drift and other effects increase the mutation frequency. For the frequencies that are larger than a critical amount the hubs turn off; and as a result, many mutations can affect phenotype. This effect can serve as an engine for evolution. We show that this engine is very effective: the evolution acceleration is an exponential function of gene redundancy. Finally, we show that the Eldredge-Gould concept of punctuated evolution results from the network architecture, which provides fast evolution, control of evolvability, and pattern robustness. To describe analytically the effect of exponential acceleration, we use mathematical methods developed recently for hard combinatorial problems, in particular, for so-called k-SAT problem, and numerical simulations. PMID:24996115
Dolev, Danny; Függer, Matthias; Posch, Markus; Schmid, Ulrich; Steininger, Andreas; Lenzen, Christoph
2014-01-01
We present the first implementation of a distributed clock generation scheme for Systems-on-Chip that recovers from an unbounded number of arbitrary transient faults despite a large number of arbitrary permanent faults. We devise self-stabilizing hardware building blocks and a hybrid synchronous/asynchronous state machine enabling metastability-free transitions of the algorithm's states. We provide a comprehensive modeling approach that permits to prove, given correctness of the constructed low-level building blocks, the high-level properties of the synchronization algorithm (which have been established in a more abstract model). We believe this approach to be of interest in its own right, since this is the first technique permitting to mathematically verify, at manageable complexity, high-level properties of a fault-prone system in terms of its very basic components. We evaluate a prototype implementation, which has been designed in VHDL, using the Petrify tool in conjunction with some extensions, and synthesized for an Altera Cyclone FPGA. PMID:26516290
Vasantha, Vivek Arjunan; Junhui, Chen; Ying, Tay Boon; Parthiban, Anbanandam
2015-10-13
Metal nanoparticles (MNps) tend to be influenced by environmental factors such as pH, ionic strength, and temperature, thereby leading to aggregation. Forming stable aqueous dispersions could be one way of addressing the environmental toxicity of MNps. In contrast to the electrolyte-induced aggregation of MNps, novel zwitterionic sulfabetaine polymers reported here act as stabilizers of MNps even under high salinity. Polysulfabetaines exhibited unique solubility and swelling tendencies in brine and deionized water, respectively. The polysulfabetaines derived from methacrylate (PSBMA) and methacrylamide (PSBMAm) also showed reversible salt-responsive and thermoresponsive behaviors as confirmed by cloud-point titration, transmittance, and dynamic light scattering studies. The brine soluble nature was explored for its ability to be used as a capping agents to form metal nanoparticles using formic acid as a reducing agent. Thus, silver and noble metal (gold and palladium) nanoparticles were synthesized. The nanoparticles formed were characterized by UV-vis, XRD, TEM, EDX, and DLS studies. The size of the nanoparticles remained more or less the same even after 2 months of storage in 2 M sodium chloride solution under ambient conditions and also at elevated temperatures as confirmed by light-scattering measurements. The tunable, stimuli-responsive polysulfabetaine-capped stable MNp formed under low (hyposalinity) and hypersalinity could find potential applications in a variety of areas. PMID:26394088
Linear or Exponential Number Lines
ERIC Educational Resources Information Center
Stafford, Pat
2011-01-01
Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather than linear,…
Exponential Finite-Difference Technique
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.
1989-01-01
Report discusses use of explicit exponential finite-difference technique to solve various diffusion-type partial differential equations. Study extends technique to transient-heat-transfer problems in one dimensional cylindrical coordinates and two and three dimensional Cartesian coordinates and to some nonlinear problems in one or two Cartesian coordinates.
Exponential tilting in Bayesian asymptotics
Kharroubi, S. A.; Sweeting, T. J.
2016-01-01
We use exponential tilting to obtain versions of asymptotic formulae for Bayesian computation that do not involve conditional maxima of the likelihood function, yielding a more stable computational procedure and significantly reducing computational time. In particular we present an alternative version of the Laplace approximation for a marginal posterior density. Implementation of the asymptotic formulae and a modified signed root based importance sampler are illustrated with an example. PMID:27279661
Exponential estimates of symplectic slow manifolds
NASA Astrophysics Data System (ADS)
Kristiansen, K. U.; Wulff, C.
2016-07-01
In this paper we prove the existence of an almost invariant symplectic slow manifold for analytic Hamiltonian slow-fast systems with finitely many slow degrees of freedom for which the error field is exponentially small. We allow for infinitely many fast degrees of freedom. The method we use is motivated by a paper of MacKay from 2004. The method does not notice resonances, and therefore we do not pose any restrictions on the motion normal to the slow manifold other than it being fast and analytic. We also present a stability result and obtain a generalization of a result of Gelfreich and Lerman on an invariant slow manifold to (finitely) many fast degrees of freedom.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Saad, Ahmed S; Ismail, Nahla S; Soliman, Marwa; Zaazaa, Hala E
2016-03-01
A sensitive and highly selective stability-indicating gradient HPLC method was developed and validated for simultaneous determination of clorsulon (CLO) and ivermectin (IVM) in the presence of their degradation products. The drugs were subjected to different stress conditions, including acid and alkaline hydrolysis, oxidative, thermal, and photolytic forced degradation. The robustness of the proposed method was assessed using the Plackett-Burman experimental design, the factors affecting system performance were defined, and nonsignificant intervals for the significant factors were determined. The separation was carried out on a ZORBAX SB phenyl analytical column (250 × 4.6 mm id, 5 μm particle size), with gradient elution utilizing 10 mM sodium dihydrogen phosphate and acetonitrile as mobile phase. UV detection was performed for CLO and IVM at 254 nm over a concentration range of 4-140 and 5-50 μg/mL, respectively, with mean percentage recoveries of 99.90 ± 1.30 and 98.59 ± 1.16%, respectively. The proposed method was successfully applied to a pharmaceutical dosage form containing the investigated drugs. The results were statistically compared with the official HPLC methods, and no significant differences were found. PMID:26997479
NASA Astrophysics Data System (ADS)
Tulsi, Avatar
2016-07-01
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers significant robustness to certain systematic errors. To search N items, our recursive algorithm can tolerate errors of size O(1{/}√{ln N}) which is exponentially better than quantum walk algorithms for which tolerable error size is only O(ln N{/}√{N}). Also, our algorithm does not need any ancilla qubit. Thus our algorithm is much easier to implement experimentally compared to quantum walk algorithms.
NASA Astrophysics Data System (ADS)
Tulsi, Avatar
2016-04-01
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers significant robustness to certain systematic errors. To search N items, our recursive algorithm can tolerate errors of size O(1{/}√{N}) which is exponentially better than quantum walk algorithms for which tolerable error size is only O(ln N{/}√{N}) . Also, our algorithm does not need any ancilla qubit. Thus our algorithm is much easier to implement experimentally compared to quantum walk algorithms.
Robust stability under additive perturbations
NASA Technical Reports Server (NTRS)
Bhaya, A.; Desoer, C. A.
1985-01-01
A MIMO linear time-invariant feedback system 1S(P,C) is considered which is assumed to be U-stable. The plant P is subjected to an additive perturbation Delta P which is proper but not necessarily stable. It is proved that the perturbed system is U-stable if and only if Delta P(I + Q x Delta P) exp -1 is U-stable.
Derivatives of Siegel modular forms and exponential functions
NASA Astrophysics Data System (ADS)
Bertrand, D.; Zudilin, W. W.
2001-08-01
We show that the differential field generated by Siegel modular forms and the differential field generated by exponentials of polynomials are linearly disjoint over \\mathbb C. Combined with our previous work [3], this provides a complete multidimensional extension of Mahler's theorem on the transcendence degree of the field generated by the exponential function and the derivatives of a modular function. We give two proofs of our result, one purely algebraic, the other analytic, but both based on arguments from differential algebra and on the stability under the action of the symplectic group of the differential field generated by rational and modular functions.
Exponential Formulae and Effective Operations
NASA Technical Reports Server (NTRS)
Mielnik, Bogdan; Fernandez, David J. C.
1996-01-01
One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).
Robust controls with structured perturbations
NASA Technical Reports Server (NTRS)
Keel, Leehyun
1993-01-01
This final report summarizes the recent results obtained by the principal investigator and his coworkers on the robust stability and control of systems containing parametric uncertainty. The starting point is a generalization of Kharitonov's theorem obtained in 1989, and its generalization to the multilinear case, the singling out of extremal stability subsets, and other ramifications now constitutes an extensive and coherent theory of robust parametric stability that is summarized in the results contained here.
Fully exponentially correlated wavefunctions for small atoms
Harris, Frank E.
2015-01-22
Fully exponentially correlated atomic wavefunctions are constructed from exponentials in all the interparticle coordinates, in contrast to correlated wavefunctions of the Hylleraas form, in which only the electron-nuclear distances occur exponentially, with electron-electron distances entering only as integer powers. The full exponential correlation causes many-configuration wavefunctions to converge with expansion length more rapidly than either orbital formulations or correlated wavefunctions of the Hylleraas type. The present contribution surveys the effectiveness of fully exponentially correlated functions for the three-body system (the He isoelectronic series) and reports their application to a four-body system (the Li atom)
Simple robust control laws for robot manipulators. Part 1: Non-adaptive case
NASA Technical Reports Server (NTRS)
Wen, J. T.; Bayard, D. S.
1987-01-01
A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.
A Spectral Lyapunov Function for Exponentially Stable LTV Systems
NASA Technical Reports Server (NTRS)
Zhu, J. Jim; Liu, Yong; Hang, Rui
2010-01-01
This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.
EXPONENTIAL GALAXY DISKS FROM STELLAR SCATTERING
Elmegreen, Bruce G.; Struck, Curtis E-mail: curt@iastate.edu
2013-10-01
Stellar scattering off of orbiting or transient clumps is shown to lead to the formation of exponential profiles in both surface density and velocity dispersion in a two-dimensional non-self gravitating stellar disk with a fixed halo potential. The exponential forms for both nearly flat rotation curves and near-solid-body rotation curves. The exponential does not depend on initial conditions, spiral arms, bars, viscosity, star formation, or strong shear. After a rapid initial development, the exponential saturates to an approximately fixed scale length. The inner exponential in a two-component profile has a break radius comparable to the initial disk radius; the outer exponential is primarily scattered stars.
Giving Exponential Functions a Fair Shake
ERIC Educational Resources Information Center
Wanko, Jeffrey J.
2005-01-01
This article details an exploration of exponential decay and growth relationships using M&M's and dice. Students collect data for mathematical models and use graphing calculators to make sense of the general form of the exponential functions. (Contains 10 figures and 2 tables.)
The matrix exponential in transient structural analysis
NASA Technical Reports Server (NTRS)
Minnetyan, Levon
1987-01-01
The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties that are observed in biological systems at many different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be large enough to confer: intrinsic robustness for tolerating intrinsic parameter fluctuations; genetic robustness for buffering genetic variations; and environmental robustness for resisting environmental disturbances. Network robustness is needed so phenotype stability of biological network can be maintained, guaranteeing phenotype robustness. Synthetic biology is foreseen to have important applications in biotechnology and medicine; it is expected to contribute significantly to a better understanding of functioning of complex biological systems. This paper presents a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation for synthetic gene networks in synthetic biology. Further, from the unifying mathematical framework, we found that the phenotype robustness criterion for synthetic gene networks is the following: if intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in synthetic biology can also be investigated through corresponding phenotype robustness criteria from the systematic point of view. Finally, a robust synthetic design that involves network evolution algorithms with desired behavior under intrinsic parameter fluctuations, genetic variations, and environmental
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties that are observed in biological systems at many different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be large enough to confer: intrinsic robustness for tolerating intrinsic parameter fluctuations; genetic robustness for buffering genetic variations; and environmental robustness for resisting environmental disturbances. Network robustness is needed so phenotype stability of biological network can be maintained, guaranteeing phenotype robustness. Synthetic biology is foreseen to have important applications in biotechnology and medicine; it is expected to contribute significantly to a better understanding of functioning of complex biological systems. This paper presents a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation for synthetic gene networks in synthetic biology. Further, from the unifying mathematical framework, we found that the phenotype robustness criterion for synthetic gene networks is the following: if intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in synthetic biology can also be investigated through corresponding phenotype robustness criteria from the systematic point of view. Finally, a robust synthetic design that involves network evolution algorithms with desired behavior under intrinsic parameter fluctuations, genetic variations, and environmental
Huang, Dong; Cabral, Ricardo; De la Torre, Fernando
2016-02-01
Discriminative methods (e.g., kernel regression, SVM) have been extensively used to solve problems such as object recognition, image alignment and pose estimation from images. These methods typically map image features ( X) to continuous (e.g., pose) or discrete (e.g., object category) values. A major drawback of existing discriminative methods is that samples are directly projected onto a subspace and hence fail to account for outliers common in realistic training sets due to occlusion, specular reflections or noise. It is important to notice that existing discriminative approaches assume the input variables X to be noise free. Thus, discriminative methods experience significant performance degradation when gross outliers are present. Despite its obvious importance, the problem of robust discriminative learning has been relatively unexplored in computer vision. This paper develops the theory of robust regression (RR) and presents an effective convex approach that uses recent advances on rank minimization. The framework applies to a variety of problems in computer vision including robust linear discriminant analysis, regression with missing data, and multi-label classification. Several synthetic and real examples with applications to head pose estimation from images, image and video classification and facial attribute classification with missing data are used to illustrate the benefits of RR. PMID:26761740
A Simulation To Model Exponential Growth.
ERIC Educational Resources Information Center
Appelbaum, Elizabeth Berman
2000-01-01
Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)
Exponential fitting quadrature rule for functional equations
NASA Astrophysics Data System (ADS)
Cardone, A.; Paternoster, B.; Santomauro, G.
2012-09-01
A Gaussian quadrature rule for periodic integrand function is presented. The weights and nodes depend on the frequency of the problem and they are constructed by following the exponential fitting theory. The composite rule based on this formula is derived. The analysis of the error is carried out and it proves that the exponentially fitted Gaussian rule is more accurate than the classical Gauss-Legendre rule when oscillatory functions are treated. Some numerical tests are presented.
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.
Zhu, Zonglong; Bai, Yang; Liu, Xiao; Chueh, Chu-Chen; Yang, Shihe; Jen, Alex K-Y
2016-08-01
Highly crystalline SnO2 is demonstrated to serve as a stable and robust electron-transporting layer for high-performance perovskite solar cells. Benefiting from its high crystallinity, the relatively thick SnO2 electron-transporting layer (≈120 nm) provides a respectable electron-transporting property to yield a promising power conversion efficiency (PCE)(18.8%) Over 90% of the initial PCE can be retained after 30 d storage in ambient with ≈70% relative humidity. PMID:27168338
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties observed in biological systems at different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be enough to confer intrinsic robustness in order to tolerate intrinsic parameter fluctuations, genetic robustness for buffering genetic variations, and environmental robustness for resisting environmental disturbances. With this, the phenotypic stability of biological network can be maintained, thus guaranteeing phenotype robustness. This paper presents a survey on biological systems and then develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation in systems and evolutionary biology. Further, from the unifying mathematical framework, it was discovered that the phenotype robustness criterion for biological networks at different levels relies upon intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness. When this is true, the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in systems and evolutionary biology can also be investigated through their corresponding phenotype robustness criterion from the systematic point of view. PMID:23515240
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties observed in biological systems at different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be enough to confer intrinsic robustness in order to tolerate intrinsic parameter fluctuations, genetic robustness for buffering genetic variations, and environmental robustness for resisting environmental disturbances. With this, the phenotypic stability of biological network can be maintained, thus guaranteeing phenotype robustness. This paper presents a survey on biological systems and then develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation in systems and evolutionary biology. Further, from the unifying mathematical framework, it was discovered that the phenotype robustness criterion for biological networks at different levels relies upon intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness. When this is true, the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in systems and evolutionary biology can also be investigated through their corresponding phenotype robustness criterion from the systematic point of view. PMID:23515240
Phylogenetic Stochastic Mapping Without Matrix Exponentiation
Irvahn, Jan; Minin, Vladimir N.
2014-01-01
Abstract Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organism carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and works well for small state spaces. The computations slow down considerably for larger state spaces (e.g., space of codons), because current methodology relies on exponentiating CTMC infinitesimal rate matrices—an operation whose computational complexity grows as the size of the CTMC state space cubed. In this work, we introduce a new approach, based on a CTMC technique called uniformization, which does not use matrix exponentiation for phylogenetic stochastic mapping. Our method is based on a new Markov chain Monte Carlo (MCMC) algorithm that targets the distribution of trait histories conditional on the trait data observed at the tips of the tree. The computational complexity of our MCMC method grows as the size of the CTMC state space squared. Moreover, in contrast to competing matrix exponentiation methods, if the rate matrix is sparse, we can leverage this sparsity and increase the computational efficiency of our algorithm further. Using simulated data, we illustrate advantages of our MCMC algorithm and investigate how large the state space needs to be for our method to outperform matrix exponentiation approaches. We show that even on the moderately large state space of codons our MCMC method can be significantly faster than currently used matrix exponentiation methods. PMID:24918812
Finite Higher Spin Transformations from Exponentiation
NASA Astrophysics Data System (ADS)
Monnier, Samuel
2015-05-01
We study the exponentiation of elements of the gauge Lie algebras hs(λ) of three-dimensional higher spin theories. Exponentiable elements generate one-parameter groups of finite higher spin symmetries. We show that elements of hs(λ) in a dense set are exponentiable, when pictured in certain representations of hs(λ), induced from representations of in the complementary series. We also provide a geometric picture of higher spin gauge transformations clarifying the physical origin of these representations. This allows us to construct an infinite-dimensional topological group HS(λ) of finite higher spin symmetries. Interestingly, this construction is possible only for 0 ≤ λ ≤ 1, which are the values for which the higher spin theory is believed to be unitary and for which the Gaberdiel-Gopakumar duality holds. We exponentiate explicitly various commutative subalgebras of hs(λ). Among those, we identify families of elements of hs(λ) exponentiating to the unit of HS(λ), generalizing the logarithms of the holonomies of BTZ black hole connections. Our techniques are generalizable to the Lie algebras relevant to higher spin theories in dimensions above three.
Sniedovich, Moshe
2012-10-01
One would have expected the considerable public debate created by Nassim Taleb's two best selling books on uncertainty, Fooled by Randomness and The Black Swan, to inspire greater caution to the fundamental difficulties posed by severe uncertainty. Yet, methodologies exhibiting an incautious approach to uncertainty have been proposed recently in a range of publications. So, the objective of this short note is to call attention to a prime example of an incautious approach to severe uncertainty that is manifested in the proposition to use the concept radius of stability as a measure of robustness against severe uncertainty. The central proposition of this approach, which is exemplified in info-gap decision theory, is this: use a simple radius of stability model to analyze and manage a severe uncertainty that is characterized by a vast uncertainty space, a poor point estimate, and a likelihood-free quantification of uncertainty. This short discussion serves then as a reminder that the generic radius of stability model is a model of local robustness. It is, therefore, utterly unsuitable for the treatment of severe uncertainty when the latter is characterized by a poor estimate of the parameter of interest, a vast uncertainty space, and a likelihood-free quantification of uncertainty. PMID:22384828
Why does human culture increase exponentially?
Enquist, M; Ghirlanda, S; Jarrick, A; Wachtmeister, C-A
2008-08-01
Historical records show that culture can increase exponentially in time, e.g., in number of poems, musical works, scientific discoveries. We model how human capacities for creativity and cultural transmission may make such an increase possible, suggesting that: (1) creativity played a major role at the origin of human culture and for its accumulation throughout history, because cultural transmission cannot, on its own, generate exponentially increasing amounts of culture; (2) exponential increase in amount of culture can only occur if creativity is positively influenced by culture. The evolution of cultural transmission is often considered the main genetic bottleneck for the origin of culture, because natural selection cannot favor cultural transmission without any culture to transmit. Our models suggest that an increase in individual creativity may have been the first step toward human culture, because in a population of creative individuals there may be enough non-genetic information to favor the evolution of cultural transmission. PMID:18571686
Decoherence and Exponential Law: A Solvable Model
NASA Technical Reports Server (NTRS)
Pascazio, Saverio; Namiki, Mikio
1996-01-01
We analyze a modified version of the 'AgBr' Hamiltonian, solve exactly the equations of motion in terms of SU(2) coherent states, and study the weak-coupling, macroscopic limit of the model, obtaining an exponential behavior at all times. The asymptotic dominance of the exponential behavior is representative of a purely stochastic evolution and can be derived quantum mechanically in the so-called van Hove's limit (which is a weak-coupling, macroscopic limit). At the same time, a temporal behavior of the exponential type, yielding a 'probability dissipation' is closely related to dephasing ('decoherence') effects and one can expect a close connection with a dissipative and irreversible behavior. We stress the central relevance of the problem of dissipation to the quantum measurement theory and to the general topic of decoherence.
Modeling aftershocks as a stretched exponential relaxation
NASA Astrophysics Data System (ADS)
Mignan, A.
2015-11-01
The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Although other expressions have been proposed in recent decades to describe the temporal behavior of aftershocks, the number of model comparisons remains limited. After reviewing the aftershock models published from the late nineteenth century until today, I solely compare the power law, pure exponential and stretched exponential expressions defined in their simplest forms. By applying statistical methods recommended recently in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simple relaxation process, in accordance with most other relaxation processes observed in Nature.
Method for exponentiating in cryptographic systems
Brickell, Ernest F.; Gordon, Daniel M.; McCurley, Kevin S.
1994-01-01
An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a preapproved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g.sup.e ; transmitting the value g.sup.e to a remote facility by a communications network; receiving the value g.sup.e at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g.sup.xi ; computi The United States Government has rights in this invention pursuant to Contract No. DE-AC04-76DP00789 between the Department of Energy and AT&T Company.
A method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1971-01-01
A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
Exponential Growth of Nonlinear Ballooning Instability
Zhu, P.; Hegna, C. C.; Sovinec, C. R.
2009-06-12
Recent ideal magnetohydrodynamic (MHD) theory predicts that a perturbation evolving from a linear ballooning instability will continue to grow exponentially in the intermediate nonlinear phase at the same linear growth rate. This prediction is confirmed in ideal MHD simulations. When the Lagrangian compression, a measure of the ballooning nonlinearity, becomes of the order of unity, the intermediate nonlinear phase is entered, during which the maximum plasma displacement amplitude as well as the total kinetic energy continues to grow exponentially at the rate of the corresponding linear phase.
ERIC Educational Resources Information Center
Ellis, Amy B.; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Amidon, Joel
2016-01-01
This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…
Hayes, Roger; LeLacheur, Richard; Dumont, Isabelle; Couerbe, Philippe; Safavi, Afshin; Islam, Rafiq; Pattison, Colin; Cape, Stephanie; Rocci, Mario; Briscoe, Chad; Cojocaru, Laura; Groeber, Elizabeth; Silvestro, Luigi; Bravo, Jennifer; Shoup, Ron; Verville, Manon; Zimmer, Jennifer; Caturla, Maria Cruz; Khadang, Ardeshir; Bourdage, James; Hughes, Nicola; Fatmi, Saadya; Di Donato, Lorella; Sheldon, Curtis; Keyhani, Anahita; Satterwhite, Christina; Yu, Mathilde; Fiscella, Michele; Hulse, James; Lin, Zhongping John; Garofolo, Wei; Savoie, Natasha; Xiao, Yi Qun; Kurylak, Kai; Harris, Sarah; Saxena, Manju; Buonarati, Mike; Lévesque, Ann; Boudreau, Nadine; Lin, Jenny; Khan, Masood U; Ray, Gene; Liu, Yansheng; Xu, Allan; Soni, Gunjan; Ward, Ian; Kingsley, Clare; Ritzén, Hanna; Tabler, Edward; Nicholson, Bob; Bennett, Patrick; van de Merbel, Nico; Karnik, Shane; Bouhajib, Mohammed; Wieling, Jaap; Mulvana, Daniel; Ingelse, Benno; Allen, Mike; Malone, Michele; Fang, Xinping
2016-03-01
The 9th GCCClosed Forum was held just prior to the 2015 Workshop on Recent Issues in Bioanalysis (WRIB) in Miami, FL, USA on 13 April 2015. In attendance were 58 senior-level participants, from eight countries, representing 38 CRO companies offering bioanalytical services. The objective of this meeting was for CRO bioanalytical representatives to meet and discuss scientific and regulatory issues specific to bioanalysis. The issues selected at this year's closed forum include CAPA, biosimilars, preclinical method validation, endogenous biomarkers, whole blood stability, and ELNs. A summary of the industry's best practices and the conclusions from the discussion of these topics is included in this meeting report. PMID:26916197
Graphical Models via Univariate Exponential Family Distributions
Yang, Eunho; Ravikumar, Pradeep; Allen, Genevera I.; Liu, Zhandong
2016-01-01
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical data. In this paper, we consider a general sub-class of graphical models where the node-wise conditional distributions arise from exponential families. This allows us to derive multivariate graphical model distributions from univariate exponential family distributions, such as the Poisson, negative binomial, and exponential distributions. Our key contributions include a class of M-estimators to fit these graphical model distributions; and rigorous statistical analysis showing that these M-estimators recover the true graphical model structure exactly, with high probability. We provide examples of genomic and proteomic networks learned via instances of our class of graphical models derived from Poisson and exponential distributions. PMID:27570498
A Simple Mechanical Experiment on Exponential Growth
ERIC Educational Resources Information Center
McGrew, Ralph
2015-01-01
With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…
Intersection of the Exponential and Logarithmic Curves
ERIC Educational Resources Information Center
Boukas, Andreas; Valahas, Theodoros
2009-01-01
The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…
Exponential asymptotics of the Voigt functions
NASA Astrophysics Data System (ADS)
Paris, R. B.
2015-06-01
We obtain the asymptotic expansion of the Voigt functionss K( x, y) and L( x, y) for large (real) values of the variables x and y, paying particular attention to the exponentially small contributions. A Stokes phenomenon is encountered as with x > 0 fixed. Numerical examples are presented to demonstrate the accuracy of these new expansions.
Kovalevskaya exponents of systems with exponential interaction
Emel'yanov, K V; Tsygvintsev, A V
2000-10-31
The Kovalevskaya exponents are calculated for a class of systems generalizing Toda chains: systems with exponential interaction. It is shown that the known cases of algebraic integrability have no direct analogues in the case of spaces with pseudo-Euclidean metrics because the full-parameter expansions of the general solution contain complex powers of the independent variable.
Kovalevskaya exponents of systems with exponential interaction
NASA Astrophysics Data System (ADS)
Emel'yanov, K. V.; Tsygvintsev, A. V.
2000-10-01
The Kovalevskaya exponents are calculated for a class of systems generalizing Toda chains: systems with exponential interaction. It is shown that the known cases of algebraic integrability have no direct analogues in the case of spaces with pseudo-Euclidean metrics because the full-parameter expansions of the general solution contain complex powers of the independent variable.
Robust impedance shaping telemanipulation
Colgate, J.E.
1993-08-01
When a human operator performs a task via a bilateral manipulator, the feel of the task is embodied in the mechanical impedance of the manipulator. Traditionally, a bilateral manipulator is designed for transparency; i.e., so that the impedance reflected through the manipulator closely approximates that of the task. Impedance shaping bilateral control, introduced here, differs in that it treats the bilateral manipulator as a means of constructively altering the impedance of a task. This concept is particularly valuable if the characteristic dimensions (e.g., force, length, time) of the task impedance are very different from those of the human limb. It is shown that a general form of impedance shaping control consists of a conventional power-scaling bilateral controller augmented with a real-time interactive task simulation (i.e., a virtual environment). An approach to impedance shaping based on kinematic similarity between tasks of different scale is introduced and illustrated with an example. It is shown that an important consideration in impedance shaping controller design is robustness; i.e., guaranteeing the stability of the operator/manipulator/task system. A general condition for the robustness of a bilateral manipulator is derived. This condition is based on the structured singular value ({mu}). An example of robust impedance shaping bilateral control is presented and discussed.
Robustness analysis applied to substructure controller synthesis
NASA Technical Reports Server (NTRS)
Gonzalez-Oberdoerffer, Marcelo F.; Craig, Roy R., Jr.
1993-01-01
The stability and robustness of the controlled system obtained via the substructure control synthesis (SCS) method of Su et al. (1990) were examined using a six-bay truss model, and employing an LQG control design method to obtain controllers for two separate structures. It is found that the assembled controller provides a stability in this instance. A qualitative assessment of the stability robustness of the system with controller designed with the SCS method is provided by obtaining a controller using the complete truss model and comparing the robustness of the corresponding closed-loop systems.
Moradi, Hojjatullah; Majd, Vahid Johari
2016-05-01
In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation. PMID:26924600
Joly, Damien; Pellejà, Laia; Narbey, Stéphanie; Oswald, Frédéric; Chiron, Julien; Clifford, John N.; Palomares, Emilio; Demadrille, Renaud
2014-01-01
Among the new photovoltaic technologies, the Dye-Sensitized Solar Cell (DSC) is becoming a realistic approach towards energy markets such as BIPV (Building Integrated PhotoVoltaics). In order to improve the performances of DSCs and to increase their commercial attractiveness, cheap, colourful, stable and highly efficient ruthenium-free dyes must be developed. Here we report the synthesis and complete characterization of a new purely organic sensitizer (RK1) that can be prepared and synthetically upscaled rapidly. Solar cells containing this orange dye show a power conversion efficiency of 10.2% under standard conditions (AM 1.5G, 1000 Wm−2) using iodine/iodide as the electrolyte redox shuttle in the electrolyte, which is among the few examples of DSC using an organic dyes and iodine/iodide red/ox pair to overcome the 10% efficiency barrier. We demonstrate that the combination of this dye with an ionic liquid electrolyte allows the fabrication of solar cells that show power conversion efficiencies of up to 7.36% that are highly stable with no measurable degradation of initial performances after 2200 h of light soaking at 65°C under standard irradiation conditions. RK1 achieves one of the best output power conversion efficiencies for a solar cell based on the iodine/iodide electrolyte, combining high efficiency and outstanding stability. PMID:24504344
Photocounting distributions for exponentially decaying sources.
Teich, M C; Card, H C
1979-05-01
Exact photocounting distributions are obtained for a pulse of light whose intensity is exponentially decaying in time, when the underlying photon statistics are Poisson. It is assumed that the starting time for the sampling interval (which is of arbitrary duration) is uniformly distributed. The probability of registering n counts in the fixed time T is given in terms of the incomplete gamma function for n >/= 1 and in terms of the exponential integral for n = 0. Simple closed-form expressions are obtained for the count mean and variance. The results are expected to be of interest in certain studies involving spontaneous emission, radiation damage in solids, and nuclear counting. They will also be useful in neurobiology and psychophysics, since habituation and sensitization processes may sometimes be characterized by the same stochastic model. PMID:19687829
Exponential integration algorithms applied to viscoplasticity
NASA Technical Reports Server (NTRS)
Freed, Alan D.; Walker, Kevin P.
1991-01-01
Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps.
Exponential Decay of Correlations Implies Area Law
NASA Astrophysics Data System (ADS)
Brandão, Fernando G. S. L.; Horodecki, Michał
2015-01-01
We prove that a finite correlation length, i.e., exponential decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is exponential in the correlation length of the state, thus reproducing as a particular case Hastings's proof of an area law for groundstates of 1D gapped Hamiltonians. As a consequence, we show that 1D quantum states with exponential decay of correlations have an efficient classical approximate description as a matrix product state of polynomial bond dimension, thus giving an equivalence between injective matrix product states and states with a finite correlation length. The result can be seen as a rigorous justification, in one dimension, of the intuition that states with exponential decay of correlations, usually associated with non-critical phases of matter, are simple to describe. It also has implications for quantum computing: it shows that unless a pure state quantum computation involves states with long-range correlations, decaying at most algebraically with the distance, it can be efficiently simulated classically. The proof relies on several previous tools from quantum information theory—including entanglement distillation protocols achieving the hashing bound, properties of single-shot smooth entropies, and the quantum substate theorem—and also on some newly developed ones. In particular we derive a new bound on correlations established by local random measurements, and we give a generalization to the max-entropy of a result of Hastings concerning the saturation of mutual information in multiparticle systems. The proof can also be interpreted as providing a limitation on the phenomenon of data hiding in quantum states.
Wang, Le; Zhang, Hong; Wang, Xiao-Jun; Dierre, Benjamin; Suehiro, Takayuki; Takeda, Takahashi; Hirosaki, Naoto; Xie, Rong-Jun
2015-06-28
Knowing the physicochemical properties of a material is of great importance to design and utilize it in a suitable way. In this paper, we conduct a comprehensive survey of photoluminescence spectra, localized cathodoluminescence, temperature-dependent luminescence efficiency, and applications of Eu(2+)-doped Sr0.5Ba0.5Si2O2N2 in solid-state lighting. This phosphor exhibits a broad emission band with a maximum at 560-580 nm and a full-width at half maximum of 92-103 nm upon blue light excitation, whereas a dual-band emission (i.e., 470 nm and 550 nm) is observed under electron beam irradiation due to perhaps the intergrowth of BaSi2O2N2:Eu(2+) and Sr0.5+σBa0.5-σSi2O2N2:Eu(2+) in each phosphor particle. Under 450 nm blue light irradiation, this yellow phosphor exhibits excellent luminescence properties with absorption, internal and external efficiencies of 83.2, 87.7 and 72.6%, respectively. Furthermore, it also possesses high thermal stability, with the quantum efficiency being decreased by only 4.2% at 150 °C and a high quenching temperature of 450 °C. High-efficiency white LEDs using the title phosphor have a luminous efficacy, color temperature and color rendition of ∼120 lm W(-1), 6000 K and 61, respectively, validating its suitability for use in solid-state white lighting. PMID:26016417
Method for exponentiating in cryptographic systems
Brickell, E.F.; Gordon, D.M.; McCurley, K.S.
1992-12-31
An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a pre-approved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g{sup e}; transmitting the value g{sup e} to a remote facility by a communications network; receiving the value g{sup e} at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g{sup xi}, computing a{sub i} representations for a integer base b, where a{sub i} represents the weighing factor of the ith digit of the integer e; computing the individual values of c{sub d} according to the rule: c{sub d}={product}a{sub i}=d g{sup x {sub i}}; and computing the product of {product}{sup h}/{sub d=1} c{sub d}{sup d} from the stored values of from the plurality of memory locations so as to determine a value for g{sup e}.
Twofold PT symmetry in doubly exponential optical lattices
NASA Astrophysics Data System (ADS)
Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.
2016-01-01
We introduce a family of non-Hermitian optical potentials that are given in terms of double-exponential periodic functions. The center of PT symmetry is not around zero and the potential satisfies a shifted PT -symmetry relation at two distinct locations. Motivated by wave transmission through thin phase screens and gratings, we examine these refractive index modulations from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics, abrupt phase transitions in the eigenvalue spectrum, and exceptional points in the band structure are examined in detail. In addition, the nonlinear properties of wave propagation in Kerr nonlinearity media are studied. In particular, coherent structures such as lattice solitons are numerically identified by applying the spectral renormalization method. The spatial symmetries of such lattice solitons follow the shifted PT -symmetric relations. Furthermore, such lattice solitons have a power threshold and their linear and nonlinear stabilities are critically dependent on their spatial symmetry point.
On Using Exponential Parameter Estimators with an Adaptive Controller
NASA Technical Reports Server (NTRS)
Patre, Parag; Joshi, Suresh M.
2011-01-01
Typical adaptive controllers are restricted to using a specific update law to generate parameter estimates. This paper investigates the possibility of using any exponential parameter estimator with an adaptive controller such that the system tracks a desired trajectory. The goal is to provide flexibility in choosing any update law suitable for a given application. The development relies on a previously developed concept of controller/update law modularity in the adaptive control literature, and the use of a converse Lyapunov-like theorem. Stability analysis is presented to derive gain conditions under which this is possible, and inferences are made about the tracking error performance. The development is based on a class of Euler-Lagrange systems that are used to model various engineering systems including space robots and manipulators.
Applications of an exponential finite difference technique
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.; Keith, Theo G., Jr.
1988-01-01
An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.
Exponential sensor array geometry and simulation
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.
1988-01-01
The polar exponential arrays whose geometric parameters are presently analyzed have proven superior to X-Y raster imaging sensors when wide FOV, high central resolution, and rotation- and zoom-invariance are required; attractive applications for such arrays are in spacecraft docking/tracking/stationkeeping and mobile robot navigation. Attention is given to optimal designs minimizing sensor configuration and computation requirements, and the relation of geometric parameters to the three-dimensional sensing precision requirements driving sensor design. A method for smooth patching of the 'blind-spot' singularity in the sensor with a uniformly high-resolution 'fovea' is also presented.
Robust control with structured perturbations
NASA Technical Reports Server (NTRS)
Keel, Leehyun
1988-01-01
Two important problems in the area of control systems design and analysis are discussed. The first is the robust stability using characteristic polynomial, which is treated first in characteristic polynomial coefficient space with respect to perturbations in the coefficients of the characteristic polynomial, and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l(sup 2) stability margin for both monic and non-monic cases. Following this, a method is extended to reveal much larger stability region. This result has been extended to the parameter space so that one can determine the stability margin, in terms of ranges of parameter variations, of the closed loop system when the nominal stabilizing controller is given. The stability margin can be enlarged by a choice of better stabilizing controller. The second problem describes the lower order stabilization problem, the motivation of the problem is as follows. Even though the wide range of stabilizing controller design methodologies is available in both the state space and transfer function domains, all of these methods produce unnecessarily high order controllers. In practice, the stabilization is only one of many requirements to be satisfied. Therefore, if the order of a stabilizing controller is excessively high, one can normally expect to have a even higher order controller on the completion of design such as inclusion of dynamic response requirements, etc. Therefore, it is reasonable to have a lowest possible order stabilizing controller first and then adjust the controller to meet additional requirements. The algorithm for designing a lower order stabilizing controller is given. The algorithm does not necessarily produce the minimum order controller; however, the algorithm is theoretically logical and some simulation results show that the algorithm works in general.
Exponential evolution: implications for intelligent extraterrestrial life.
Russell, D A
1983-01-01
Some measures of biologic complexity, including maximal levels of brain development, are exponential functions of time through intervals of 10(6) to 10(9) yrs. Biological interactions apparently stimulate evolution but physical conditions determine the time required to achieve a given level of complexity. Trends in brain evolution suggest that other organisms could attain human levels within approximately 10(7) yrs. The number (N) and longevity (L) terms in appropriate modifications of the Drake Equation, together with trends in the evolution of biological complexity on Earth, could provide rough estimates of the prevalence of life forms at specified levels of complexity within the Galaxy. If life occurs throughout the cosmos, exponential evolutionary processes imply that higher intelligence will soon (10(9) yrs) become more prevalent than it now is. Changes in the physical universe become less rapid as time increases from the Big Bang. Changes in biological complexity may be most rapid at such later times. This lends a unique and symmetrical importance to early and late universal times. PMID:11542467
The Matrix Exponential Approach To Elementary Operations
NASA Astrophysics Data System (ADS)
Delosme, Jean-Marc
1986-04-01
In 1971, J.S. Walther generalized and unified J.E. Volder's coordinate rotation (CORDIC) algorithms. Using Walther's algorithms a few commonly used functions such as divide, multiply-and-accumulate, arctan, plane rotation, arctanh, hyperbolic rotation can be implemented on the same simple hardware (shifters and adders, elementary controller) and computed in approximately the same time. Can other useful functions be computed on the same hardware by further generalizing these algorithms? Our positive answer lies in a deeper understanding of Walther's unification: the key to the CORDIC algorithms is that all of them effect the multiplication of a vector by the exponential of a 2 X 2 matrix. The importance of this observation is readily demonstrated as it easily yields the convergence conditions for the CORDIC algorithms and an efficient way of extending the domain of convergence for the hyperbolic functions. A correspondence may be established between elementary functions such as square-root, √(x2+y) , inverse square-root or cubic root and exponentials of simple matrices. Whenever such a correspondence is found, a CORDIC-like algorithm for computing the function can be synthesized in a very straightforward manner. The algorithms thus derived have a simple structure and exhibit uniform convergence inside an adjustable, precisely defined, domain.
A natural spline interpolation and exponential parameterization
NASA Astrophysics Data System (ADS)
Kozera, R.; Wilkołazka, M.
2016-06-01
We consider here a natural spline interpolation based on reduced data and the so-called exponential parameterization (depending on parameter λ ∈ [0, 1]). In particular, the latter is studied in the context of the trajectory approximation in arbitrary euclidean space. The term reduced data refers to an ordered collection of interpolation points without provision of the corresponding knots. The numerical verification of the intrinsic asymptotics α(λ) in γ approximation by natural spline γ^3'N is conducted here for regular and sufficiently smooth curve γ sampled more-or-less uniformly. We select in this paper the substitutes for the missing knots according to the exponential parameterization. The outcomes of the numerical tests manifest sharp linear convergence orders α(λ) = 1, for all λ ∈ [0, 1). In addition, the latter results in unexpected left-hand side dis-continuity at λ = 1, since as shown again here a sharp quadratic order α(1) = 2 prevails. Remarkably, the case of α(1)=2 (derived for reduced data) coincides with the well-known asymptotics established for a natural spline to fit non-reduced data determined by the sequence of interpolation points supplemented with the corresponding knots (see e.g. [1]).
Exponential gradient maker using a disposable syringe.
Domingo, A
1990-08-15
With a simple modification, any disposable syringe can become a reliable and easy to use exponential gradient maker. The modification consists of two notches, made with a razor blade, in the borders of the rubber sealing tip of the plunger. A clamp in the tube connected to the syringe allows control over solution flow. With the clamp prohibiting drainage, the body of the syringe is filled with the desired volume of starting solution I. A magnetic stir bar, small enough to spin inside the syringe is included. The notched plunger is introduced until no air space remains. This forms the fixed volume, closed mixing chamber, while the rest of the volume of the syringe forms the open chamber. The two chambers are connected through the notches in the plunger. The ending solution II is poured after the introduction of the plunger. Opening the clamp allows solution I in the closed chamber to flow out, and the solution II in the open chamber flows through the notches and mixes with solution I. This exponential gradient maker can be reused many times, but the low cost of the components makes it potentially disposable. This feature is especially useful when using toxic chemicals, or when pouring polyacrylamide gradient gels, since the apparatus may be disposed of after contamination or eventual polymerization. PMID:2278394
Measuring Entanglement Spectrum via Density Matrix Exponentiation
NASA Astrophysics Data System (ADS)
Zhu, Guanyu; Seif, Alireza; Pichler, Hannes; Zoller, Peter; Hafezi, Mohammad
Entanglement spectrum (ES), the eigenvalues of the reduced density matrix of a subsystem, serves as a powerful theoretical tool to study many-body systems. For example, the gap and degeneracies of the entanglement spectrum have been used to identify various topological phases. However, the usefulness of such a concept in real experiments has been debated, since it is believed that obtaining the ES requires full state tomography, at a cost which exponentially grows with the systems size. Inspired by a recent density matrix exponentiation technique, we propose a scheme to measure ES by evolving the system with a Hamiltonian that is the subsystem's own reduced density matrix. Such a time evolution can be induced by an ancilla photon that is coupled to multiple qubits at the same time. The phase associated with the time evolution can be detected and converted into ES through either a digital or an analogue scheme. The digital scheme involves a modified quantum phase estimation algorithm based on random time evolution, while the analogue scheme is in the spirit of Ramsey interferometry. Both schemes are not limited by the size of the system, and are especially sensitive to the gap and degeneracies. We also discuss the implementation in cavity/circuit-QED and ion trap systems.
Exponential Size Distribution of von Willebrand Factor
Lippok, Svenja; Obser, Tobias; Müller, Jochen P.; Stierle, Valentin K.; Benoit, Martin; Budde, Ulrich; Schneppenheim, Reinhard; Rädler, Joachim O.
2013-01-01
Von Willebrand Factor (VWF) is a multimeric protein crucial for hemostasis. Under shear flow, it acts as a mechanosensor responding with a size-dependent globule-stretch transition to increasing shear rates. Here, we quantify for the first time, to our knowledge, the size distribution of recombinant VWF and VWF-eGFP using a multilateral approach that involves quantitative gel analysis, fluorescence correlation spectroscopy, and total internal reflection fluorescence microscopy. We find an exponentially decaying size distribution of multimers for recombinant VWF as well as for VWF derived from blood samples in accordance with the notion of a step-growth polymerization process during VWF biosynthesis. The distribution is solely described by the extent of polymerization, which was found to be reduced in the case of the pathologically relevant mutant VWF-IIC. The VWF-specific protease ADAMTS13 systematically shifts the VWF size distribution toward smaller sizes. This dynamic evolution is monitored using fluorescence correlation spectroscopy and compared to a computer simulation of a random cleavage process relating ADAMTS13 concentration to the degree of VWF breakdown. Quantitative assessment of VWF size distribution in terms of an exponential might prove to be useful both as a valuable biophysical characterization and as a possible disease indicator for clinical applications. PMID:24010664
Aston, Elizabeth; Channon, Alastair; Day, Charles; Knight, Christopher G.
2013-01-01
Understanding the effect of population size on the key parameters of evolution is particularly important for populations nearing extinction. There are evolutionary pressures to evolve sequences that are both fit and robust. At high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness. This is survival-of-the-flattest, and has been observed in digital organisms, theoretically, in simulated RNA evolution, and in RNA viruses. We introduce an algorithmic method capable of determining the relationship between population size, the critical mutation rate at which individuals with greater robustness to mutation are favoured over individuals with greater fitness, and the error threshold. Verification for this method is provided against analytical models for the error threshold. We show that the critical mutation rate for increasing haploid population sizes can be approximated by an exponential function, with much lower mutation rates tolerated by small populations. This is in contrast to previous studies which identified that critical mutation rate was independent of population size. The algorithm is extended to diploid populations in a system modelled on the biological process of meiosis. The results confirm that the relationship remains exponential, but show that both the critical mutation rate and error threshold are lower for diploids, rather than higher as might have been expected. Analyzing the transition from critical mutation rate to error threshold provides an improved definition of critical mutation rate. Natural populations with their numbers in decline can be expected to lose genetic material in line with the exponential model, accelerating and potentially irreversibly advancing their decline, and this could potentially affect extinction, recovery and population management strategy. The effect of population size is particularly strong in small populations with 100 individuals or less; the exponential model has
Human-chimpanzee alignment: ortholog exponentials and paralog power laws.
Gao, Kun; Miller, Jonathan
2014-12-01
Genomic subsequences conserved between closely related species such as human and chimpanzee exhibit an exponential length distribution, in contrast to the algebraic length distribution observed for sequences shared between distantly related genomes. We find that the former exponential can be further decomposed into an exponential component primarily composed of orthologous sequences, and a truncated algebraic component primarily composed of paralogous sequences. PMID:25443749
NASA Astrophysics Data System (ADS)
Duan, Lian; Huang, Lihong; Guo, Zhenyuan
2016-07-01
In this paper, the problems of robust dissipativity and robust exponential dissipativity are discussed for a class of recurrent neural networks with time-varying delay and discontinuous activations. We extend an invariance principle for the study of the dissipativity problem of delay systems to the discontinuous case. Based on the developed theory, some novel criteria for checking the global robust dissipativity and global robust exponential dissipativity of the addressed neural network model are established by constructing appropriate Lyapunov functionals and employing the theory of Filippov systems and matrix inequality techniques. The effectiveness of the theoretical results is shown by two examples with numerical simulations.
Duan, Lian; Huang, Lihong; Guo, Zhenyuan
2016-07-01
In this paper, the problems of robust dissipativity and robust exponential dissipativity are discussed for a class of recurrent neural networks with time-varying delay and discontinuous activations. We extend an invariance principle for the study of the dissipativity problem of delay systems to the discontinuous case. Based on the developed theory, some novel criteria for checking the global robust dissipativity and global robust exponential dissipativity of the addressed neural network model are established by constructing appropriate Lyapunov functionals and employing the theory of Filippov systems and matrix inequality techniques. The effectiveness of the theoretical results is shown by two examples with numerical simulations. PMID:27475061
Robust nonlinear control of vectored thrust aircraft
NASA Technical Reports Server (NTRS)
Doyle, John C.; Murray, Richard; Morris, John
1993-01-01
An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.
A Robustly Stabilizing Model Predictive Control Algorithm
NASA Technical Reports Server (NTRS)
Ackmece, A. Behcet; Carson, John M., III
2007-01-01
A model predictive control (MPC) algorithm that differs from prior MPC algorithms has been developed for controlling an uncertain nonlinear system. This algorithm guarantees the resolvability of an associated finite-horizon optimal-control problem in a receding-horizon implementation.
Robust fuzzy logic control of mechanical systems
NASA Astrophysics Data System (ADS)
Kohn-Rich, Sylvia
An approach for the design of robust fuzzy control laws for a large class of mechanical systems was developed. The approach applies Lyapunov's Stability Theory to ensure closed loop stability in the presence of plant perturbations and bounded disturbances. It uses inherent properties of an important class of mechanical and aerospace systems, such as robotic manipulators and large spacecraft, to derive closed-loop stability conditions. Based on these conditions, a methodology for the design of robust fuzzy control systems with guaranteed closed-loop stability was developed. Two classes of control laws for mechanical systems were considered. First, a methodology for point-to-point control was formulated. It combines an energy-type approach with Lyapunov's Stability Theory and its extensions, to obtain robust stability conditions for the closed-loop system. A procedure for control system development based on the above conditions is presented. Finally, a procedure for the implementation of the fuzzy control system with guaranteed performance and closed-loop stability characteristics is formulated. In the second part of the dissertation, the problem of robust tracking for mechanical systems was considered. Based on Lyapunov's Stability Theory and its extensions due to Leitmann and Corless, conditions were developed to prove robust stability and performance in the presence of plant uncertainties, bounded disturbances and control saturation. These conditions involve a large number of parameters and functional dependencies that can be chosen by the designer, therefore are well suited for Fuzzy Logic Control implementation. Three different fuzzy implementation methods for the proposed controls system were analyzed and their relative advantages were discussed. An extensive simulation study of the proposed approach was conducted. It demonstrated the excellent performance of the proposed control systems. The proposed method showed superior performance compared to other robust
An exponentiation method for XML element retrieval.
Wichaiwong, Tanakorn
2014-01-01
XML document is now widely used for modelling and storing structured documents. The structure is very rich and carries important information about contents and their relationships, for example, e-Commerce. XML data-centric collections require query terms allowing users to specify constraints on the document structure; mapping structure queries and assigning the weight are significant for the set of possibly relevant documents with respect to structural conditions. In this paper, we present an extension to the MEXIR search system that supports the combination of structural and content queries in the form of content-and-structure queries, which we call the Exponentiation function. It has been shown the structural information improve the effectiveness of the search system up to 52.60% over the baseline BM25 at MAP. PMID:24696643
Radiating stars with exponential Lie symmetries
NASA Astrophysics Data System (ADS)
Mohanlal, R.; Maharaj, S. D.; Tiwari, Ajey K.; Narain, R.
2016-07-01
We analyze the general model of a radiating star in general relativity. A group analysis of the under determined, nonlinear partial differential equation governing the model's gravitational potentials is performed. This analysis is an extension of previous group analyses carried out and produces new group invariant solutions. We find that the gravitational potentials depend on exponential functions owing to the choice of the Lie symmetry generator. The fundamental boundary equation to be solved is in general a Riccati equation. Several new exact families of solutions to the boundary condition are generated. Earlier models of Euclidean stars and generalized Euclidean stellar models are regained as special cases. Linear equations of state can be found for shear-free and shearing spacetimes.
Universal stretched exponential relaxation in nanoconfined water
NASA Astrophysics Data System (ADS)
Shekhar, Adarsh; Kalia, Rajiv K.; Nakano, Aiichiro; Vashishta, Priya; Alm, Camilla K.; Malthe-Sørenssen, Anders
2014-10-01
Understanding the behavior of water confined at the nanometer scale is a fundamental problem not only in physics but also in life sciences, geosciences, and atmospheric sciences. Here, we examine spatial and dynamic heterogeneities in water confined in nanoporous silica using molecular dynamics (MD) simulations. The simulations reveal intermixed low-density water and high-density water with distinct local structures in nanopores of silica. The MD simulations also show dynamic heterogeneities in nanoconfined water. The temporal decay of cage correlation functions for room temperature and supercooled, nanoconfined water is very well described by stretched exponential relaxation, exp(-(t/τ)β). The exponent β has a unique value, d/(d + 2), which agrees with an exact result for diffusion in systems with static, random traps in d = 3 dimensions.
Fluctuation Bounds in the Exponential Bricklayers Process
NASA Astrophysics Data System (ADS)
Balázs, Márton; Komjáthy, Júlia; Seppäläinen, Timo
2012-04-01
This paper is the continuation of our earlier paper (Balázs et al. in Ann. Inst. Henri Poincaré Probab. Stat. 48(1):151-187, 2012), where we proved t 1/3-order of current fluctuations across the characteristics in a class of one dimensional interacting systems with one conserved quantity. We also claimed two models with concave hydrodynamic flux which satisfied the assumptions which made our proof work. In the present note we show that the totally asymmetric exponential bricklayers process also satisfies these assumptions. Hence this is the first example with convex hydrodynamics of a model with t 1/3-order current fluctuations across the characteristics. As such, it further supports the idea of universality regarding this scaling.
An Exponentiation Method for XML Element Retrieval
2014-01-01
XML document is now widely used for modelling and storing structured documents. The structure is very rich and carries important information about contents and their relationships, for example, e-Commerce. XML data-centric collections require query terms allowing users to specify constraints on the document structure; mapping structure queries and assigning the weight are significant for the set of possibly relevant documents with respect to structural conditions. In this paper, we present an extension to the MEXIR search system that supports the combination of structural and content queries in the form of content-and-structure queries, which we call the Exponentiation function. It has been shown the structural information improve the effectiveness of the search system up to 52.60% over the baseline BM25 at MAP. PMID:24696643
Modified OMP Algorithm for Exponentially Decaying Signals
Kazimierczuk, Krzysztof; Kasprzak, Paweł
2015-01-01
A group of signal reconstruction methods, referred to as compressed sensing (CS), has recently found a variety of applications in numerous branches of science and technology. However, the condition of the applicability of standard CS algorithms (e.g., orthogonal matching pursuit, OMP), i.e., the existence of the strictly sparse representation of a signal, is rarely met. Thus, dedicated algorithms for solving particular problems have to be developed. In this paper, we introduce a modification of OMP motivated by nuclear magnetic resonance (NMR) application of CS. The algorithm is based on the fact that the NMR spectrum consists of Lorentzian peaks and matches a single Lorentzian peak in each of its iterations. Thus, we propose the name Lorentzian peak matching pursuit (LPMP). We also consider certain modification of the algorithm by introducing the allowed positions of the Lorentzian peaks' centers. Our results show that the LPMP algorithm outperforms other CS algorithms when applied to exponentially decaying signals. PMID:25609044
Exponential family models and statistical genetics.
Palmgren, J
2000-02-01
This article describes the evolution of applied exponential family models, starting at 1972, the year of publication of the seminal papers on generalized linear models and on Cox regression, and leading to multivariate (i) marginal models and inference based on estimating equations and (ii) random effects models and Bayesian simulation-based posterior inference. By referring to recent work in genetic epidemiology, on semiparametric methods for linkage analysis and on transmission/disequilibrium tests for haplotype transmission this paper illustrates the potential for the recent advances in applied probability and statistics to contribute to new and unified tools for statistical genetics. Finally, it is emphasized that there is a need for well-defined postgraduate education paths in medical statistics in the year 2000 and thereafter. PMID:10826159
Arsenic for the fool: an exponential connection.
Dani, Sergio U
2010-03-15
Anthropogenic arsenic is insidiously building up together with natural arsenic to a level unprecedented in the history of mankind. Arsenopyrite (FeAsS) is the principal ore of arsenic and gold in hard rock mines; it is formed by a coupled substitution of sulphur by arsenic in the structure of pyrite (FeS(2)) - nicknamed "fool's gold". Other important sources of anthropogenic arsenic are fossil fuels such as coal and oil. Here I report on the first indication that the environmental concentration of total arsenic in topsoils - in the 7-18ppm range - is exponentially related to the prevalence and mortality of Alzheimer's disease and other dementias in European countries. This evidence defies the imputed absence of verified cases of human morbidity or mortality resulting from exposure to low-level arsenic in topsoils. PMID:20123147
Random walk with an exponentially varying step
NASA Astrophysics Data System (ADS)
de La Torre, A. C.; Maltz, A.; Mártin, H. O.; Catuogno, P.; García-Mata, I.
2000-12-01
A random walk with exponentially varying step, modeling damped or amplified diffusion, is studied. Each step is equal to the previous one multiplied by a step factor s (01/s relating different processes. For s<1/2 and s>2, the process is retrodictive (i.e., every final position can be reached by a unique path) and the set of all possible final points after infinite steps is fractal. For step factors in the interval [1/2,2], some cases result in smooth density distributions, other cases present overlapping self-similarity and there are values of the step factor for which the distribution is singular without a density function.
Cascade DNA nanomachine and exponential amplification biosensing.
Xu, Jianguo; Wu, Zai-Sheng; Shen, Weiyu; Xu, Huo; Li, Hongling; Jia, Lee
2015-11-15
DNA is a versatile scaffold for the assembly of multifunctional nanostructures, and potential applications of various DNA nanodevices have been recently demonstrated for disease diagnosis and treatment. In the current study, a powerful cascade DNA nanomachine was developed that can execute the exponential amplification of p53 tumor suppressor gene. During the operation of the newly-proposed DNA nanomachine, dual-cyclical nucleic acid strand-displacement polymerization (dual-CNDP) was ingeniously introduced, where the target trigger is repeatedly used as the fuel molecule and the nicked fragments are dramatically accumulated. Moreover, each displaced nicked fragment is able to activate the another type of cyclical strand-displacement amplification, increasing exponentially the value of fluorescence intensity. Essentially, one target binding event can induce considerable number of subsequent reactions, and the nanodevice was called cascade DNA nanomachine. It can implement several functions, including recognition element, signaling probe, polymerization primer and template. Using the developed autonomous operation of DNA nanomachine, the p53 gene can be quantified in the wide concentration range from 0.05 to 150 nM with the detection limit of 50 pM. If taking into account the final volume of mixture, the detection limit is calculated as lower as 6.2 pM, achieving an desirable assay ability. More strikingly, the mutant gene can be easily distinguished from the wild-type one. The proof-of-concept demonstrations reported herein is expected to promote the development and application of DNA nanomachine, showing great potential value in basic biology and medical diagnosis. PMID:26042874
NASA Technical Reports Server (NTRS)
Wen, John T.; Kreutz, Kenneth; Bayard, David S.
1988-01-01
A class of joint-level control laws for all-revolute robot arms is introduced. The analysis is similar to the recently proposed energy Liapunov function approach except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. By using energy Liapunov functions with the modified potential energy, a much simpler analysis can be used to show closed-loop global asymptotic stability and local exponential stability. When Coulomb and viscous friction and model parameter errors are present, a sliding-mode-like modification of the control law is proposed to add a robustness-enhancing outer loop. Adaptive control is also addressed within the same framework. A linear-in-the-parameters formulation is adopted, and globally asymptotically stable adaptive control laws are derived by replacing the model parameters in the nonadaptive control laws by their estimates.
Robust Inflation from fibrous strings
NASA Astrophysics Data System (ADS)
Burgess, C. P.; Cicoli, M.; de Alwis, S.; Quevedo, F.
2016-05-01
Successful inflationary models should (i) describe the data well; (ii) arise generically from sensible UV completions; (iii) be insensitive to detailed fine-tunings of parameters and (iv) make interesting new predictions. We argue that a class of models with these properties is characterized by relatively simple potentials with a constant term and negative exponentials. We here continue earlier work exploring UV completions for these models—including the key (though often ignored) issue of modulus stabilisation—to assess the robustness of their predictions. We show that string models where the inflaton is a fibration modulus seem to be robust due to an effective rescaling symmetry, and fairly generic since most known Calabi-Yau manifolds are fibrations. This class of models is characterized by a generic relation between the tensor-to-scalar ratio r and the spectral index ns of the form r propto (ns‑1)2 where the proportionality constant depends on the nature of the effects used to develop the inflationary potential and the topology of the internal space. In particular we find that the largest values of the tensor-to-scalar ratio that can be obtained by generalizing the original set-up are of order r lesssim 0.01. We contrast this general picture with specific popular models, such as the Starobinsky scenario and α-attractors. Finally, we argue the self consistency of large-field inflationary models can strongly constrain non-supersymmetric inflationary mechanisms.
NASA Astrophysics Data System (ADS)
Carmele, Alexander; Heyl, Markus; Kraus, Christina; Dalmonte, Marcello
2015-11-01
We investigate the resilience of symmetry-protected topological edge states at the boundaries of Kitaev chains in the presence of a bath which explicitly introduces symmetry-breaking terms. Specifically, we focus on single-particle losses and gains, violating the protecting parity symmetry, which could generically occur in realistic scenarios. For homogeneous systems we show that the Majorana mode decays exponentially fast. By the inclusion of strong disorder, where the closed system enters a many-body localized phase, we find that the Majorana mode can be stabilized substantially. The decay of the Majorana converts into a stretched exponential form for particle losses or gains occurring in the bulk. In particular, for pure loss dynamics we find a universal exponent α ≃2 /3 . We show that this holds both in the Anderson and many-body localized regimes. Our results thus provide a first step to stabilize edge states even in the presence of symmetry-breaking environments.
Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth.
Yan, Wanfeng; van Tuyll van Serooskerken, Edgar
2015-01-01
Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator. PMID:26339793
Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth
Yan, Wanfeng; van Tuyll van Serooskerken, Edgar
2015-01-01
Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator. PMID:26339793
Mechanisms for Robust Cognition.
Walsh, Matthew M; Gluck, Kevin A
2015-08-01
To function well in an unpredictable environment using unreliable components, a system must have a high degree of robustness. Robustness is fundamental to biological systems and is an objective in the design of engineered systems such as airplane engines and buildings. Cognitive systems, like biological and engineered systems, exist within variable environments. This raises the question, how do cognitive systems achieve similarly high degrees of robustness? The aim of this study was to identify a set of mechanisms that enhance robustness in cognitive systems. We identify three mechanisms that enhance robustness in biological and engineered systems: system control, redundancy, and adaptability. After surveying the psychological literature for evidence of these mechanisms, we provide simulations illustrating how each contributes to robust cognition in a different psychological domain: psychomotor vigilance, semantic memory, and strategy selection. These simulations highlight features of a mathematical approach for quantifying robustness, and they provide concrete examples of mechanisms for robust cognition. PMID:25352094
Stretched Exponential relaxation in pure Se glass
NASA Astrophysics Data System (ADS)
Dash, S.; Ravindren, S.; Boolchand, P.
A universal feature of glasses is the stretched exponential relaxation, f (t) = exp[ - t / τ ] β . The model of diffusion of excitations to randomly distributed traps in a glass by Phillips1 yields the stretched exponent β = d[d +2] where d, the effective dimensionality. We have measured the enthalpy of relaxation ΔHnr (tw) at Tg of Se glass in modulated DSC experiments as glasses age at 300K and find β = 0.43(2) for tw in the 0
Rearranging the exponential wall for large N-body systems.
Watson, Deborah K; Dunn, Martin
2010-07-01
The work required to solve for the fully interacting N boson wave function, which is widely believed to scale exponentially with N, is rearranged so the problem scales order by order in a perturbation series as N0. The exponential complexity reappears in an exponential scaling with the order of our perturbation series allowing exact analytical calculations for very large N systems through low order. PMID:20867687
Using Differentials to Differentiate Trigonometric and Exponential Functions
ERIC Educational Resources Information Center
Dray, Tevian
2013-01-01
Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.
An exponential filter model predicts lightness illusions
Zeman, Astrid; Brooks, Kevin R.; Ghebreab, Sennay
2015-01-01
Lightness, or perceived reflectance of a surface, is influenced by surrounding context. This is demonstrated by the Simultaneous Contrast Illusion (SCI), where a gray patch is perceived lighter against a black background and vice versa. Conversely, assimilation is where the lightness of the target patch moves toward that of the bounding areas and can be demonstrated in White's effect. Blakeslee and McCourt (1999) introduced an oriented difference-of-Gaussian (ODOG) model that is able to account for both contrast and assimilation in a number of lightness illusions and that has been subsequently improved using localized normalization techniques. We introduce a model inspired by image statistics that is based on a family of exponential filters, with kernels spanning across multiple sizes and shapes. We include an optional second stage of normalization based on contrast gain control. Our model was tested on a well-known set of lightness illusions that have previously been used to evaluate ODOG and its variants, and model lightness values were compared with typical human data. We investigate whether predictive success depends on filters of a particular size or shape and whether pooling information across filters can improve performance. The best single filter correctly predicted the direction of lightness effects for 21 out of 27 illusions. Combining two filters together increased the best performance to 23, with asymptotic performance at 24 for an arbitrarily large combination of filter outputs. While normalization improved prediction magnitudes, it only slightly improved overall scores in direction predictions. The prediction performance of 24 out of 27 illusions equals that of the best performing ODOG variant, with greater parsimony. Our model shows that V1-style orientation-selectivity is not necessary to account for lightness illusions and that a low-level model based on image statistics is able to account for a wide range of both contrast and assimilation effects
An exponential filter model predicts lightness illusions.
Zeman, Astrid; Brooks, Kevin R; Ghebreab, Sennay
2015-01-01
Lightness, or perceived reflectance of a surface, is influenced by surrounding context. This is demonstrated by the Simultaneous Contrast Illusion (SCI), where a gray patch is perceived lighter against a black background and vice versa. Conversely, assimilation is where the lightness of the target patch moves toward that of the bounding areas and can be demonstrated in White's effect. Blakeslee and McCourt (1999) introduced an oriented difference-of-Gaussian (ODOG) model that is able to account for both contrast and assimilation in a number of lightness illusions and that has been subsequently improved using localized normalization techniques. We introduce a model inspired by image statistics that is based on a family of exponential filters, with kernels spanning across multiple sizes and shapes. We include an optional second stage of normalization based on contrast gain control. Our model was tested on a well-known set of lightness illusions that have previously been used to evaluate ODOG and its variants, and model lightness values were compared with typical human data. We investigate whether predictive success depends on filters of a particular size or shape and whether pooling information across filters can improve performance. The best single filter correctly predicted the direction of lightness effects for 21 out of 27 illusions. Combining two filters together increased the best performance to 23, with asymptotic performance at 24 for an arbitrarily large combination of filter outputs. While normalization improved prediction magnitudes, it only slightly improved overall scores in direction predictions. The prediction performance of 24 out of 27 illusions equals that of the best performing ODOG variant, with greater parsimony. Our model shows that V1-style orientation-selectivity is not necessary to account for lightness illusions and that a low-level model based on image statistics is able to account for a wide range of both contrast and assimilation effects
Review of "Going Exponential: Growing the Charter School Sector's Best"
ERIC Educational Resources Information Center
Garcia, David
2011-01-01
This Progressive Policy Institute report argues that charter schools should be expanded rapidly and exponentially. Citing exponential growth organizations, such as Starbucks and Apple, as well as the rapid growth of molds, viruses and cancers, the report advocates for similar growth models for charter schools. However, there is no explanation of…
101 Ways to Teach About Exponential Growth and Its Consequences.
ERIC Educational Resources Information Center
Allen, Rodney F., Ed.
Exponential growth is a mega-concept which has many applications. It is fundamental to understanding how and why systems work and fail, be they natural or man-made systems. Lessons/activities in this booklet are designed for Florida teachers to help provide their students with an understanding of the nature and implications of exponential growth.…
Exponential Correlation of IQ and the Wealth of Nations
ERIC Educational Resources Information Center
Dickerson, Richard E.
2006-01-01
Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…