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Acta Mathematica Scientia 2009年第3期29卷 650-672页

作者：陈翰馥 Key Laboratory of Systems and Control Institute of Systems Science AMSS Chinese Academy of SciencesBeijing 100190 China

Most of existing methods in system identification with possible exception of those for linear systems are off-line in nature, and hence are nonrecursive. This paper demonstrates the recent progress in recursive system identification. The recursive identification algorithms are presented not only for linear systems （multivariate ARMAX systems） but also for nonlinear systems such as the Hammerstein and Wiener systems, and the nonlinear ARX systems. The estimates generated by the algorithms are online updated and converge a.s. to the true values as time tends to infinity.

关键词： recursive identification ARMAX Hammerstein systems Wiener systems nonlinear ARX systems stochastic approximation convergence

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Convergence of Self-Tuning Regulators under Conditional Heteroscedastic Noises 36

Convergence of Self-Tuning Regulators under Conditional Hete...

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第36届中国控制会议

作者： Yaqi Zhang Lei Guo Key Laboratory of Systems and Control AMSSChinese Academy of Sciences

ISBN: (纸本)9781538629185

Traditional convergence theory of self-tuning regulators requires boundedness of the conditional variances of the systems noise processes. However, this requirement cannot be satisfied for many practical models such the well-known ARCH(Autoregressive Conditional Heteroscedasticity) model in economic systems. The aim of this paper is to provide a convergence theory of self-tuning regulators for linear uncertain systems with conditional heteroscedastic noises, where the conditional variance is unbounded. To be specific, we consider weighted least-squares-based self-tuning regulators, and establish both the global stability and the optimality of tracking under some natural conditions on the system models as well as on the conditional heteroscedastic noises. To the best of the authors’ knowledge, this is the first paper that investigates this kind of problems with a convergence theory, and makes the self-tuning regulators applicable to systems with noised modeled by ARCH.

关键词： Self-Tuning Regulator Conditional Heteroscedasticity ARCH Model Weighted Least-Squares Algorithm Convergence

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Stability of diffusion adaptive filters 19

Stability of diffusion adaptive filters

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19th IFAC World Congress on International Federation of Automatic control, IFAC 2014

作者： Chen, Chen Liu, Zhixin Guo, Lei Key Laboratory of Systems and Control Institute of Systems Science AMSS Beijing100190 China

ISBN: (纸本)9783902823625

In this paper, we consider the diffusion adaptive filters where a set of sensors is required to collectively estimate time-varying signals (or parameters) from noisy measurements in a way of information diffusion. We will establish the stability of the diffusion least mean square (DLMS) algorithm, without requiring stationarity, independency, and boundedness assumptions of the system signals, which means that our results can be applied to more general and practical class of stochastic systems than those studied in the literature. We will present theoretical results concerning stability and bounds on the mean square error (MSE) of the filtering. We will also show that the network of sensors can cooperate to guarantee the stability of the filtering, even though any single sensor does not have such a capability. This clearly reveals the advantages of the DLMS algorithm vs. standard least mean square (LMS) algorithm. Numerical simulations will also be presented to support the theoretical justifications. © IFAC.

关键词： Adaptive filters

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Vector metric of boolean matrices and its application to stability and stabilization of boolean networks

Vector metric of boolean matrices and its application to sta...

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2010 8th IEEE International Conference on control and Automation, ICCA 2010

作者： Cheng, Daizhan Qi, Hongsheng Li, Zhiqiang Key Laboratory of Systems and Control AMSS Chinese Academy of Sciences Beijing 100190 China

ISBN: (纸本)9781424451951

The ring structure and Boolean variables are investigated and they are used to define the product of Boolean matrices. The logical operators have also been extended to the operators on Boolean matrices. Based on these, the vector distance between Boolean matrices is defined. Some properties are revealed. Finally, the vector distance is used to the analysis of the stability of Boolean networks and the stabilization of Boolean control networks. © 2010 IEEE.

关键词： Stabilization

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Algebraic approach to dynamics of multivalued networks

Algebraic approach to dynamics of multivalued networks

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作者： Li, Zhiqiang Cheng, Daizhan Key Laboratory of Systems and Control AMSS Chinese Academy of Sciences Beijing 100190 China

Using semi-tensor product of matrices, a matrix expression for multivalued logic is proposed, where a logical variable is expressed as a vector, and a logical function is expressed as a multilinear mapping. Under this framework, the dynamics of a multivalued logical network is converted into a standard discrete-time linear system. Analyzing the network transition matrix, easily computable formulas are obtained to show (a) the number of equilibriums;(b) the numbers of cycles of different lengths;(c) transient period, the minimum time for all points to enter the set of attractors, respectively. A method to reconstruct the logical network from its network transition matrix is also presented. This approach can also be used to convert the dynamics of a multivalued control network into a discrete-time bilinear system. Then, the structure and the controllability of multivalued logical control networks are revealed. © World Scientific Publishing Company.

关键词： Dynamics

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Block-oriented nonlinear system identification by stochastic approximation

Block-oriented nonlinear system identification by stochastic...

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作者： Chen, Han-Fu Chen, Xing-Min Key Laboratory of Systems and Control Institute of Systems Science AMSS Chinese Academy of Sciences Beijing 100080 China

ISBN: (纸本)9783902661937

First, it is shown that identification of many block-oriented nonlinear systems can be reduced to estimating parameters even if the nonlinearity is not parameterized. It is then shown that the parameter estimation problem can be transformed to seeking roots of some unknown function called as regression function. This is the topic of stochastic approximation (SA). It is demonstrated by example how to appropriately select the regression function and the corresponding observations in order the resulting observation errors to be suitable for convergence analysis. The classical Robbins-Monro algorithm in SA is modified to the stochastic approximation algorithm with expanding truncations (SAAWET), and for it a general convergence theorem is presented. The proposed approach is then applied to identify the MIMO Hammerstein systems with linear block being an ARX system whose input and output both are corrupted by random noises. The recursive algorithms are derived for estimating f(u) with fixed u and the matrix coefficients of the linear subsystem, where the vector function f(·) is the static nonlinearity of the system. All estimates are convergent to the true values with probability one under reasonable conditions. A numerical example shows that the simulation results are consistent with the theoretical analysis. © 2011 IFAC.

关键词： Nonlinear systems

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Markov chain approach to identifying Wiener systems

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Science China(Information Sciences) 2012年第5期55卷 1201-1217页

作者： ZHAO WenXiao 1,2 & CHEN HanFu 1,2 1 key laboratory of systems and control,Institute of systems Science,amss,Chinese Academy of Sciences,Beijing 100190,China 2 National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences,Beijing 100190,China 1. Key Laboratory of Systems and Control Institute of Systems Science AMSS Chinese Academy of Sciences Beijing 100190 China2. National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing 100190 China

Identification of the Wiener system composed of an infinite impulse response (IIR) linear subsystem followed by a static nonlinearity is *** recursive estimates for unknown coefficients of the linear subsystem and for the values of the nonlinear function at any fixed points are given by the stochastic approx-imation algorithms with expanding truncations (SAAWET).With the help of properties of the Markov chain connected with the linear subsystem,all estimates derived in the paper are proved to be strongly *** comparison with the existing results on the topic,the method presented in the paper simplifies the convergence analysis and requires weaker conditions.A numerical example is given,and the simulation results are consistent with the theoretical analysis.

关键词： Wiener system recursive identification stochastic approximation Markov chain strong consis-tency

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A minimum adequate set of multi-valued logic

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control Theory and Technology 2021年第4期19卷 425-429页

作者： Daizhan Cheng Jun-e Feng Jianli Zhao Shihua Fu Research Center of Semi-tensor Product of Matrices:Theory and Applications Liaocheng UniversityLiaochengChina Key Laboratory of Systems and Control AMSSChinese Academy of SciencesBeijing 100190China School of Mathematics Shandong UniversityJinanChina

An adequate set of k-valued logic is provided,which contains only two *** is also proved that this adequate set is of minimum size。

关键词： k-valued logic Normal form Adequate set(ADS) Structure matrix of logical functions Semi-tensor product of matrices

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Cooperative Output Regulation of a Class of Linear Multi-Agent systems

Cooperative Output Regulation of a Class of Linear Multi-Age...

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第三十二届中国控制会议

作者： Jingchao LOU Zairong XI Key Laboratory of Systems and Control AMSS CAS

ISBN: (纸本)9781479900305

In this note, we do something in the cooperative output regulation of linear multi-agent systems. The linear multi-agent systems which we consider is a class of leader-follower systems, only part of agents can access the exogenous signal. What we do is design a simple control law with a dynamic compensator to solve the cooperative output regulation problem. We consider two situations in designing control law, one is using full information of state, another is using part information.

关键词： linear multi-agent systems, cooperative control, output regulation dynamic compensator, full information, part information.

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Block-Oriented Nonlinear System Identification by Stochastic Approximation

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IFAC Proceedings Volumes 2011年第1期44卷 11171-11176页

作者： Han-Fu Chen Xing-Min Chen Key Laboratory of Systems and Control Institute of Systems Science AMSS Chinese Academy of Sciences Beijing 100080 China (Tel: 86-10-62579540) Key Laboratory of Systems and Control Institute of Systems Science AMSS Chinese Academy of Sciences Beijing 100080 China

Abstract First, it is shown that identification of many block-oriented nonlinear systems can be reduced to estimating parameters even if the nonlinearity is not parameterized. It is then shown that the parameter estimation problem can be transformed to seeking roots of some unknown function called as regression function. This is the topic of stochastic approximation (SA). It is demonstrated by example how to appropriately select the regression function and the corresponding observations in order the resulting observation errors to be suitable for convergence analysis. The classical Robbins-Monro algorithm in SA is modified to the stochastic approximation algorithm with expanding truncations (SAAWET), and for it a general convergence theorem is presented. The proposed approach is then applied to identify the MIMO Hammerstein systems with linear block being an ARX system whose input and output both are corrupted by random noises. The recursive algorithms are derived for estimating f ( u ) with fixed u and the matrix coefficients of the linear subsystem, where the vector function f (·) is the static nonlinearity of the system. All estimates are convergent to the true values with probability one under reasonable conditions. A numerical example shows that the simulation results are consistent with the theoretical analysis.

关键词： Recursive identification MIMO Hammerstein system stochastic approximation strong consistency

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