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Robust integral stabilization of regular linear systems

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Science in china(Series F) 2004年第5期47卷 545-554页

作者： XUChengzhong FENGDexing Lagep Bat.308GUniversitedeLyon43Bddu11/11/191869622Villeurbannecedex-France InstituteofSystemsScience AcademyofMathematicsandSystemSciencesChineseAcademyofSciencesBeijing100080China

We consider regular systems with control and observation. We prove some necessary and sufficient condition for an exponentially stable regular system to admit an integral stabilizing controller. We propose also some r... 详细信息

关键词： infinite-dimensional system C0-semigroup integral controllers exponential stabilization.

THE EXPONENTIAL STABILIZATION FOR A SEMILINEAR WAVE EQUATION WITH LOCALLY DISTRIBUTED FEEDBACK

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Chinese Annals of Mathematics,Series B 2005年第3期26卷 323-334页

作者： JIACHAOHUA FENGDEXING InstituteofSystemsScience AcademyofMathematicsandSystemsScienceChineseAcademyofSciencesBeijing100080China／／GraduateSchooloftheChineseAcademyofSciencesBeijing100049China InstituteofSystemsScience AcademyofMathematicsandSystemsScienceChineseAcademyofSciencesBeijing100080China

This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that... 详细信息

关键词： Wave equations Exponential decay Distributed damping Variable coefficients Riemannian manifold

Logic and logic-based control

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控制理论与应用（英文版） 2008年第1期6卷 26-36页

作者： Hongsheng QI Daizhan CHENG Institute of Systems Science Chinese Academy of Sciences Beijing 100080 China

This paper gives a matrix expression of logic. Under the matrix expression, a general description of the logical operators is proposed. Using the semi-tensor product of matrices, the proofs of logical equivalences, implications, etc., can be simplified a lot. Certain general properties are revealed. Then, based on matrix expression, the logical operators are extended to multi-valued logic, which provides a foundation for fuzzy logical inference. Finally, we propose a new type of logic, called mix-valued logic, and a new design technique, called logic-based fuzzy control. They provide a numerically computable framework for the application of fuzzy logic for the control of fuzzy systems.

关键词： Semi-tensor product Matrix expression of logic Mix-valued logic Logic-based fuzzy control

Connectivity and synchronization of Vicsek model

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Science in china(Series F) 2008年第7期51卷 848-858页

作者： LIU ZhiXin GUO Lei Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190 China

The collective behavior of multi-agent systems is an important studying point for the investigation of complex systems, and a basic model of multi-agent systems is the so called Vicsek model, which possesses some key features of complex systems, such as dynamic behavior, local interaction, changing neighborhood, etc. This model looks simple, but the nonlinearly coupled relationship makes the theoretical analysis quite complicated. Jadbabaie et al. analyzed the linearized heading equations in this model and showed that all agents will synchronize eventually, provided that the neighbor graphs associated with the agents＇ positions satisfy a certain connectivity condition. Much subsequent research effort has been devoted to the analysis of the Vicsek model since the publication of Jadbabaie＇s work. However, an unresolved key problem is when such a connectivity is satisfied. This paper given a sufficient condition to guarantee the synchronization of the Vicsek model, which is imposed on the model parameters only. Moreover, some counterexamples are given to show that the connectivity of the neighbor graphs is not sufficient for synchronization of the Vicsek model if the initial headings are allowed to be in [0,2π）, which reveals some fundamental differences between the Vicsek model and its linearized version.

关键词： Vicsek model synchronization stochastic matrix connectivity neighbor graph

Minimal-order observer and output-feedback stabilization control design of stochastic nonlinear systems

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Science in china(Series F) 2004年第4期47卷 527-544页

作者： LIUYungang ZHANGJifeng SchoolofControlScienceandEngineering ShandongUniversityJinan250061China AcademyofMathematicsandSystemSciences ChineseAcademyofSciencesBeijing100080China

A minimal-order observer and output-feedback stabilization control are given for single-input multi-output stochastic nonlinear systems with unobservable states, un- modelled dynamics and stochastic disturbances. Based on the observer designed, the estimates of all observable states of the system are given, and the convergence of the es- timation errors are analyzed. In addition, by using the integrator backstepping approach, an output-feedback stabilization control is constructively designed, and sufficient condi- tions are obtained under which the closed-loop system is asymptotically stable in the large or bounded in probability, respectively.

关键词： nonlinear systems minimal-order integrator backstepping approach stabilization control.

On global controllability of affine nonlinear systems with a triangular-like structure

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Science in china(Series F) 2007年第6期50卷 831-845页

作者： SUN YiMin MEI ShengWe LU Qiang Department of Electrical Engineering Tsinghua University Beijing 100084 China

In this paper, we investigate a class of affine nonlinear systems with a triangular-like structure and present its necessary and sufficient condition for global controllability, by using the techniques developed by Su... 详细信息

关键词： affine nonlinear systems global controllability vector field

Recursive identification for multidimensional ARMA processes with increasing variances

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Science in china(Series F) 2005年第5期48卷 596-614页

作者： CHEN Hanfu Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy ofSciences Beijing 100080 China

In time series analysis, almost all existing results are derived for the case where the driven noise {wn} in the MA part is with bounded variance （or conditional variance）. In contrast to this, the paper discusses how to identify coefficients in a multidimensional ARMA process with fixed orders, but in its MA part the conditional moment E（｜｜wn｜｜^β｜Fn-1）, β 〉 2 is possible to grow up at a rate of a power of logn. The wellknown stochastic gradient （SG） algorithm is applied to estimating the matrix coefficients of the ARMA process, and the reasonable conditions are given to guarantee the estimate to be strongly consistent.

关键词： multidimensional ARMA increasing variance recursive estimation martingale difference sequence

EXTENDED CASIMIR APPROACH TO CONTROLLED HAMILTONIAN SYSTEMS

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Journal of Systems Science & Complexity 2006年第2期19卷 211-218页

作者： Yuqian GUO Daizhan CHENG Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China.

In this paper, we first propose an extended Casimir method for energy-shaping. Then it is used to solve some control problems of Hamiltonian systems. To solve the Hoo control problem, the energy function of a Hamiltonian system is shaped to such a form that could be a candidate solution of HJI inequality. Next, the energy function is shaped as a candidate of control ISS-Lyapunov function, and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved. Some easily verifiable sufficient conditions are presented.

关键词： Casimir function Energy-shaping H∞ control Input-to-state stabilization.

Identification of Wiener systems with nonlinearity being piecewise-linear function

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Science in china(Series F) 2008年第1期51卷 1-12页

作者： HUANG YiQing CHEN HanFu FANG HaiTao Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Graduate School of the Chinese Academy of Sciences Beijing 100039 China

Identification of the Wiener system with the nonlinear block being a piecewiselinear function is considered in the paper, generalizing the results given by H. E. Chen to the case of noisy observation. Recursive algorithms are given for estimating all unknown parameters contained in the system, and their strong consistency is proved. The estimation method is similar to that used by H. E. Chen for Hammerstein systems with the same nonlinearity. However, the assumption imposed by H. E. Chen on the availability of an upper bound for the nonsmooth points of the piecewise-linear function has been removed in this paper with the help of designing an additional algorithm for estimating the upper bound.

关键词： Wiener system recursive identification strong consistency piecewise-linear function stochastic approximation