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Jiling Ding,Weihai Zhang,Junsheng Zhao 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.4
This paper studies the problem of output regulation for a class of high-order nonlinear systems with dynamic uncertainties and unknown powers. Based on the characters of input-to-state stable Lyapunov function and the technique of changing supply rate, a partial-state feedback controller is designed under event-triggered mechanism framework. In the proposed control law, an adaptive dynamic gain is constructed to deal with system uncertainties and eliminate the bad effect of the event-triggered sampling error, and a term of higher power is introduced to compensate the unknown system powers. It is verified that the output tracking error converges into any prescribed small set of the origin and all the closed-loop signals are globally bounded by the proposed partialstate feedback controller, while the Zeno phenomenon is avoided. The effectiveness of the proposed scheme is verified by some simulation results.
Regulation Control for Discrete-time Stochastic Nonlinear Active Suspension
Likang Feng,Weihai Zhang,Xiaoyu Zhao,Jianwei Xia,Yajuan Liu 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.3
The regulation problem of discrete-time stochastic nonlinear active suspension is considered in this paper. Firstly, a stability theorem of practically stable in the mean square sense for discrete-time stochastic systems is given. Secondly, the nonlinear active suspension subject to random disturbances modeled by the stochastic difference equation is obtained by the Euler-Maruyama approximation. Thirdly, a state feedback controller is worked out by a discrete backstepping approach such that the states of the discrete-time stochastic nonlinear active suspension can be regulated to a neighbourhood of zero. Finally, the efficiency can be verified by the simulation results.
Huanshui Zhang,Xiao Lu,Weihai Zhang,Wei Wang 대한전기학회 2007 International Journal of Control, Automation, and Vol.5 No.4
The paper deals with the Kalman stochastic filtering problem for linear continuous-time systems with both instantaneous and time-delayed measurements. Different from the standard linear system, the system state is corrupted by multiplicative white noise, and the instantaneous measurement and the delayed measurement are also corrupted by multiplicative white noise. A new approach to the problem is presented by using projection formulation and re-organized innovation analysis. More importantly, the proposed approach in the paper can be applied to solve many complicated problems such as stochastic H∞ estimation, H∞ control stochastic system with preview and so on.
Stability and Stabilization of Stochastic Systems with Multiplicative Noise
Huiying Sun,Meng Li,Weihai Zhang 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.2
In this paper, stability and stabilization of linear stochastic time-invariant systems are studied based on spectrum technique. Firstly, the relationship among mean square exponential stability, asymptotical mean square stability, second-order moment exponential stability and the spectral location of the systems is revealed with the help of a spectrum operator LA,C. Then, we focus on almost sure exponential stability and stochastic stabilization. A criterion on almost sure exponential stability based on spectrum technique is obtained. Sufficient conditions for mean square exponentially stability and asymptotic mean square stability are given via linear matrix inequality approach and some numerical examples to illustrate the effectiveness of our results are presented.
Huiying Sun,Liuyang Jiang,Weihai Zhang 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.5
In this paper, we consider the feedback control on nonzero-sum linear quadratic (LQ) differential games in finite horizon for discrete-time stochastic systems with Markovian jump parameters and multiplicative noise. Four-coupled generalized difference Riccati equations (GDREs) are obtained, which are essential to find the optimal Nash equilibrium strategies and the optimal cost values of the LQ differential games. Furthermore, an iterative algorithm is given to solve the four-coupled GDREs. Finally, a suboptimal solution of the LQ differential games is proposed based on a convex optimization approach and a simplification of the suboptimal solution is given. Simulation examples are presented to illustrate the effectiveness of the iterative algorithm and the suboptimal solution.
Yan, Zhiguo,Zhang, Weihai,Park, Ju H.,Liu, Xiaoping IET 2017 IET control theory & applications Vol.11 No.16
<P>This study is concerned about the quantitative exponential stability (QES) and stabilisation of discrete-time Markov jump systems with multiplicative noises. First, the defects of exponential stability in practical applications are analysed. Based on this analysis, a concept of the QES is given, and two stability criteria are derived. By utilising an auxiliary definition of general finite-time stability (GFTS), the relations among QES, GFTS and finite-time stability are established. Moreover, the quantitative exponential stabilisation is studied, and state feedback controller and the observer-based controller are designed. Subsequently, the relation between the states' upper bound and states' decay rate of considered systems is quantitatively shown by a searching method. Finally, an example is used to illustrate the effectiveness of the authors' obtained results.</P>
Critical Stability and Stabilization of Discrete-Time Stochastic Systems and Its Applications
Huiying Sun,Meng Li,Weihai Zhang 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.6
In this paper, critical stability and critical stabilization for discrete stochastic systems with both state and control dependent noise are discussed via the spectrum technique. The Popov-Belevitch-Hautus (PBH) criterion for exact observability in a discrete version is presented. As applications, some interesting results on a class of generalized Lyapunov equations (GLE), unremovable spectra and dis-crete generalized algebraic Riccati equation (GARE) are obtained. Finally, the problem of assigning the spectra of discrete stochastic systems in a specified disk is considered and some numerical examples are given to demonstrate our results.
Mixed H2/H∞ Control for Linear Infinite-Dimensional Systems
Kai-Ning Wu,Baozhu Guo,Weihai Zhang,Bor-Sen Chen 제어·로봇·시스템학회 2016 International Journal of Control, Automation, and Vol.14 No.1
In this paper, we consider mixed H2=H∞ control problems for linear infinite-dimensional systems. Thefirst part considers the state feedback control for the H2=H∞ control problems of linear infinite-dimensional systems. The cost horizon can be infinite or finite time. The solutions of the H2=H∞ control problem for linear infinitedimensionalsystems are presented in terms of the solutions of the coupled operator Riccati equations and coupleddifferential operator Riccati equations. The second part addresses the observer-based H2=H∞ control of linearinfinite-dimensional systems with infinite horizon and finite horizon costs. The solutions for the observer-basedH2=H∞ control problem of linear infinite-dimensional systems are represented in terms of the solutions of coupledoperator Riccati equations. The first-order partial differential system examples are presented for illustration. Inparticular, for these examples, the Riccati equations are represented in terms of the coefficients of first-order partialdifferential systems.
A unified framework for asymptotic and transient behavior of linear stochastic systems
Yan, Zhiguo,Park, Ju H.,Zhang, Weihai Elsevier 2018 Applied mathematics and computation Vol.325 No.-
<P><B>Abstract</B></P> <P>This paper is concerned with a unified framework for asymptotic and transient behavior of stochastic systems. In order to explain this problem explicitly, a concept of mean square (<I>γ, α</I>)-stability is first introduced and two stability criteria are derived. By utilizing an auxiliary definition of mean square (<I>γ</I>, T)-stability, the relations among mean square (<I>γ, α</I>)-stability, mean square (<I>γ</I>, T)-stability and finite-time stochastic stability are established. Subsequently, two new sufficient conditions for the existence of state and output feedback mean square (<I>γ, α</I>)-stabilization controllers are presented in terms of matrix inequalities. A numerical algorithm is given to obtain the relation between <I>γ</I> <SUB>min </SUB> and <I>α</I>. Finally, an example is given to illustrate our results.</P>