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Fault estimation and fault-tolerant control for linear discrete time-varying stochastic systems

Science China(Information Sciences) 2021年第10期64卷 5-20页

作者： Tianliang ZHANG Feiqi DENG Yuan SUN Peng SHI School of Automation Science and Engineering South China University of Technology School of Electrical and Electronic Engineering University of Adelaide

This paper presents a scheme for simultaneous fault estimation and fault-tolerant control of linear discrete time-varying stochastic systems. An observer is proposed to estimate the system state and the fault simultaneously. The estimation errors of both the system state and fault can achieve exponential stability in mean square sense even if the fault arbitrarily changes or is unbounded. The controllers of the drift term and diffusion term are designed separately, and then based on the estimated fault, the fault compensation is performed to realize fault tolerance. For the parameter design in the estimator and controllers, we provide two different algorithms via the cone complementarity linearization and the state transition matrix methods,respectively. As an extension, a class of quasi-linear systems is also discussed. A simulation example with two different fault types and an application in electromechanical servo systems are provided to illustrate the usefulness of the proposed scheme.

关键词： linear discrete stochastic systems fault estimation fault-tolerant control state transition matrix exponentialstability in mean square

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Theory and application of stability for stochastic reaction diffusion systems

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Science in China(Series F) 2008年第2期51卷 158-170页

作者： LUO Qi DENG FeiQi MAO XueRong BAO JunDong ZHANG YuTian College of Information and Control Nanjing University of Information Science & Technology Nanjing 210044 China College of Automation South China University of Technology Guangzhou 410640 China Department of Statistics and Modelling Science University of-Strathc/yde Glasgow G1 IXH Scotland UK Coilege of Mathematics Science Inner Mongolia Normal'University Huhhot 010000 China College of Mathematics and Physics Nanjing University of Information Science & Technology Nanjing 210044 China

So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding It6 formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the It6 stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, and exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob- tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.

关键词： stochastic reaction diffusion system stability in probability asymptotic stability in probability exponentialstability in mean square

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