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stability in probability and Inverse Optimal Control of Evolution Systems Driven by Levy Processes

IEEE/CAA Journal of Automatica Sinica 2020年第2期7卷 405-419页

作者： Khac Duc Do School of Civil and Mechanical Engineering CurtinUniversity

This paper first develops a Lyapunov-type theorem to study global well-posedness(existence and uniqueness of the strong variational solution)and asymptotic stability in probability of nonlinear stochastic evolution systems(SESs)driven by a special class of Levy processes,which consist of Wiener and compensated Poisson *** theorem is then utilized to develop an approach to solve an inverse optimal stabilization problem for SESs driven by Levy *** inverse optimal control design achieves global well-posedness and global asymptotic stability of the closed-loop system,and minimizes a meaningful cost functional that penalizes both states and *** approach does not require to solve a Hamilton-Jacobi-Bellman equation(HJBE).An optimal stabilization of the evolution of the frequency of a certain genetic character from the population is included to illustrate the theoretical developments.

关键词： Evolution system inverse optimal control Levy processes stability in probability well-posedness

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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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Output-Feedback Robust Adaptive Control for Strict-feedback Stochastic Nonlinear Systems under Inverse Optimality Costs

Output-Feedback Robust Adaptive Control for Strict-feedback ...

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2010 Chinese Control and Decision Conference

作者： Jingsheng Wang,Jun Wang,Wei Liu,Ping Ji Key Lab.of Machine Vision and Intelligence Control Technology,Hefei University,Hefei,230022 P.R.China

The solvable problem of adaptive inverse optimal stabilization in probability is discussed,and control laws of global asymptotic stability in probability and adaptive inverse optimal stabilization in probability are developed for output-feedback stochastic nonlinear continuous systems with additive standard Wiener noises and constant unknown parameters by using Ito’s differentiation rule and adaptive backstepping *** adaptive control law and the parameter update laws can be obtained at same time by this design scheme.

关键词： Output-feedback Wiener noises Backstepping algorithm Inverse optimality stability in probability

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Output-Feedback Robust Adaptive Control for Strict-feedback Stochastic Nonlinear Systems under Inverse Optimality Costs

Output-Feedback Robust Adaptive Control for Strict-feedback ...

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第二十四届中国控制会议

作者： Wang Jun, Zhang Mei, Xi Hongsheng, Cheng Rong (Department of Automation, USTC. Hefei 230026)

＜正＞ The solvable problem of adaptive inverse optimal stabilization in probability is discussed and control laws of global asymptotic stability in probability and adaptive inverse optimal stabilization in probability are developed for out-feedback stochastic nonlinear continuous systems with additive standard Wiener noises and constant unknown parameters by using Ito’s differentiation rule and adaptive backstepping algorithms. The adaptive control law and the parameter update laws can be obtained at same time by this design scheme.

关键词： out-feedback Wiener noises Ito’s differentiation rule Backstepping algorithm inverse optimahty stability in probability

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