控制理论与应用2024，Vol.41Issue(5)：895-904,10.DOI:10.7641/CTA.2022.10807
带Markov跳的离散时间随机控制系统的最大值原理
A maximum principle for optimal control of discrete-time stochastic systems with Markov jump
摘要
Abstract
The maximum principle(MP)of the discrete-time nonlinear stochastic optimal control problem is proved,in which the control systems are driven by both Markov jumps and multiplicative noise.Firstly,based on the adapted solutions of the backward stochastic difference equation,the linear functional with the constraint of a linear difference equation is represented.The Riesz theorem is used to prove the uniqueness of such representation.Secondly,the spike variation method is extend to the nonlinear stochastic difference equation with Markov jumps.The variation equation of such state equation is obtained.Thirdly,by introducing a Hamiltonian function,a necessary condition of the discrete-time nonlinear stochastic optimal control system with Markov jump is obtained.It is proved that the adjoint equation of the maximum principle of the system is a pair of backward stochastic difference equations.Moreover,a sufficient condition is also given and the corresponding Hamilton-Jacobi-Bellman equation is derived.Finally,a practical example is given to illustrate the practicability and feasibility of the proposed theory.关键词
最大值原理/最优控制/Markov跳/倒向随机差分方程/Hamilton-Jacobi-Bellman方程Key words
maximum principle/optimal control/Markov jump/backward stochastic difference equations/Hamilton-Jacobi-Bellman equations引用本文复制引用
蔺香运,王鑫瑞,张维海..带Markov跳的离散时间随机控制系统的最大值原理[J].控制理论与应用,2024,41(5):895-904,10.基金项目
国家自然科学基金项目(62273212,61973198),山东省泰山学者项目研究基金项目,山东省自然科学基金项目(ZR2020MF062)资助.Supported by the National Natural Science Foundation of China(62273212,61973198),the Research Fund for the Taishan Scholar Project of Shan-dong Province of China and the National Natural Science Foundation of Shandong Province of China(ZR2020MF062). （62273212,61973198）
