离散时间平均场随机系统的滚动时域控制  

Receding horizon control for discrete-timemean-field stochastic systems

作　　者：叶志勇 贾亚琪 张春梅 杨路 陈柏江 宋江敏 YE Zhiyong;JIA Yaqi;ZHANG Chunmei;YANG Lu;CHEN Bojiang;SONG Jiangmin(Collge of Science,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《重庆理工大学学报（自然科学）》2024年第2期343-352,共10页Journal of Chongqing University of Technology：Natural Science

基　　金：重庆市自然科学基金项目(2019cc27)。

摘　　要：研究了一类离散时间平均场随机时变系统的滚动时域控制(RHC)镇定问题。定义一个新的条件期望型的性能指标;通过利用随机极值原理,得到RHC控制器。基于最优性能指标的单调非增性,得到了使平均场随机系统在RHC控制器下均方镇定的条件,即当2个耦合的Lyapunov型不等式被满足时,由RHC策略控制的系统是均方镇定的。通过数值算例得到在RHC控制器下,其状态轨迹满足渐近均方镇定的条件,即平均场随机系统是渐近均方镇定的,验证了该结论的有效性。This paper investigates the stabilization of receding horizon control(RHC)for a class of discrete-timemean field stochastic time-varying systems.First,a new cost function with the type of conditional expectation is designed.Second,through the stochastic maximum principle,the explicit solution of the RHC is obtained.Based on monotonically non-increasing of the optimal cost,the stabilization conditions of the mean-field stochastic system RHC are derived.That is,when the two coupled Lyapunov-type inequalities are satisfied,the system controlled by RHC is stabilizable.Finally,a numerical example is given to illustrate that under RHC controller,the state trajectory satisfies the condition of asymptotic mean square stabilization.In other words,mean-field stochastic system is asymptotically mean-square stabilized,illustrating the conclusion’s effectiveness.

关 键 词：滚动时域控制(RHC) 平均场随机系统 均方镇定 离散时间 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]