常微分方程周期脉冲控制问题的均方turnpike性质  

MEAN SQUARE TURNPIKE PROPERTY OF PERIODIC IMPULSIVE CONTROL PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

作　　者：闫奇姝 赵睿 YAN Qi-shu;ZHAO Rui(School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《数学杂志》2023年第5期447-458,共12页Journal of Mathematics

基　　金：河北省自然科学基金资助(A2020202033);河北省研究生创新资助项目基金资助(CXZZSS2022056)。

摘　　要：本文研究了一类常微分方程的最优控制问题,其中控制以脉冲的形式周期地施加到系统中.首先,给出了该问题及其参考控制问题的最大值原理.其次,在控制系统能控的假设条件下,证明了系统的能观性不等式.最后,利用最大值原理以及能观性不等式,获得了两个最优控制问题的最优状态和最优控制在时间足够长时的收敛关系—均方turnpike性质.In this paper,we study the optimal control problem of a class of ordinary di erential equations,in which the control periodically acts into the system in the form of impulses.Firstly,we give the maximum principles of the optimal control problem and the reference control problem,respectively.Secondly,under the assumption that the control system is controllable,the observability inequality of the system is proved.Finally,by using the maximum principles and the observability inequality,the convergence relationship of the optimal states and optimal controls between two optimal control problems is obtained when the time range is large enough|the mean square turnpike property.

关 键 词：周期脉冲控制系统 turnpike性质 最大值原理 

分 类 号：O231.1[理学—运筹学与控制论]