STABILIZATION OF STOCHASTIC MCKEAN--VLASOV EQUATIONS WITH FEEDBACK CONTROL BASED ON DISCRETE-TIME STATE OBSERVATION

被引：9
|
作者：
Wu, Hao [1 ]
Hu, Junhao [1 ]
Gao, Shuaibin [2 ]
Yuan, Chenggui [3 ]
机构：
[1] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430000, Hubei, Peoples R China
[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[3] Swansea Univ, Dept Math, Bay Campus, Swansea SA1 8EN, W Glam, Wales
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2022年 / 60卷 / 05期
基金：
中国国家自然科学基金;
关键词：
McKean-Vlasov; feedback control; stabilization; discrete-time state observation; distribution observation; DIFFERENTIAL-EQUATIONS; STABILITY; SYSTEMS;
D O I：
10.1137/21M1454997
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we study the stability of solutions of stochastic McKean-Vlasov equations via feedback control based on discrete-time state observation. By using a specific Lyapunov function, the H\infty stability, asymptotic stability and exponential stability in mean square for the solution of the controlled systems are obtained. Since the distribution of the solution is difficult to observe, we study the corresponding particle system which can be observed for the feedback control. We prove that the exponential stability of control system is equivalent to the the exponential stability of the corresponding particle system. Finally, an example is provided to show the effectiveness of the theory.
引用
收藏
页码：2884 / 2901
页数：18
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