Linear-Quadratic Optimal Control for Discrete-Time Mean-Field Systems With Input Delay

被引：0

作者：

Qi, Qingyuan

Xie, Lihua ^{[1
,2
]}

Zhang, Huanshui ^{[3
]}

机构：

[1] Qingdao Univ, Inst Complex Sci, Coll Automat, Qingdao 266071, Peoples R China

[2] Nanyang Technol Univ Singapore, Sch Elect & Elect Engn, Singapore 639798, Singapore

[3] Shandong Univ Sci & Technol, Coll Elect Engn & Automat, Qingdao 266590, Peoples R China

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2022年 / 67卷 / 08期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Optimal control; Delays; Standards; Symmetric matrices; Riccati equations; Difference equations; Control theory; Forward and backward stochastic difference equations; input delay; mean-field systems; optimal control; stabilization; STOCHASTIC DIFFERENTIAL-EQUATIONS; RICCATI-EQUATIONS; STABILIZATION; BEHAVIOR; LIMIT;

D O I：

10.1109/TAC.2021.3106877

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The linear-quadratic (LQ) optimal control and stabilization problems for mean-field systems with input delay (MFSID) are investigated in this article. The necessary and sufficient solvability conditions for LQ control of MFSID are first given in terms of a convexity condition and the solvability of equilibrium conditions. Consequently, by solving the associated mean-field forward and backward stochastic difference equations, the optimal control is derived in terms of the solution of a modified Riccati equation. Furthermore, for the infinite-horizon case, the stabilization problem for MFSID is studied, and the necessary and sufficient stabilizability conditions are obtained. We show that MFSID can be mean square stabilizable if and only if a modified algebraic Riccati equation admits a unique positive-definite solution.

引用

页码：3806 / 3821

页数：16

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