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

• 成果类型: Article
• 署名作者: Qi, Qingyuan; Xie, Lihua; Zhang, Huanshui
• 署名单位: Qingdao University; Nanyang Technological University; Shandong University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3106877
• 发表日期: 2022
• 页码: 3806-3821
• 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

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.