Open-Loop H2/H∞ Control for Discrete-Time Mean-Field Stochastic Systems

• 成果类型: Article
• 署名作者: Ma, Hongji; Mou, Chenchen; Ho, Daniel W. C.
• 署名单位: Shandong University of Science & Technology; City University of Hong Kong
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3395018
• 发表日期: 2024
• 页码: 6074-6088
• 关键词: stochastic systems; noise; Symmetric matrices; optimal control; games; attenuation; vectors; H-infinity control; mean-field theory; stochastic optimal control; Stochastic systems

摘要

This article is concerned with the finite-horizon H-2/H-infinity control problem about discrete-time mean-field linear stochastic systems with (x, u, v) -multiplicative noises. We first present a mean-field stochastic bounded real lemma (MF-SBRL), which gives a necessary and sufficient condition for the linear perturbation operator of mean-field systems to gain an H-infinity norm less than a prescribed disturbance attenuation level. Through a mean-field forward-backward stochastic difference equation, an equivalent condition is proposed for the existence of the open-loop H-2/H-infinity control strategy. Based on the established MF-SBRL, it is further shown that the considered H-2/H-infinity control problem is closed-loop solvable if and only if four coupled difference Riccati equations (CDREs) admit a set of positive-semidefinite solutions. Moreover, the state-feedback gains of the closed-loop H-2/H-infinity control strategy are constructed in terms of the solutions to CDREs. As a by-product, the relationship is clarified between the open-loop solvability and the closed-loop solvability of the finite-horizon mean-field H-2/H-infinity control problem. Finally, a recursive algorithm appended with a numerical example is supplied to demonstrate that the adopted CDREs can be solved effectively.