LQR and Stabilization for Discrete-Time Systems With Multiplicative Noises and Input Delays

• 成果类型: Article
• 署名作者: Wang, Hongxia; Zhang, Huanshui; Li, Lin; Fu, Minyue
• 署名单位: Shandong University of Science & Technology; Shandong Agricultural University; Southern University of Science & Technology; Southern University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3307218
• 发表日期: 2024
• 页码: 3515-3530
• 关键词: Delays; Stochastic systems; Stochastic processes; Symmetric matrices; Delay effects; discrete-time systems; COSTS; Input delays; Linear quadratic regulation (LQR); multiplicative noise; Networked control; stochastic system

摘要

This article is concerned with linear quadratic regulation (LQR) and stabilization problems for discrete-time stochastic systems with multiple input channels and input delays. In comparison with single-input-channel problems, a key difficulty, induced by the different delays in different input channels, is that the information sets for multiple controllers are required to be asymmetric and coupled. A novel technique, referred to as orthogonal decomposition-reorganization, is proposed to conquer the coupling between channels. After the technique is used, a new method based on some refined decompositions is provided to solve the delayed forward-backward stochastic difference equations, which overcomes the asymmetry and amounts to finding the solvability condition of the underlying LQR problems. The complete solutions of the finite- and infinite-horizon LQR problems are given by newly developing Riccati-type equations. Also, a necessary and sufficient stabilizing condition is obtained for the system restricted by a performance index. Finally, the effectiveness of the results is evaluated by a numerical example.