Stabilization and Optimal Control for Markov Jump Linear System With Two Controllers Over Multiple Erasure Channels

• Published in: International journal of control, automation, and systems Vol. 22; no. 1; pp. 93 - 105
• Main Authors: Li, Xueyang, Han, Chunyan, Xu, Juanjuan, Wang, Wei
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 2024; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Algorithms; Channels; Control; Controllers; Engineering; Mechatronics; Network control; Optimal control; Regular Papers; Remote control; Riccati equation; Robotics; Stabilization; 제어계측공학; Local control and remote control; networked control systems; optimal control; multiple erasure channels; stabilization; Markov jump linear system
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-022-0553-2

This paper considers the stabilization and optimal control of networked control systems possessing two controllers, in which the local controller and the remote controller transmit state information over multiple erasure channels. Multiple controllers are introduced for the first time in this multi-mode system. The coupling of the two controllers and the dependence of the adjacent-time jumping parameters make the control problem more difficult. For the finite horizon, the existence conditions and the explicit solutions to the optimal controllers are given in virtue of two coupled difference Riccati equations (CDREs). For the infinite horizon, the necessary and sufficient conditions of stabilizability are presented and the corresponding optimal controllers are derived with a new set of coupled algebraic Riccati equations (CAREs). Numerical examples are used to demonstrate the effectiveness of the proposed algorithms.