Co-Design of Adaptive Event-Triggered Mechanism and Asynchronous H∞ Control for 2-D Markov Jump Systems via Genetic Algorithm

• Published in: IEEE transactions on cybernetics Vol. 53; no. 9; pp. 5729 - 5740
• Main Authors: Cheng, Peng, Zhang, Guoqing, Zhang, Weidong, He, Shuping
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.09.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Adaptive event-triggered mechanism (AETM); binary-based genetic algorithm (BGA); Closed loops; Co-design; Controllers; Genetic algorithms; H-infinity control; hidden Markov model (HMM); Hidden Markov models; H∞ control; Linear matrix inequalities; Markov chains; Markov processes; Stability; Symmetric matrices; System performance; Two dimensional displays; two-dimensional (2-D) Markov jump systems (MJSs)
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2022.3169530

This article concerns the co-design scheme of the adaptive event-triggered mechanism (AETM) and asynchronous <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> control for two-dimensional (2-D) Markov jump systems. First, we introduce a hidden Markov model with the observation that the asynchronous phenomenon is inevitable between the plant mode and the controller mode. Besides, for economizing the communication times, an innovative 2-D AETM is constructed, which can dynamically regulate the event-triggered thresholds to strive for better system performance. Then, by utilizing the 2-D Lyapunov stability theory, nonlinear matrix inequalities are built to ensure the asymptotic mean-square stability with an <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> performance for the closed-loop 2-D system. To avoid introducing any conservatism when handling the above nonlinear matrix inequalities, a binary-based genetic algorithm (BGA) is exploited to treat some variables as known, such that derive some directly solvable linear matrix inequalities. Finally, a simulation example is provided to verify the effectiveness of the proposed 2-D AETM-based asynchronous controller strategy with a BGA.