Co-Design of Adaptive Event-Triggered Mechanism and Asynchronous <i>H<sub>∞</sub> </i> Control for 2-D Markov Jump Systems via Genetic Algorithm
Cheng Peng, Guoqing Zhang, Weidong Zhang, Shuping He
Abstract
This article concerns the co-design scheme of the adaptive event-triggered mechanism (AETM) and asynchronous <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <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.