Optimal H∞ Event-Triggered Control for Markov Jump Linear Systems Based on Actor-Critic Q-Learning Approach

In this paper, the optimal ${\mathcal {H}}_{\infty } $ control problem is investigated for a class of Markov jump linear systems, under event-triggering mechanism. To this end, a two-player zero-sum differential game-theoretic problem is formulated and a mode-dependent event-triggered version of Hamiltonian function is established and compared with its time-triggered counterpart. Based on this, the corresponding triggering event is given to ensure the stochastic stability of the considered system with a predefined ${\mathcal {H}}_{\infty } $ noise attenuation level index and the existence of a saddle point for the defined cost function is proved. The difference in the optimal cost between the time-triggered case and the event-triggered one is also shown. Further to derive an online solution without the full knowledge of the system model, a Q-learning framework is adopted to approximate the optimal cost and the optimal event-triggered control law combined with an actor-critic network. The error dynamics of the learning algorithm are analyzed and the convergence is proved. The stochastic stability of the resulting closed-loop system is also confirmed. Finally, a numerical example is given to show the effectiveness of the proposed results. Note to Practitioners—The wide applications of Markov jump system have gained its reputation in modeling systems with random changes from internal structure or external parameters. This work is motivated by the optimal ${\mathcal {H}}_{\infty } $ event-triggered control problem for Markov jump system. Existing results are mostly based on linear matrix inequality approach which is strictly model-based and offline thus vulnerable to modeling uncertainties. The optimality of the event-triggered controller has rarely been discussed. In this paper we adopt a Q-learning based actor-critic approach to perform the optimal ${\mathcal {H}}_{\infty } $ event-triggered controller design with respect to a user-defined triggering condition. The stability of the closed-loop system is proved as well as the convergence of the learning algorithm. It is data-based and easy to be implemented online without the full knowledge of the system parameters. Examples are given in the end to demonstrate the performance of the obtained results. In future research, network-induced disturbances such as time-delays, malicious attacks will be considered and discussed under the proposed method.