Optimal H_∞ Event-Triggered Control for Markov Jump Linear Systems Based on Actor-Critic <i>Q</i>-Learning Approach

In this paper, the optimal H<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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 H<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i>-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.