Optimal H∞ Control of Nonlinear Systems via Static and Dynamic Triggering Critic Learning

In this paper, a novel dynamic triggering based critic learning algorithm is proposed to solve the optimal H
∞
control problem of a continuous-time nonlinear system. First, the H
∞
control problem is formulated as a two-player zero-sum differential game. Then, an adaptive critic learning algorithm is adopted to acquire the approximate solution of the optimal control law under the worst-case external disturbance. Meanwhile, to improve the computational efficiency for the critic learning control method, an event-triggering mechanism is introduced to compute the approximate optimal control law. Then two kinds of triggering conditions, namely, static triggering scheme and dynamic triggering scheme, are designed for determining the event instants in the training process of the learning algorithm. In addition, the stability of the closed-loop system with the proposed triggering learning control method and the convergence of critic weight training procedure are both proved through Lyapunov theories. Finally, a simulation is carried out to demonstrate the effectiveness and performance of the proposed triggering based critic learning methods.