Approximate-optimal control algorithm for constrained zero-sum differential games through event-triggering mechanism

This paper investigates the optimization problem of two-player zero-sum differential game with control constraints in the framework of event triggering. Relying on reinforcement learning, an adaptive dynamic programming algorithm is developed to approximate the optimal solution of zero-sum game, i.e., the saddle-point equilibrium. A single-network structure is adopted, wherein a critic neural network (NN) evaluates the action. First, the constrained Hamilton-Jacobi-Isaacs equation is mathematically derived in the presence of control constraints; the event-triggering mechanism is then incorporated to reduce calculations and actions. Then, based on the gradient-descent technique, a novel weight updating law is designed for the critic NN, which ensures the solution can converge to the optimal value online. Moreover, the stability of closed-loop system is guaranteed and the unfavorable Zeno behavior is excluded by calculating the theoretical minimum triggering interval. Finally, two numerical examples are provided to verify the reliability and effectiveness of proposed algorithm.