Event-Triggered Safe Control for the Zero-Sum Game of Nonlinear Safety-Critical Systems With Input Saturation

Abstract

In this paper, a novel adaptive dynamic programming (ADP)-based event-triggered safe control method is proposed to solve the zero-sum game problem of nonlinear safety-critical systems with safety constraints and input saturation. First, the barrier function-based system transformation, the zero-sum game problem with safety constraints and input saturation is transformed into an equivalent input saturation zero-sum game problem, so as to guarantee that the system does not violate the safety constraints. Furthermore, the non-quadratic utility function is introduced into the performance function to solve input saturation. Then, a critic neural network (NN) is constructed to approximate the optimal safety value function. Subsequently, a novel event-triggered scheme is developed to determine the update instant of the control law and the disturbance law. Therefore, the proposed ADP-based event-triggered safe control method can ensure that the states of nonlinear safety-critical systems satisfy the safety constraints, while greatly reducing the amount of calculation and saving communication resources. In addition, during the learning process, the concurrent learning is used to relax the persistence of excitation (PE) condition. According to the Lyapuov theory, it is proved that the weight estimation error of the critic neural network and the states are uniformly ultimately bounded (UUB), and the Zeno behavior is excluded. Finally, a simulation example verifies the effectiveness of the proposed method.

Keywords

• Adaptive dynamic programming
• barrier function
• event-triggered control
• input saturation
• safety constraints
• zero-sum game