A novel event-triggered mechanism-based optimal safe control for nonlinear multi-player systems using adaptive dynamic programming

Abstract

In this paper, an approximate optimal safe control method is proposed for nonlinear multi-player systems under a novel event-triggered mechanism (ETM). First, a control barrier function is introduced into the performance index function for ensuring the safety of the system. Then, the coupled Hamilton–Jacobi equations (HJEs) are obtained for multi-player nonzero-sum games. By utilizing a novel event-triggered adaptive dynamic programming algorithm, the Nash equilibrium solutions of HJEs are approximated under a critic architecture. Under the developed novel ETM, signals between sensors, controllers, and actuators are updated aperiodically, significantly saving communication resources. Meanwhile, the approximate optimal controllers are completely discretized, which provides conditions for wireless communications. Based on the Lyapunov theory, state- and weight-dependent triggering conditions are designed to guarantee the stability of the closed-loop system. Finally, a simulation example is presented to exemplify the effectiveness of the proposed control scheme.