Online event-triggered adaptive critic design for multi-player zero-sum games of partially unknown nonlinear systems with input constraints

Abstract

This paper focuses on the design of online event-triggered optimal control strategy for multi-player zero-sum games (MP-ZSGs) with control constraints when the system model is partially unknown. Non-quadratic functions are utilized to construct the cost functions under the condition of control constraints. The proposed algorithm is designed based on the framework of identifier-critic networks. The unknown drift dynamics model is reconstructed by an identifier neural network (INN) using the input and output data. The near-optimal event-based controls and time-based disturbances are designed by training a critic neural network (CNN). With the aid of the designed event-triggered mechanism (ETM), the needless computing and communication actions of the system signals have been reduced so as to save computing/communication resources. Meanwhile, to remove the persistence of excitation (PE) condition, the historical and current data are utilized to construct a modified tuning law of CNN. Theoretically, the uniform ultimate boundedness (UUB) properties of the system states and the critic weights errors are proved by Lyapunov approach. Moreover, the Zeno behavior is proved to be excluded under the designed triggering condition. Finally, the convergence and performance of the online method are verified by simulating a representative example.