Robust optimal control for finite-horizon zero-sum differential games via a plug-n-play event-triggered scheme

Abstract This paper proposes a robust optimal control strategy for finite-horizon two-player Zero-Sum(ZS) differential games with partially unknown dynamics by incorporating an event-triggered scheme and the critic-only adaptive dynamic programming(ADP) method. Firstly, an online identifier is designed to reconstruct unknown system dynamics based on the data-driven technique. The identifier is running in the solving process rather than as a priori part of the solution, which simplifies the system structure and decreases the computational cost. To deal with the finite-horizon constraints, a time-varying value function and a additional term are considered to such that the terminal constraint error is minimised. A critic neural network(CNN) is used to solve the event-triggered Hamilton-Jacobi-Isaacs (HJI) equation under a plug-n-play structure, which reduces the redundant information transmission as well as receives all measurement information immediately. According to the Lyapunov theory, the uniformly ultimately bounded (UUB) for the event-triggered closed-loop system and the CNN weight error are demonstrated, in the meantime the asymptotic stability of the identifier weight error is proved. Finally, the application in the missile-target interception system validates the feasibility and efficacy of the proposed method.