Event-triggered robust hierarchical control for uncertain multiplayer Stackelberg games via adaptive dynamic programming

Abstract

This paper investigates the event-triggered robust hierarchical control (ETRHC) problem of uncertain multi-player nonlinear systems subject to actuator faults by using adaptive dynamic programming and integral sliding mode technique. Different from existing results where the control policies of all players are updated simultaneously, a hierarchical decision-making problem is considered as a Stackelberg game. The Stackelberg game consists of a single leader and multiple followers, the leader acts a control policy in advance by considering the responses of all the followers, and each follower responds optimally to the leader’s policy. The proposed control structure comprises of two components, namely integral sliding mode control and ETRHC. In the first step, the integral sliding mode control policy is developed to cope with actuator faults and matched uncertainties, and then, the fault-free multi-player nonlinear systems with mismatched uncertainties is obtained. In the second step, by designing an appropriate performance index function for each player, the ETRHC of the fault-free multi-player nonlinear system with mismatched uncertainties is converted to an event-triggered approximate optimal control of its nominal form, and the hierarchical decision-making problem is addressed. Subsequently, the ETRHC laws are derived by solving event-triggered Hamilton–Jacobi equations with the critic-only learning. Theoretical analysis demonstrates that the integral sliding mode-based ETRHC scheme guarantees the multi-player uncertain nonlinear systems with actuator faults to be asymptotically stable. Finally, the quadrotor attitude system is adopted to verify the effectiveness of the present scheme.