Stackelberg differential game-based fuzzy adaptive hierarchical optimal control for a nonlinear system with unknown...

This paper explores the hierarchical optimal control strategy for high-order nonlinear systems with unknown dynamics, with a focus on two-player scenarios. The Stackelberg differential game theory provides a leader-follower framework to investigate the optimal control problem for players within a predefined sequential decision order. The optimized controllers for the corresponding subsystems of each player are designed using the command filtered backstepping method. In each subsystem, an adaptive dynamic programming architecture is employed to derive the Stackelberg equilibrium solution for the player. To this end, actor-critic functions are introduced to approximate the cost function and execute the control behavior for all players. An identifier based on fuzzy logic systems is utilized to estimate the unknown nonlinear dynamics arising from modeling inaccuracies. To avoid repeated differentiation of the virtual control law, a command filter is adopted to reduce the computational burden by directly obtaining virtual control without differentiation. Finally, simulation results demonstrate that the proposed optimal control scheme can achieve the desired control objective under the hierarchical performance index.