Optimal finite-horizon tracking control in affine nonlinear systems: A Stackelberg game approach with H2/H∞ framework

Abstract

In this paper, we address the finite-time optimal tracking control problem within the context of a Stackelberg game structure, characterized by the mixed $H_2/H_{\infty }$ framework. This objective is accomplished through the innovative design and implementation of a novel Adaptive Dynamic Programming (ADP) algorithm. Initially, we establish a time-varying coupled Hamilton-Jacobi-Isaacs (HJI) equations, posing a significant challenge in deriving an analytical solution for the optimal leader. Subsequently, we elucidate the existence of Nash equilibrium points, confirming the algorithm's convergence and providing theoretical foundations for its practical application. Furthermore, we introduce a novel ADP algorithm that incorporates time-varying activation functions. The use of the Lyapunov direct method ensures the stability of the closed-loop affine nonlinear system under the ADP control scheme, thereby guaranteeing the system's uniformly ultimately bounded (UUB). Finally, the effectiveness of the aforementioned ADP-based control approach is validated through numerical simulations.