Finite‐Time Cooperative Tracking of Multi‐Agent Systems With Input Saturation via Dual‐Critic Architecture Optimized Control

ABSTRACT This paper investigates the problem of adaptive finite‐time optimal control for stochastic nonlinear multi‐agent systems (MASs) subject to input saturation. To address the challenges posed by unknown dynamics and the Hamilton‐Jacobi‐Bellman (HJB) equation, a novel double critic‐actor architecture is developed, enabling efficient approximation of both the value function and system uncertainties. By integrating the command filter technique and function approximation within a backstepping framework, a finite‐time optimal tracking control scheme is constructed. An auxiliary system is further introduced to explicitly handle input saturation. Rigorous analysis based on the finite‐time stochastic Lyapunov theorem ensures that the tracking error remains within a prescribed bound in finite time, and the closed‐loop system achieves semi‐globally finite‐time stability in probability (SGFSP). The effectiveness of the proposed approach is validated through its successful application to a single‐link manipulator system.