Adaptive Fixed‐Time Bipartite Containment Control for Saturated Nonlinear Multi‐Agent Systems Based on Optimized Backstepping Technique

ABSTRACT This paper studies the fixed‐time optimal bipartite containment control problem for nonlinear multi‐agent systems (MASs) with input saturation. First, the conventional bipartite containment problem is reformulated as an optimal control problem on the communication topology by constructing a performance cost function that incorporates both control inputs and tracking errors. Then, a novel identifier–actor–critic reinforcement learning (RL) architecture based on neural networks (NNs) is developed to solve the Hamilton–Jacobi–Bellman (HJB) equation online without requiring prior knowledge of system dynamics. In addition, an auxiliary system is designed to compensate for the negative effect of input saturation, enabling reliable control under actuator constraints. Subsequently, a fixed‐time optimal controller is proposed to ensure that tracking errors converge to a small domain near the origin in a fixed time with minimal cost, and all the closed‐loop signals are bounded. Finally, two examples are used to illustrate the effectiveness of the proposed control method.