Bipartite Consensus Tracking via Reinforcement-Learning-Based Time-Synchronized Control

This brief proposes an optimized TSC method based on reinforcement learning for the bipartite consensus tracking problem. The study considers multiagent system comprising leaders and followers, where followers interact through signed directed graphs. Some agents track the leader’s state, while others converge to its opposite value. The proposed method employs a time-synchronized sliding mode control framework to ensure fixed-time bipartite consensus among agents with signed interaction topology. Reinforcement learning is integrated to optimize the control process, wherein an actor–critic architecture is utilized to minimize the Bellman residual, enabling optimal control performance. Theoretical analysis proves the fixed-time convergence and Bellman optimality of the system, with the upper bound of convergence time explicitly determined by controller parameters. Simulation experiments validate the effectiveness of the proposed method: all followers simultaneously achieve bipartite consensus within a fixed time, while reinforcement learning significantly and adaptively optimizes the control process.