Prescribed-time formation tracking in multi-agent systems via reinforcement learning-based hybrid impulsive control with time delays

This paper addresses the prescribed-time formation stabilization in nonlinear multi-agent systems using a novel reinforcement learning-based hybrid impulsive control framework that incorporates delayed control impulses. The approach leverages Lyapunov functionals, impulsive comparison theory, average impulsive interval methods, and graph theory to derive sufficient conditions for achieving prescribed-time formation stabilization. These conditions are formulated in terms of continuous and impulsive feedback gains, time delay durations, and average impulsive interval lengths. Importantly, the inclusion of stabilizing control impulses counteracts the destabilizing effects of continuous dynamics. Additionally, deep reinforcement learning techniques are employed to optimize the impulsive control sequence, aiming to maximize rewards derived from the control objectives and system states. Numerical simulation examples are presented to demonstrate the effectiveness and validity of the proposed analytical results, providing comparative assessments of overall control performance.