Prescribed-Time Optimal Formation Control Using Fuzzy Reinforcement Learning for Second-Order Multiagent Systems

This article investigates the prescribed-time (PT) optimal formation control issue for second-order multiagent system. A novel formation scheme that integrates reinforcement learning with a fuzzy logic system is presented, incorporating actor, critic, and identifier components to estimate the optimal control, the optimal cost function, and the uncertain system dynamics (including unknown nonlinearities, external disturbances, and leader input), respectively. To achieve PT formation, we introduce a prescribed performance function and a filtered variable, which are then used to develop an error transformation function for the controller design. Unlike existing PT control approaches, this method eliminates initial value limitations, ensuring that both the prescribed performance function's initial condition and the error transformation parameter are independent of the initial tracking error and system dynamics. We further demonstrate that the developed scheme ensures the prescribed performance of the filtered error, guaranteeing that all formation errors converge to a bounded region within the PT while achieving satisfactory transient performance. Finally, we illustrate the effectiveness of the scheme through two simulated examples.