Adaptive Prescribed-Time Exact Tracking Control for Uncertain Strict-Feedback Systems with Global Prescribed-Performance

For uncertain strict-feedback systems under the prescribed performance control (PPC) problem, an innovative adaptive prescribed-time tracking control method is proposed. This method combines a novel error transformation function with the prescribed-time stability theory, thereby achieving exact tracking of desired trajectories within a prescribed time while ensuring that the tracking error stays within predefined boundaries globally. By integrating a newly-designed Lyapunov-like energy function with dynamic surface control, it resolves the error surface issues that result in the semi-global boundedness of tracking error in traditional approaches. Furthermore, through a generalized Filippov solution definition, this approach overcomes the issue of non-existence of the system solution, which arises during the prescribed-time stability analysis due to the discontinuous control input. Simulation results validate the effectiveness of the proposed method.