Time-Specified Adaptive Robust Control Framework for Managing Nonlinear System Uncertainties

This paper addresses the issue of prescribed-time control for a specific class of uncertain nonlinear systems. Initially, a stability theorem based on prescribed time is introduced, utilizing adaptive techniques for the first time. Building on this theorem, a novel state feedback control approach is presented, employing the backstepping method for high-order nonlinear systems with unknown parameters to ensure convergence within the prescribed time. Furthermore, the proposed prescribed-time controller is derived in the form of continuous time-varying feedback, enabling all system states to converge to zero within the specified time. Notably, the prescribed time is independent of the system’s initial conditions, allowing it to be set arbitrarily within the physical constraints. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed algorithm.