Prescribed-Time Tracking Over Total-Time-Domain for Nonlinear Systems Subject to Mismatched Disturbance: An ESO-Based Control Strategy

This article aims to investigate the performance-guaranteed tracking problem for a class of uncertain nonlinear systems. The main goal is to attain control performance within prescribed-time (PT) limits despite the existence of mismatched disturbances. First, the mismatched disturbances are transformed into the equivalent forms. Second, for the unknown disturbance estimation, a PT extended state observer (PTESO) is developed to switch between the prescribed settling time ${\mathcal {T}}_{p}$ , the order is diminished to alleviate the occurrence of the peaking phenomenon. Furthermore, an ESO-based PT control strategy is constructed with time-varying gains. This allows real-time compensation of disturbances, and the prescribed performance is attained by virtue of a Lyapunov function employed combines both barrier and quadratic forms. Ultimately, the benefits and efficacy are illustrated via a numerical demonstration involving a wheeled mobile robot. The key features of this article include the observer capability to estimate unknown mismatching disturbances and the full effectiveness of the proposed controller for $t \in [t_{0}, \infty $ ), ensuring the convergence of tracking error to zero within any PT. Consequently, in addition to achieving the output tracking objective, the system can also exhibit favorable transient performance.