Prescribed-Time Control With Bounded Feedback Gain: A Nonscaling and Structural Adaptation-Based Approach

Achieving full state regulation within a prescribed-time for uncertain nonlinear systems under any initial condition is rather challenging although highly desirable, whereas most existing prescribed-time control results are literally contingent upon infinite feedback gain at the equilibrium. This article presents a new prescribed-time control design method that is able to ensure prescribed-time stability with bounded feedback gain and bounded control action during the entire process of system operation, elegantly circumventing the infinite feedback gain problem. As a nonscaling-based method with structural adaptation is utilized, the proposed control scheme is able to regulate all the states to zero well before the prescribed-time, yet in the presence of time-varying and mismatched structural uncertainties, substantially reducing the numerical computational complexity induced by scaling-based methods. The theoretical results are supported by two numerical simulations.