Adaptive Prescribed Finite Time Control for Strict-Feedback Systems

Abstract

In this paper we address the prescribed finite time control problem for a class of strict-feedback systems with unknown parameters. A backstepping based adaptive prescribed-time control algorithm is proposed for second-order strict-feedback systems, where the global stability of system is ensured, and a dynamic surface control (DSC) based adaptive prescribed-time algorithm is designed for the system in high-order case. For the DSC based method, a novel first-order filter is constructed to guarantee the boundedness of “virtual error”, which avoids the so-called “Differential Explosion” problem, however, the control result is only semi-global. Both the developed algorithms are capable of ensuring the regulation in prescribed time with a unique converging feature in that the convergence time is independent of any initial conditions and other design parameters that can be pre-assigned freely by the designer according to the control requirements. The key to achieve the objective in prescribed finite time is the introduction of a descending power time-varying feedback into the controller design. Both the theory analysis and simulation confirm the effectiveness of the proposed methods.