Adaptive Prescribed Finite Time Control for Strict-Feedback Systems

In this article, 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 the 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 semiglobal. 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 preassigned 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.