Immersion and invariance based adaptive command filtered backstepping control design for a class of SISO uncertain nonlinear systems in strict-feedback form

Abstract

In this article, an immersion and invariance based adaptive command filtered backstepping control method (I&I ACFBC) is proposed for a class of single-input and single-output (SISO) uncertain nonlinear systems in strict-feedback form. The problem of the explosion of complexity inherent to the traditional adaptive backstepping control design is solved by applying the proposed adaptive control technique, and the compensating signals are constructed to reduce the effect of the known filtering errors produced by the command filters. The adaptive laws are achieved by an immersion and invariance method. The Lyapunov stability theory is utilized to ensure the boundedness of all the signals in the closed-loop system. The feasibility and validity of the proposed adaptive control scheme are demonstrated by the simulation and experimental results on a DC-DC buck converter system.