Integral backstepping Lyapunov redesign control of uncertain nonlinear systems

Abstract

This paper intends to design an integral backstepping Lyapunov redesign controller (IBLRC) for various uncertain strict-feedback-form nonlinear systems. The pros and cons of backstepping Lyapunov redesign resulted in the design idea. An integral term is incorporated in conventional backstepping with Lyapunov redesign to indirectly decrease chattering and steady-state error of a reference signal tracking when unknown static parameters and matched and unmatched dynamic uncertainties exist. The closed-loop system is mathematically confirmed as stable in a Lyapunov frame, and we ultimately reach uniformly semi-global boundedness of all signals. Simulation results of the proposed IBLRC are juxtaposed with those of the classic backstepping with the Lyapunov redesign. The proposed IBLRC realizes excellent tracking and enhanced robust performance than the BLRC for time-varying and step tracking references.