Adaptive Fuzzy Super-twisting Backstepping Control Design for MIMO Nonlinear Strict Feedback Systems

Abstract

This paper presents a new backstepping control (BSC) combined with a super-twisting algorithm (STA) for multiple-input, multiple-output (MIMO) nonlinear strict-feedback systems. The STA state variables form a type of second order sliding mode control and virtual tracking errors are defined to help design virtual controls for the recursive backstepping procedures. This enables finite-time tracking performance and enforcement robustness on the conventional BSC system, in which controllers are designed for infinite-time and contain complex repeated differentials of virtual controls. To extend controllers to MIMO unknown nonlinear systems, a fuzzy logic system is proposed to approximate unknown nonlinear functions of the strict-feedback system. Repeated differential terms, which appear in each recursive BSC step, are included in these approximation functions to simplify BSC controller. Thus, the problem of controller order explosion in conventional BSC is significantly reduced. The proposed STA based fuzzy BSC scheme provides improved tracking convergence time, robustness to uncertainty, and significantly simpler controller structure than conventional infinite-time based BSC system. The proposed control scheme was evaluated using simulation incorporating a MIMO nonlinear quadrotor unmanned aerial vehicle.