Tuning functions based adaptive backstepping control for uncertain strict-feedback nonlinear systems using barrier Lyapunov functions with full state constraints

Abstract

This paper investigates the tuning functions based adaptive backstepping control for a class of uncertain strict-feedback nonlinear systems using barrier Lyapunov functions with full state constraints. The proposed adaptive control scheme is constructed by combining the barrier Lyapunov functions (BLFs) with the tuning functions based adaptive backstepping control technique. Compared with the relevant results, the proposed adaptive control scheme is constructed to guarantee that the overparametrization problem inherent to the conventional adaptive backstepping control method is avoided and the full state constraints are not violated by introducing BLFs. Moreover, it is proved that all the signals in the closed-loop system are uniformly ultimately bounded (UUB) and the tracking errors converge to a small neighborhood around zero by appropriately choosing design parameters. Simulation results of an electromechanical system are provided to verify the feasibility of the proposed adaptive control method. The simulation results clearly prove the effectiveness of our approach compared with the tuning functions based adaptive backstepping control (TFABC) and the traditional backstepping control design (BC) schemes that system state without constraints.