Fuzzy adaptive stabilization control for nonlinear systems with FSCs

This paper proposes a new full-state constraints (FSCs) control scheme for stabilizing nonlinear systems with unknown functions. This scheme solves the “explosion of terms (EOT)” problem of backstepping using a lemma and introduces fuzzy control to approximate the unknown functions. This ensures that all signals are semi-globally uniformly ultimately bounded (SGUUB), and the system state converges to a neighborhood of the origin. In order to get a smaller neighborhood and higher accuracy, a new time-varying constraint function is proposed to solve the FSCs. This method can directly design the constraint functions according to actual needs, and it is easy to implement, thus avoiding the shortcomings of the barrier Lyapunov functions (BLFs) and the mapping constraint functions. And it affects the steady-state performance of the states. Therefore, the constraint functions can be constructed to make the states approach a smaller neighborhood, thus making the steady-state performance error of the states is smaller. Thirdly, the algorithm is applied to Chua's circuit system, which verifies its validity.