Adaptive fuzzy tracking control for non‐strict‐feedback non‐linear systems with non‐constant delays and full state constraints

Abstract

This paper aims at the tracking control problem of the non-strict-feedback non-linear systems with non-constant unknown delays and full state constraints. A constrained exponential Lyapunov-Krasovskii function-based fuzzy adaptive dynamic surface control (CELK-FADSC) method is proposed. In order to achieve the goal of full state constraints, the tan-type Barrier Lyapunov function (BLF) is used. Furthermore, to reduce the influence of the non-constant unknown delays on the system, an exponential Lyapunov-Krasovskii function is constructed. At the same time, sliding mode differentiator is adopted to the dynamic surface control (DSC) method, by which the 'complexity explosion' problem in backstepping is solved. In addition, the proposed adaptive tracking controller can ensure that the states in the closed-loop system do not violate their constraint, and the semi-global uniformly ultimately bounded (SGUUB) can be achieved. Finally, simulation outcomes can prove the validity of the proposed method.