Adaptive Dynamic Surface Control Design for a Class of Uncertain Nonlinear Systems With Asymmetric Full-State Constraints of Arbitrary Time Period

Abstract

This article investigates the tracking control problem for a class of uncertain nonlinear systems with time-varying asymmetric state constraints of arbitrary time period. State constraints of arbitrary time period refer to the system states that are constrained during arbitrary finite time and are free for the other time (i.e., unconstrained), it is more common. This article addresses this issue for the first time. A novel shifting function is defined which moves any states or tracking errors out of the constraint area to the desired positions. Then, a barrier Lyapunov function is designed for the tracking error after shifting transformation, which ensures the satisfaction of state constraints. Dynamic surface control is used to avoid the high-order derivation of functions which solves the complexity problem caused by item explosion in backstepping design. Lastly, a simulation illustration is given to verify the effectiveness and outstanding features of the proposed method. It demonstrates that state constraints of arbitrary time period are satisfied, all signals in the closed-loop system are ultimately bounded, and the tracking error converges to an adjustable neighborhood of origin.