Asymptotic tracking control for deferred full-state constrained nonlinear systems based on shifting function and exponential Lyapunov function

Abstract

This paper proposes an adaptive control method based on shifting functions and state transformations for strict-feedback nonlinear systems with deferred state constraints. To address the system’s complex characteristics, including parametric/nonparametric uncertainties and external disturbances, a shifting function is devised to cope with unknown initial conditions, while a nonlinear state transformation converts time-varying state constraints into a boundedness analysis of transformed variables. To achieve asymptotic tracking performance, a novel approach is proposed that incorporates an exponential function into the construction of error variables and develops a recursive control strategy within a backward design framework. Theoretical analysis confirms that the proposed adaptive controller guarantees all closed-loop signals are uniformly ultimately bounded, strictly satisfies the state constraints immediately after the deferred period, and enables the system output to achieve asymptotic tracking of reference signals. By constructing a composite Lyapunov function, this paper rigorously proves the effectiveness of the proposed control law in simultaneously handling time-varying deferred constraints, suppressing system uncertainties, and achieving the goal of asymptotic tracking.