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Asymptotic tracking control for uncertain strict‐feedback nonlinear systems with delayed full‐state constraints

This article investigates the asymptotic tracking control problem for a class of strict‐feedback nonlinear systems with delayed full‐state constraints and nonparametric uncertainties. It is worth mentioning that delayed constraints, which represent a type of constraints that may be violated initially but required to be satisfied sometime after system operation, are frequently encountered in practice and yet not well addressed in existing works. In addition, it is extremely difficult to guarantee exact tracking performance for nonlinear systems when nonparametric uncertainties are considered in the control design. In this article, we propose a new state‐shifting transformation (SST) and a novel asymptotic Lyapunov function (ALF) to deal with delayed constraints and achieve asymptotic tracking, respectively. The transformed states grow to infinity as the original ones approach their limits, and the tracking errors converge to zero as time goes to infinity if the related ALF is always bounded. Hence, the delayed full‐state constraints and asymptotic tracking can be guaranteed if the boundness of the transformed states and the related ALF are both ensured. For this purpose, a novel fuzzy adaptive backstepping control scheme based on the proposed SST and ALF is developed. And the effectiveness of the proposed control scheme is theoretically authenticated and numerically validated.