Exponential Tracking Control With Guaranteed Performance for Strict-Feedback Systems Under Deferred Full-State Asymmetric Constraints

This work provides an exponential tracking control solution for a class of nonlinear systems characterized by unmatched, non-vanishing uncertainties and deferred full-state constraints. The presence of both non-vanishing and unmatched uncertainties complicates the task of achieving exponential tracking rather than regulation, particularly in scenarios involving deferred full-state asymmetric constraints alongside steady-state and transient performance requirements. To address these challenges, several key techniques are employed. Firstly, a time-varying feedback gain technique is utilized to ensure exponential tracking of the strict-feedback system. Secondly, we develop an asymmetric constraint mapping function that integrates the system state, tracking error, a finite-time adjustment function (AF), and an exponential AF to tackle performance issues without violating the deferred full-state asymmetric constraints, even when the initial conditions are unknown. Thirdly, an important lemma is derived to guarantee the boundedness of virtual controller derivatives, even as the exponential AF approaches infinity. Additionally, all signals in the closed-loop system are ultimately uniformly bounded. The effectiveness of the proposed scheme is validated through two examples. Note to Practitioners—In most existing studies on constrained systems, the results primarily focus on ensuring ultimately uniformly bounded behavior or asymptotic stability, with exponential tracking being rarely achieved. This paper aims to address this gap by proposing a robust adaptive control solution for uncertain strict-feedback systems under deferred full-state asymmetric constraints, achieving state-of-the-art exponential tracking performance. Furthermore, the steady-state and transient performance can be tailored by selecting an appropriate exponential adjustment function. Notably, the proposed approach ensures that system states remain within the asymmetric constraint boundaries after a finite time T, even with unknown initial conditions. This scenario is particularly relevant to physical systems transitioning from an unconstrained to a constrained state. The feasibility of the proposed method is demonstrated through a simulation example and a physical experiment on the Turtlebot 3-Burger robot. Future work will explore extending this approach to multi-agent systems for tasks such as formation control and consensus achievement.