Composite-variable-based adaptive tracking control for state-constrained nonlinear systems and its application to crane

This paper focuses on investigating the adaptive tracking problem for a kind of nonsmooth nonlinear systems subject to full-state constraints. Through the utilization of carefully designed auxiliary signals, the challenge posed by full-state constraints is reduced to a constraint problem for two composite variables. This transformation enables the direct proposal of the controller without involving recursive procedures. Consequently, the conventional backstepping method is unnecessary, subsequently effectively mitigating the issues of complexity explosion and feasibility condition. These problems are inherent within the traditional backstepping framework, typically arising from the necessity for repeated differentiation and explicit upper bounds of virtual controllers, respectively. The stability of the closed-loop system and the asymptotic convergence of the tracking error are all proven by strict analysis. Finally, the proposed control method is applied to a crane system, and the control effectiveness is verified through experiment results.