Adaptive Tracking Controller for FAS With State Constraints and its Application to Underactuated Overhead Cranes: Design and Experiment

Abstract

Guaranteeing state constraints is critical for maintaining system safety and reliability. Current methods primarily employ barrier Lyapunov functions (BLF) or nonlinear mappings (NM) to enforce constraints. The former relies on feasibility conditions for virtual controllers, while the latter involves complex state-dependent transformations. This article introduces a new solution for a class of fully actuated systems (FASs) subject to state constraints, which eliminates the need for strict conditions and state-dependent transformations. First, the issue of full-state constraints in FASs is reduced to a constraint problem for a composite variable using carefully designed auxiliary signals. Then, an adaptive anti-disturbance controller is proposed by adopting the direct method to control and constrain the composite variable. This direct approach simplifies the design process and enhances the computational efficiency. Rigorous mathematical proof demonstrates that the proposed method not only ensures the state constraints but also achieves the asymptotic convergence of tracking errors. Finally, the proposed control method is applied to the overhead crane system, with its feasibility and efficacy being verified by simulation and experiment.