Low-Complexity Prescribed Performance Control of Nonlinear Systems With Full-State Constraints

This brief studies a prescribed performance control (PPC) problem of nonlinear systems subject to deferred full-state constraints. By introducing a $ln$ -type performance function, a constraint of tracking error is developed to simultaneously prescribe the performance and state constraints. To solve this error constraint, both mapping and barrier error transformations are utilized to convert a constraint-handling issue into a stabilization one of transformed system. Then a backstepping controller is devised to stabilize the transformed system, resulting in a PPC algorithm with low complexity and no assumption of initial error condition. Based on the Lyapunov inverse proof, it is verified that the proposed controller can ensure the boundedness of closed-loop system and the satisfaction of constraints. The effectiveness of the result is illustrated via numerical simulations.