A quantitative trade-off between state and tracking error constraints for uncertain nonlinear systems

Addressing the tracking control problem for uncertain nonlinear systems with interdependent state and tracking error constraints presents significant challenges. In this work, we establish a bijective nonlinear mapping that transforms the constrained system into an equivalent unconstrained one, thereby converting the constrained control problem into a stabilization task. Building on such transformation, we propose a computationally efficient control scheme free of any nonlinear approximator while requiring only minimal prior knowledge of system nonlinearities. The proposed approach integrates all constraint functions into the control design via an innovative Lyapunov-based stability analysis framework. It is authenticated that all the closed-loop signals are uniformly ultimately bounded (UUB) and the constraints are never violated. Furthermore, the feasibility condition to detect the bounds of virtual signals is fully eliminated.