Control of nonlinear systems with full state constraint using a Barrier Lyapunov Function

Abstract

This paper presents a control for state-constrained nonlinear systems in strict feedback form to achieve output tracking. To prevent states from violating the constraints, we employ a Barrier Lyapunov Function, which grows to infinity whenever its arguments approaches some limits. By ensuring boundedness of the Barrier Lyapunov Function in the closed loop, we guarantee that the limits are not transgressed.We show that asymptotic output tracking is achieved without violation of state constraints, and that all closed loop signals are bounded, provided that some feasibility conditions on the initial states and control parameters are satisfied. Sufficient conditions to ensure feasibility are provided, and they can be checked offline by solving a static constrained optimization problem. The performance of the proposed control is illustrated through a simulation example.