Control of state-constrained nonlinear systems using Integral Barrier Lyapunov Functionals

This paper presents a control design for nonlinear systems with state constraints, based on the use of our newly introduced Integral Barrier Lyapunov Functionals (iBLF). The integral functional allow the mixing of the original state constraints with the errors in a form amenable to stable backstepping control design. This reduces some of the conservatism associated with the use of purely error-based functions with transformed error constraints. We show that, under the proposed iBLF-based control, output tracking error is bounded by an exponentially decreasing function of time, all states always remain in the constrained state space, and that the stabilizing functions and control input are bounded, subject to significantly relaxed feasibility conditions. A numerical example illustrates the performance of the proposed control.