Explicit reference governor for continuous time nonlinear systems subject to convex constraints

Abstract

This paper introduces a novel control law that dynamically modifies the reference of a pre-compensated nonlinear system so as to ensure the satisfaction of convex constraints. This is done by translating the state space constraints into a constraint on the Lyapunov function which is then limited by modulating the velocity of the applied reference. The main advantage of this approach is that it systematically provides a closed-form expression of the control law. The theory is introduced for general nonlinear systems subject to convex constraints and is then specialized to the large and highly relevant class of nonlinear systems with a Lyapunov function that is lower-bounded by a quadratic form. Numerical and experimental validations are also provided.