Semiglobal stabilization of nonlinear uncertain systems via a Lyapunov-based switching logic

Abstract

An adaptive supervisory switching control scheme for nonlinear uncertain systems is developed. Such a scheme comprises: a family of nonlinear candidate controllers, designed using a convex control design methodology; and a Lyapunov-based switching criterion that orchestrates which of the candidate controllers should be put in feedback with the uncertain plant. The family of candidate controllers is designed in such a way that, for every portion of the uncertainty set there is one Lyapunov function whose derivative is decreasing with a prescribed rate. Such Lyapunov functions are used by the switching logic to assess which is the most suitable controller to be put in feedback. The resulting scheme guarantees semi-global stability with desired transient performance, in terms of decaying rate of the derivative of the Lyapunov function.