Graceful Transitions between Periodic Orbits of Parametrized Nonlinear Systems

Abstract

In this paper, we present two approaches to obtain graceful transitions between periodic orbits for nonlinear systems with parametrized periodic orbits. In the first approach we consider first a stable family of periodic orbits and show that by slowly varying the parameters, the state trajectory does not deviate far from the family of orbits. We extend this to unstable families of orbits by designing stabilizing controllers. In our second approach, we solve a sequence of tracking problems to obtain the desired graceful transition. Both approaches are illustrated on examples.