Continuous Representation for a Class of Optimal Hybrid Control Problems

Author:	Gapaillard Muriel, Laboratoire d'Ingénierie des Systèmes Automatisés, France
Topic:	1.3 Discrete Event and Hybrid Systems
Session:	Hybrid Dynamic Systems
Keywords:	hybrid systems, continuous systems, convergence, optimal control, switching times, minimization, variational analysis, gradients.

Abstract

A class of optimal hybrid control problems involving model and state jump systems is considered. The calculation of optimal switching times amounts to minimizing a cost function. A continuous representation of these problems -- based on convergence results -- is introduced. This representation simplifies the study of the initial problem as it is shown, while applying variational formalism to determine the expression of the gradients of the cost function with respect to the switching times. An application example is presented and the implementation of a descent method confirms the validity of the continuous representation.