CONTINUOUS REPRESENTATION FOR A CLASS OF OPTIMAL HYBRID CONTROL PROBLEMS

摘要

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 simplifes 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 confrms the validity of the continuous representation.