Document Type



Some optimality results for hybrid control problems are presented. The hybrid model under study consists of two subdynamics, one of a standard type governed by an ordinary differential equation, and the other of a special type having a discrete evolution. We focus on the case when the interaction between the subdynamics takes place only when the state of the system reaches a given fixed region of the state space. The controller is able to apply two controls, each applied to one of the two subdynamics, whereas the state follows a composite evolution, of continuous type and discrete type. By the relaxation technique, we prove the existence of a pair of controls that minimizes an incurred (discounted) cost. We conclude the analysis by introducing an auxiliary infinite-dimensional linear program to show the equivalence between the initial control problem and its associated relaxed counterpart.


Applied Mathematics | Control Theory | Ordinary Differential Equations and Applied Dynamics


This is a post-peer-review, pre-copyedit version of an article published in Applicationes Mathematicae. The final version is available at: