Document Type

Article

Abstract

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.

Disciplines

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

Comments

This is a post-peer-review, pre-copyedit version of an article published in Applicationes Mathematicae. The final version is available at: https://doi.org/10.4064/am2387-6-2019

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