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Relaxation and linear programs in a hybrid control model

Tom 46 / 2019

Héctor Jasso-Fuentes, Jose-Luis Menaldi Applicationes Mathematicae 46 (2019), 191-227 MSC: 49J15, 49N25, 93C15. DOI: 10.4064/am2387-6-2019 Opublikowany online: 19 September 2019

Streszczenie

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.

Autorzy

  • Héctor Jasso-FuentesDepartamento de Matemáticas
    CINVESTAV-IPN
    A. Postal 14-740
    Ciudad de México, 07000, México
    e-mail
  • Jose-Luis MenaldiDepartment of Mathematics
    Wayne State University
    Detroit, MI 48202, U.S.A.
    e-mail

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