A class of multiobjective control problems

Authors

  • V. A. de Oliveira,

    Corresponding author
    1. Faculdade de Ciências Integradas do Pontal, Universidade Federal de Uberlândia, Av. José João Dib, 2545, CEP 38302-000 Ituiutaba, MG, Brazil
    • Faculdade de Ciências Integradas do Pontal, Universidade Federal de Uberlândia, Av. José João Dib, 2545, CEP 38302-000 Ituiutaba, MG, Brazil
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  • G. N. Silva,

    1. Departamento de Ciências de Computação e Estatística, Universidade Estadual Paulista-UNESP, Rua Cristovão Colombo, 2265, CEP 15054-000 São José do Rio Preto, SP, Brazil
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  • M. A. Rojas-Medar

    1. Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Casilla 447, Chillán, Chile
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Abstract

We introduce the class of MP-pseudoinvex multiobjective optimal control problems. We show that the concept of MP-pseudoinvexity is a sufficient condition of optimality and, further, that problems such that every control process satisfying Pontryagin's maximum principle is an optimal process are necessarily MP-pseudoinvex problems. Moreover, a sub-class of the MP-pseudoinvex problems, which we call MP-invex multiobjective optimal control problems, is defined. We prove that the set of optimal solutions of MP-invex multiobjective problems coincides with the set of optimal solutions of a related scalar problem. Copyright © 2008 John Wiley & Sons, Ltd.

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