Abstract—This article after introducing fuzzy dual numbers, functions and functionals establishes necessary conditions for the optimization of fuzzy dual functionals before considering fuzzy dual optimal control problems. In a first step an extension of Euler’s necessary condition for the extremum of a fuzzy dual functional is established and then necessary conditions for fuzzy dual optimal control are developed.

Index Terms—Euler’s condition, fuzzy dual numbers, necessary conditions, optimal control, uncertainty.

Felix Mora-Camino is with ENAC, Toulouse University, 7 avenue Edouard Belin, 31055 Toulouse, France (email:felix.mora@enac.fr).
Fabio Krykhtine is with ENAC, Toulouse University, 7 avenue Edouard Belin, 31055 Toulouse, France. He is also with Labfuzzy, COPPE, Federal University of Rio de Janeiro, Centro de Tecnologia, Ilha do Fundão, Brazil.
Walid El Moudani is with Doctorate School of Sciences and Technologies, Libanese University, Tripoli Al-Koubba, Lebanon.
Carlos Alberto Nunes Cosenza is with Labfuzzy, COPPE, Federal University of Rio de Janeiro, Centro de Tecnologia, Ilha do Fundão, Brazil.

Cite: Felix Mora-Camino, Fabio Krykhtine, Walid El Moudani, Carlos Alberto Nunes Cosenza, "Necessary Conditions for Fuzzy Dual Optimal Control Problems," International Journal of Applied Physics and Mathematics vol. 7, no. 3, pp. 182-190, 2017.