hal-02091801
https://enac.hal.science/hal-02091801
doi:10.4018/978-1-5225-5091-4.ch003
[ENAC] Ecole Nationale de l'Aviation Civile
[INSMI] CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions
[TDS-MACS] Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes
[OPTIM] ENAC | Equipe de recherche Optimisation
Optimality Principles for Fuzzy Dual Uncertain Systems
Mora-Camino, Felix
Bouadi, Hakim
Faye, Roger Marcelin
Zhong, Lunlong
[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]
COUV
This chapter considers the extension of the calculus of variations to the optimization of a class of fuzzy systems where the uncertainty of variables and parameters is represented by symmetrical triangular membership functions. The concept of fuzzy dual numbers is introduced, and the consideration of the necessary differentiability conditions for functions of dual variables leads to the definition of fuzzy dual functions. It is shown that when this formalism is adopted to represent performance indexes for uncertain optimization problems, the calculus of variations can be used to establish necessary optimality conditions as an extension to this case of the Euler-Lagrange equation. Then the chapter discusses the propagation of uncertainty when the fuzzy dual formalism is adopted for the state representation of a time continuous system. This leads to the formulation of a fuzzy dual optimization problem for which necessary optimality conditions, corresponding to an extension of Pontryagine's optimality principle, are established.
2018
en
Optimization Techniques for Problem Solving in Uncertainty
IGI GLobal