INFIMAL CONVOLUTION AND DUALITY IN CONVEX OPTIMAL CONTROL PROBLEMS WITH SECOND ORDER EVOLUTION DIFFERENTIAL INCLUSIONS


Mahmudov E.

EVOLUTION EQUATIONS AND CONTROL THEORY, cilt.10, sa.1, ss.37-59, 2021 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Konu: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3934/eect.2020051
  • Dergi Adı: EVOLUTION EQUATIONS AND CONTROL THEORY
  • Sayfa Sayıları: ss.37-59

Özet

The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying infimal convolution concept of convex functions, step by step we construct the dual problems for discrete, discrete-approximate and differential inclusions and prove duality results. It seems that the Euler-Lagrange type inclusions are "duality relations" for both primary and dual problems and that the dual problem for discrete-approximate problem make a bridge between them. At the end of the paper duality in problems with second order linear discrete and continuous models and model of control problem with polyhedral DFIs are considered.