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March 2021, 10(1): 37-59. doi: 10.3934/eect.2020051
Infimal convolution and duality in convex optimal control problems with second order evolution differential inclusions
Elimhan N. Mahmudov ,
Department of Mathematics, Istanbul Technical University, Istanbul, Turkey, Azerbaijan National Academy of Sciences Institute of Control Systems, Baku, Azerbaijan
* Corresponding author: elimhan22@yahoo.com
Received May 2019 Revised January 2020 Published March 2021 Early access May 2020
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.
Keywords: Infimal convolution, duality, conjugate, Euler-Lagrange, polyhedral, discrete-approximate.
Mathematics Subject Classification: 34A60; 49J15; 49K25; 90C46.
Citation: Elimhan N. Mahmudov. Infimal convolution and duality in convex optimal control problems with second order evolution differential inclusions. Evolution Equations & Control Theory, 2021, 10 (1) : 37-59. doi: 10.3934/eect.2020051
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Elimhan N. Mahmudov