OPTIMIZATION OF THE BOLZA PROBLEM WITH HIGHER-ORDER DIFFERENTIAL INCLUSIONS AND INITIAL POINT AND STATE CONSTRAINTS

Elimhan N. Mahmudov*

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Özet

This paper is devoted to the duality of the Bolza problem with higher order differential inclusions and constraints on the initial point and state, which can make a significant contribution to the theory of optimal control. To this end in the form of Euler-Lagrange type inclusions and transversality conditions, sufficient optimality conditions are derived. It is remarkable that in a particular case the Euler-Lagrange inclusion coincides with the classical Euler-Poisson equation of the Calculus of Variations. The main idea of obtaining optimal conditions is locally conjugate mappings. It turns out that inclusions of the Euler-Lagrange type for both direct and dual problems are "duality relations". To implement this approach, sufficient optimality conditions and duality theorems are proved in the Mayer problem with a second-order linear optimal control problem and third-order polyhedral differential inclusions, reflecting the special features of the variational geometry of polyhedral sets.

Orijinal dilİngilizce
Sayfa (başlangıç-bitiş)615-639
Sayfa sayısı25
DergiJournal of Nonlinear and Convex Analysis
Hacim24
Basın numarası3
Yayın durumuYayınlandı - 2023

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© 2023 Yokohama Publications. All rights reserved.

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