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

Mahmudov E.

Journal of Nonlinear and Convex Analysis, vol.24, no.3, pp.615-639, 2023 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 24 Say: 3
  • Nəşr tarixi: 2023
  • jurnalın adı: Journal of Nonlinear and Convex Analysis
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Səhifə sayı: pp.615-639
  • Açar sözlər: Bolza, conjugate, Euler-Lagrange, polyhedral, state constraints, transversality
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

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.