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.23, no.5, pp.917-941, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 5
  • Publication Date: 2022
  • Journal Name: JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.917-941
  • Keywords: Bolza, conjugate, Euler-Lagrange, state constraints, transversality, polyhedral, DUALITY, DISCRETE
  • Istanbul Technical University Affiliated: Yes

Abstract

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.