Optimization of Lagrange Problem with Higher Order Differential Inclusions and Endpoint Constraints

Mahmudov E. N.

FILOMAT, vol.32, no.7, pp.2367-2382, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 7
  • Publication Date: 2018
  • Doi Number: 10.2298/fil1807367m
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2367-2382
  • Istanbul Technical University Affiliated: Yes


In the paper minimization of a Lagrange type cost functional over the feasible set of solutions of higher order differential inclusions with endpoint constraints is studied. Our aim is to derive sufficient conditions of optimality for m th-order convex and non-convex differential inclusions. The sufficient conditions of optimality containing the Euler-Lagrange and Hamiltonian type inclusions as a result of endpoint constraints are accompanied by so-called "endpoint" conditions. Here the basic apparatus of locally adjoint mappings is suggested. An application from the calculus of variations is presented and the corresponding Euler-Poisson equation is derived. Moreover, some higher order linear optimal control problems with quadratic cost functional are considered and the corresponding Weierstrass-Pontryagin maximum principle is constructed. Also at the end of the paper some characteristic features of the obtained result are illustrated by example with second order linear differential inclusions.