Optimal control of first-order partial differential inclusions in bounded region

Mahmudov E.

INTERNATIONAL JOURNAL OF CONTROL, vol.95, no.7, pp.1933-1943, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 95 Issue: 7
  • Publication Date: 2022
  • Doi Number: 10.1080/00207179.2021.1886328
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, zbMATH
  • Page Numbers: pp.1933-1943
  • Keywords: 35Fxx, 49K20, 49M05, 49M25, Approximate, discrete and partial differential inclusions, Euler-Lagrange, first order, necessary and sufficient, polyhedral
  • Istanbul Technical University Affiliated: Yes


The paper is devoted to the Lagrange problem in the bounded region for first-order partial differential inclusions (PDIs). For this, using discretisation method and locally adjoint mappings (LAMs), in the form of Euler-Lagrange type inclusions and conjugate boundary conditions, sufficient optimality conditions are obtained. The transition to a continuous problem with PDIs is possible using a specially proved equivalence theorem. To demonstrate this approach, some semilinear problems and polyhedral optimisation with first-order partial differential inclusions are considered. Furthermore, the numerical results also are provided.