Optimal control of 2-D wave differential inclusions with state constraints

Mahmudov E., Mardanov M. J.

Filomat, vol.39, no.17, pp.5941-5953, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 17
  • Publication Date: 2025
  • Doi Number: 10.2298/fil2517941m
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5941-5953
  • Keywords: dual cone, Euler-Lagrange, Hyperbolic/wave differential inclusions, state constraints, sufficient conditions of optimality
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

The paper discusses the optimization of 2-D wave differential inclusions (DFIs) with the Laplacian in a bounded cuboid and the first mixed initial-boundary-value problem. Particular attention is paid to problems with state constraints, for which optimality conditions are formulated in terms of the Euler-Lagrange adjoint inclusions. Next, using the well-known Green’s formula, the obtained results are generalized to the multidimensional case. In problems with convex inequalities, dual cones are calculated, which are an integral part of Euler-Lagrange inclusions. The examples show that when constructing an adjoint inclusion, it is very important to consider the phase boundary”.