Optimal control of Goursat–Darboux-type polyhedral differential inclusions

Authors

  • Elimhan N. Mahmudov Azerbaijan National Aviation Academy, Baku, Azerbaijan; Azerbaijan University of Architecture and Construction, Baku, Azerbaijan

DOI:

https://doi.org/10.3842/umzh.v78i3-4.9377

Keywords:

Approximate, discrete, Goursat-Darboux differential inclusions, Euler-Lagrange, polyhedral, necessary and sufficient

Abstract

UDC 517.96, 517.97

We study the problem of optimal control of the Goursat–Darboux-type differential inclusions (DFIs) given by polyhedral set-valued mappings and, for this purpose, pose an auxiliary problem with discrete Goursat–Darboux inclusion. By using the Farkas theorem, we compute locally adjoint mappings (LAMs) and establish necessary and sufficient optimality conditions for the polyhedral discrete Goursat–Darboux inclusions. Further, by  the discretization method, for the Goursat–Darboux-type polyhedral DFI, we formulate (by  using solely the specific features of its polyhedral property), first for a discrete-approximate problem and then, for a continuous problem, necessary and sufficient optimality conditions  in the form of Euler–Lagrange-type polyhedral inclusions.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 3-4, 2026.

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Published

28.03.2026

Issue

Vol. 78 No. 3-4 (2026)

Section

Research articles