Prof. Dr. Elmkhan Mahmudov gave a talk on “Optimal Control of Elliptic Type Polyhedral Inclusions” as an invited speaker at the 5th International Conference on Problems of Cybernetics and Informatics (PCI 2023), in Baku, Azerbaijan. This conference was supported by IEEE.

This talk is devoted to the optimization of elliptic type differential inclusions (DFI) given by polyhedral set-valued mappings. For this, an auxiliary problem with a polyhedral elliptic discrete inclusion is defined. Using the Farkas theorem, locally adjoint mappings are calculated and necessary and sufficient conditions of optimality for polyhedral elliptic discrete inclusions are proved. After that, with the help of the polyhedral elliptic discretization method for the discrete-approximate problem, necessary and sufficient optimality conditions are formulated in the Euler-Lagrange form of the adjoint polyhedral inclusion. In addition, linear discrete-approximate and continuous optimal control problems of elliptic type are also considered. Thus, using only the specifics of the polyhedrality nature of the problem, sufficient optimality conditions for a polyhedral elliptic DFI are proved. An example is given to demonstrate the proposed approach.

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