The article entitled “ Necessary optimality conditions for quasi-singular controls for systems with Caputo fractional derivatives” based on the studies conducted by Department of Mathematics member Prof. Dr. Elmkhan Mahmudov was published in Archives of Control Sciences, 33(LXIX), 2023, 463-496.

The aim of paper is considered an optimal control problem in which a dynamical system is controlled by a nonlinear Caputo fractional state equation. First, the linearized maximum principle is obtained. Further, the concept of a quasi-singular control is introduced and, on this basis, an analogue of the Legendre-Clebsch conditions is obtained. When the analogue of Legendre-Clebsch condition degenerates, a necessary high-order optimality condition is derived. An illustrative example is considered.

Other study conducted by Prof. Dr. Elmkhan Mahmudov:

The article entitled “ Optimisation of parabolic type polyhedral discrete, discrete-approximate and differential inclusions” based on the studies conducted by Department of Mathematics member Prof. Dr. Elmkhan Mahmudov was published in International Journal of Control, 2023, 1-11.

The present paper is devoted to the optimisation of parabolic type differential inclusions (DFIs) given by polyhedral set-valued mappings. For this, an auxiliary problem with a polyhedral parabolic discrete inclusion is defined. With the help of locally adjoint mappings and comparison of matrix-coefficients of discrete and discrete-approximate problems, necessary and sufficient optimality conditions for polyhedral-parabolic discrete-approximate inclusions are skilfully constructed. Thus, using the discretisation method and the features of the polyhedral nature of the problem, sufficient optimality conditions for a polyhedral parabolic DFI are proved. At the end of the paper, the numerical results are presented.

https://doi.org/10.1080/00207179.2023.2251614