Azerbaijan National Academy of Science

1.A new universal method has been proposed for the study of singular controls for optimal control problems with aggregated and distributed parameters and obtaining the necessary high-order optimality conditions;

2.The necessary first-order optimality conditions have been obtained for optimal control problems with aggregated and distributed parameters of a variable structure and singular controls have been investigated;

3.The necessary optimality conditions for non-smooth optimal control problems have been obtained;

4.Krotov's sufficient optimality conditions have been found for discrete two-parameter optimal control problems and necessary high-order optimality conditions have been obtained;

5.The necessary optimality conditions have been derived for nonlocal boundary value problems of optimal control;

6.The necessary optimality conditions for optimal control problems described by Volterra-type differential integral equations have been proven;

7.The problem of optimal control for the system of Volterra type difference equations has been posed and the necessary optimality conditions have been derived;

8.Singular controls in Rosser-type optimal control problems have been investigated;

9.Hybrid Rosser-type optimal control problems have been investigated;

10.The necessary optimality conditions have been proven in continuous-discrete optimal control problems;

11.The representation of the solution of the system of linear heterogeneous stochastic Ito equations with delay using the Cauchy matrix has been found;

12.First- and second-order necessary optimality conditions have been found for the stochastic optimal control problems described by systems of Ito equations;

13.Using the Riemann matrix, the representation of the solution of a nonlinear Goursat-Darboux system of second-order stochastic hyperbolic equations has been found;

14.First- and second-order optimality conditions have been found for optimal control problems described by stochastic Goursat-Darboux systems