В роботі розглянуто задачу оптимального керування для системи диференціальних рівнянь з імпульсною дією у нефіксовані моменти часу. Отримано достатні умови існування оптимального керування в термінах правих частин системи та критерію якості.
This paperis devoted to research the problems of optimal control for systems of differential equations with pulses at non-fixed times. To solve such problems we must be sure that optimal control exists. Due to the complexity of the differential equation with impulse action in the non-fixed time points, a decision is considered at each interval until the exit solutions to the hypersurface and due to the specificity of the hypersurface we estimated distances between the moments of pulse action. The existence of optimal control is proved without using the maximum principle, which made it possible to obtain sufficient conditions of existence. These conditions are presented in terms of right sides of the system and function which are included in the quality criterion. This research lays the foundation for further research into the existence of optimal control for systems of differential equations with pulses at non-fixed times.
