ПРО ОПТИМАЛЬНЕ ІМПУЛЬСНЕ КЕРУВАННЯ В ДЕСКРИПТОРНИХ СИСТЕМАХ

• Дата: 2025
• Автори: Vlasenko, L.A., Rutkas, A.G., Semenets, V.V., Chikrii, A.A.
• Формат: Стаття
• Мова: English
• Опубліковано: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2025
• Теми: дескрипторна система; диференціально-алгебраїчне рівняння; квадратичний функціонал якості; інтенсивності імпульсів; моменти прикладання імпульсів; оптимальне імпульсне керування; спряжений стан; двоточкова крайова задача; радіотехнічний фільтр; перехідний режим
• Онлайн доступ: https://jais.net.ua/index.php/files/article/view/648
• Назва журналу: Problems of Control and Informatics

We study the optimal impulse control problem with quadratic perfomance functional for a descriptor system. The system evolution is described by a linear differential-algebraic equation not solved with respect to the derivative of the state. The system is controlled by changing the measurable control and the pure impulse control. The pure impulse control is characterized by impulse intensities and moments of impulse applications. The main restriction is that the characteristic matrix pencil corresponding to the state equation is regular. In terms of the characteristic matrix pencil, we establish the conditions for the existence and uniqueness of the optimal control and the corresponding optimal state. The optimal control and the optimal state are constructed by using the adjoint state, which is a solution to the adjoint two-point boundary value problem. The results are illustrated on an example of descriptor system that describes transient states in a radio technical filter. For this system, we consider an energetic perfomance functional with impulse intensities characterizing the energy of inertial elements and input voltage of the filter and also moments of impulse applications. Transient states under impulsive perturbations of currents and voltages are described by using the formula of variation of constants for the impulsive descriptor system.