ВИРІШЕННЯ ОДНІЄЇ ЗАДАЧІ ОПТИМАЛЬНОГО КЕРУВАННЯ ДЛЯ РІВНЯННЯ ТРЕТЬОГО ПОРЯДКУ ПРИ РОЗПОДІЛЕНОМУ І СТАРТОВОМУ КЕРУВАННЯХ

• Дата: 2025
• Автори: Yaqubova , M.M., Zamanova , R.B.
• Формат: Стаття
• Мова: English
• Опубліковано: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2025
• Теми: початково-крайова задача; узагальнене рішення; метод Фур’є; завдання на власні значення
• Онлайн доступ: https://jais.net.ua/index.php/files/article/view/689
• Назва журналу: Problems of Control and Informatics

There are a large number of scientific articles and monographs devoted to various problems of control theory in systems described by partial differential equations, which are fairly well represented in [1–6]. However, in all these works, problems are considered that are related mainly to equations of classical types studied in courses of mathematical physics. Recently, papers have appeared that solve various problems associated with fourth-order partial differential equations, obtained from the practice. Along with it, there are numerous applied problems described by third-order equations or the so-called equations of variable type. Despite the fact that the initial-boundary value problems for such equations are studied well, but there are only a few works [12–18] in which control problems in such systems are investigated. In this paper, the minimum problem of the quadratic functional for the initial-boundary value problem for a third-order linear equation is studied. First, using the Fourier method, a representation of the solution of the initial-boundary value problem is obtained, and then the optimal control problem is reduced to a conditional extremum problem and its solution is obtained in the form of a series.