Математична теорія оптимального керування в практичних задачах

Abstract

In this article the literature analysis is provided basing on the history of the maximum principle from its’ very discovery. Also some significant examples of tasks for optimal control in different fields of application are described. Starting from this point the optimal solutions searching tasks concerning printing industry are analyzed. Basing on this the hypothetic task for optimal control in ink and water supply had been stated. While adding the typical transportation delay and the margins set by this phenomenon, the task for optimal control search had been finalized. With this the simplified point with the ink or fountain solution will travel through the complex rollers system in the printing unit that are doing the rotating, oscillating and rotating-oscillate-transporting moves.The conducted research shows the existence of ability to set the process of achieving and constant keeping the ink—water balance, while having some numbers of ink and fountain solution supply according to the number of printing and non-printing elements on the printing form in offset printing.The mathematical model for solving the task of optimal control search while setting and correcting the amounts of ink and fountain solution supply in the preprint preparation and while controlling the print-run itself was proposed. This is crucial for keeping the normalized parameters of optical density and color difference on the imprint, as the trajectory of ink of fountain solution flow change was determined for the corrections in «increase» or «decrease» directions.