Application of the averaging method to the problems of optimal control of the impulse systems

  • T.V. Koval'chuk Kyiv National University of Trade and Economics, 19 Kioto str., 02156, Kyiv, Ukraine
  • V.V. Mogylova National Technical University of Ukraine ''Igor Sikorsky Kyiv Polytechnic Institute'', 7 Peremogy av., 03056, Kyiv, Ukraine
  • O.M. Stanzhytskyi Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska str., 01601, Kyiv, Ukraine
  • T.V. Shovkoplyas Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska str., 01601, Kyiv, Ukraine
Keywords: optimal control problem, optimal control, exact problem, averaged problem, valid control, averaging condition, weak convergence, compactness, semi-continuity, quality criterion, minimizing sequence
Published online: 2020-12-30

Abstract


The problem of optimal control at finite time interval for a system of differential equations with impulse action at fixed moments of time as well as the corresponding averaged system of ordinary differential equations are considered.

It is proved the existence of optimal control of exact and averaged problems. Also, it is established that optimal control of averaged problem realize the approximate optimal synthesis of exact problem. The main result of the article is a theorem, where it is proved that optimal contol of an averaged problem is almost optimal for exact problem. Substantiation of proximity of solutions of exact and averaged problems is obtained.

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