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Fundamentals of Synthesized Optimal Control

Author

Listed:
  • Askhat Diveev

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia)

  • Elizaveta Shmalko

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia)

  • Vladimir Serebrenny

    (Department of Robotic Systems and Mechatronics, Bauman Moscow State Technical University, 105005 Moscow, Russia)

  • Peter Zentay

    (Faculty of Mechanical Engineering, Budapest University of Technology and Economics, 1111 Budapest, Hungary)

Abstract

This paper presents a new formulation of the optimal control problem with uncertainty, in which an additive bounded function is considered as uncertainty. The purpose of the control is to ensure the achievement of terminal conditions with the optimal value of the quality functional, while the uncertainty has a limited impact on the change in the value of the functional. The article introduces the concept of feasibility of the mathematical model of the object, which is associated with the contraction property of mappings if we consider the model of the object as a one-parameter mapping. It is shown that this property is sufficient for the development of stable practical systems. To find a solution to the stated problem, which would ensure the feasibility of the system, the synthesized optimal control method is proposed. This article formulates the theoretical foundations of the synthesized optimal control. The method consists in making the control object stable relative to some point in the state space and to control the object by changing the position of the equilibrium points. The article provides evidence that this approach is insensitive to the uncertainties of the mathematical model of the object. An example of the application of the method for optimal control of a group of robots is given. A comparison of the synthesized optimal control method with the direct method on the model without disturbances and with them is presented.

Suggested Citation

  • Askhat Diveev & Elizaveta Shmalko & Vladimir Serebrenny & Peter Zentay, 2020. "Fundamentals of Synthesized Optimal Control," Mathematics, MDPI, vol. 9(1), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:21-:d:467363
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    References listed on IDEAS

    as
    1. Aram Arutyunov & Dmitry Karamzin, 2020. "A Survey on Regularity Conditions for State-Constrained Optimal Control Problems and the Non-degenerate Maximum Principle," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 697-723, March.
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    Cited by:

    1. Askhat Diveev & Elizaveta Shmalko, 2023. "Adaptive Synthesized Control for Solving the Optimal Control Problem," Mathematics, MDPI, vol. 11(19), pages 1-18, September.

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