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Adaptive Synthesized Control for Solving the Optimal Control Problem

Author

Listed:
  • Askhat Diveev

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2, Vavilova Str., Moscow 119333, Russia
    These authors contributed equally to this work.)

  • Elizaveta Shmalko

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2, Vavilova Str., Moscow 119333, Russia
    These authors contributed equally to this work.)

Abstract

The development of artificial intelligence systems assumes that a machine can independently generate an algorithm of actions or a control system to solve the tasks. To do this, the machine must have a formal description of the problem and possess computational methods for solving it. This article deals with the problem of optimal control, which is the main task in the development of control systems, insofar as all systems being developed must be optimal from the point of view of a certain criterion. However, there are certain difficulties in implementing the resulting optimal control modes. This paper considers an extended formulation of the optimal control problem, which implies the creation of such systems that would have the necessary properties for its practical implementation. To solve it, an adaptive synthesized optimal control approach based on the use of numerical methods of machine learning is proposed. Such control moves the control object, optimally changing the position of the stable equilibrium point in the presence of some initial position uncertainty. As a result, from all possible synthesized controls, one is chosen that is less sensitive to changes in the initial state. As an example, the optimal control problem of a quadcopter with complex phase constraints is considered. To solve this problem, according to the proposed approach, the control synthesis problem is firstly solved to obtain a stable equilibrium point in the state space using a machine learning method of symbolic regression. After that, optimal positions of the stable equilibrium point are searched using a particle swarm optimization algorithm using the source functional from the initial optimal control problem statement. It is shown that such an approach allows for generating the control system automatically by computer, basing this on the formal statement of the problem and then directly implementing it onboard as far as the stabilization system has already been introduced.

Suggested Citation

  • Askhat Diveev & Elizaveta Shmalko, 2023. "Adaptive Synthesized Control for Solving the Optimal Control Problem," Mathematics, MDPI, vol. 11(19), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4035-:d:1245925
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    References listed on IDEAS

    as
    1. Askhat Diveev & Elizaveta Shmalko, 2022. "Machine Learning Feedback Control Approach Based on Symbolic Regression for Robotic Systems," Mathematics, MDPI, vol. 10(21), pages 1-32, November.
    2. Askhat Diveev & Elizaveta Shmalko & Vladimir Serebrenny & Peter Zentay, 2020. "Fundamentals of Synthesized Optimal Control," Mathematics, MDPI, vol. 9(1), pages 1-18, December.
    3. Elizaveta Shmalko & Askhat Diveev & Lei Liu, 2022. "Extended Statement of the Optimal Control Problem and Machine Learning Approach to Its Solution," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-12, December.
    4. Ali M. Eltamaly, 2021. "A Novel Strategy for Optimal PSO Control Parameters Determination for PV Energy Systems," Sustainability, MDPI, vol. 13(2), pages 1-28, January.
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