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Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm

Author

Listed:
  • Askhat Diveev

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

  • Elena Sofronova

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

  • Ivan Zelinka

    (Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam
    Department of Computer Science, FEI, VSB Technical University of Ostrava, 70800 Ostrava, Czech Republic)

Abstract

A numerical method based on the Pontryagin maximum principle for solving an optimal control problem with static and dynamic phase constraints for a group of objects is considered. Dynamic phase constraints are introduced to avoid collisions between objects. Phase constraints are included in the functional in the form of smooth penalty functions. Additional parameters for special control modes and the terminal time of the control process were introduced. The search for additional parameters and the initial conditions for the conjugate variables was performed by the modified self-organizing migrating algorithm. An example of using this approach to solve the optimal control problem for the oncoming movement of two mobile robots is given. Simulation and comparison with direct approach showed that the problem is multimodal, and it approves application of the evolutionary algorithm for its solution.

Suggested Citation

  • Askhat Diveev & Elena Sofronova & Ivan Zelinka, 2020. "Optimal Control Problem Solution with Phase Constraints for Group of Robots by Pontryagin Maximum Principle and Evolutionary Algorithm," Mathematics, MDPI, vol. 8(12), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2105-:d:450786
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    Citations

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    Cited by:

    1. Alena Vagaská & Miroslav Gombár & Ľuboslav Straka, 2022. "Selected Mathematical Optimization Methods for Solving Problems of Engineering Practice," Energies, MDPI, vol. 15(6), pages 1-22, March.
    2. Mikhail Posypkin & Andrey Gorshenin & Vladimir Titarev, 2022. "Preface to the Special Issue on “Control, Optimization, and Mathematical Modeling of Complex Systems”," Mathematics, MDPI, vol. 10(13), pages 1-8, June.

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