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Application of a Novel Multi-Agent Optimization Algorithm Based on PID Controllers in Stochastic Control Problems

Author

Listed:
  • Andrei Panteleev

    (Department of Mathematics and Cybernetics, Moscow Aviation Institute, National Research University, 4 Volokolamskoe Shosse, 125993 Moscow, Russia)

  • Maria Karane

    (Department of Mathematics and Cybernetics, Moscow Aviation Institute, National Research University, 4 Volokolamskoe Shosse, 125993 Moscow, Russia)

Abstract

The article considers the problem of finding the optimal on average control of the trajectories of continuous stochastic systems with incomplete feedback. This class of problems includes control problems in which the initial states are described by a given distribution law; random effects on the control object are taken into account; and it is also assumed that information is available only about some coordinates of the state vector. As special cases, the problems of determining the optimal open-loop control and control with complete feedback in the presence of information about all state vector coordinates are considered. A method for parameterization of the control law based on expansions in various systems of basis functions is described. The problem of parametric optimization obtained is solved using a new metaheuristic multi-agent algorithm based on the use of extended PID (Proportional-Integral-Derivative) controllers to control the movement of agents. Solutions of three model examples of control of nonlinear continuous stochastic systems with interval constraints on the amount of control for all possible cases of state vector awareness are presented.

Suggested Citation

  • Andrei Panteleev & Maria Karane, 2023. "Application of a Novel Multi-Agent Optimization Algorithm Based on PID Controllers in Stochastic Control Problems," Mathematics, MDPI, vol. 11(13), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2903-:d:1181975
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    References listed on IDEAS

    as
    1. Abraham Duarte & Rafael Martí & Fred Glover & Francisco Gortazar, 2011. "Hybrid scatter tabu search for unconstrained global optimization," Annals of Operations Research, Springer, vol. 183(1), pages 95-123, March.
    2. Elena Niculina Dragoi & Vlad Dafinescu, 2021. "Review of Metaheuristics Inspired from the Animal Kingdom," Mathematics, MDPI, vol. 9(18), pages 1-52, September.
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