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

Andrei Panteleev () and Maria Karane
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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

Mathematics, 2023, vol. 11, issue 13, 1-21

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.

Keywords: optimal control; stochastic system; multi-agent algorithms; parametric optimization; spectral method; PID controllers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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