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An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Author

Listed:
  • Alexander Arguchintsev

    (Institute of Mathematics, Irkutsk State University, K. Marx Street 1, 664003 Irkutsk, Russia)

  • Vasilisa Poplevko

    (Office of PhD Programs, Irkutsk State University, K. Marx Street 1, 664003 Irkutsk, Russia)

Abstract

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

Suggested Citation

  • Alexander Arguchintsev & Vasilisa Poplevko, 2021. "An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations," Games, MDPI, vol. 12(1), pages 1-9, March.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:1:p:23-:d:509851
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    Cited by:

    1. Ellina Grigorieva, 2021. "Optimal Control Theory: Introduction to the Special Issue," Games, MDPI, vol. 12(1), pages 1-4, March.

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