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Towards Tensor Representation of Controlled Coupled Markov Chains

Author

Listed:
  • Daniel McInnes

    (School of Mathematics, Monash University, Wellington Road, Clayton VIC 3800, Australia)

  • Boris Miller

    (School of Mathematics, Monash University, Wellington Road, Clayton VIC 3800, Australia
    Institute for Information Transmission Problems RAS, 19/1 Bolshoy Karetny Per., 127051 Moscow, Russia)

  • Gregory Miller

    (Institute of Informatics Problems of Federal Research Center “Computer Science and Control” RAS, 44/2 Vavilova Str., 119333 Moscow, Russia)

  • Sergei Schreider

    (Department of Management and Information Systems, Rutgers Business School, Rutgers—The State University of New Jersey, New Brunswick, NJ 07102, USA)

Abstract

For a controlled system of coupled Markov chains, which share common control parameters, a tensor description is proposed. A control optimality condition in the form of a dynamic programming equation is derived in tensor form. This condition can be reduced to a system of coupled ordinary differential equations and admits an effective numerical solution. As an application example, the problem of the optimal control for a system of water reservoirs with phase and balance constraints is considered.

Suggested Citation

  • Daniel McInnes & Boris Miller & Gregory Miller & Sergei Schreider, 2020. "Towards Tensor Representation of Controlled Coupled Markov Chains," Mathematics, MDPI, vol. 8(10), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1712-:d:423779
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    References listed on IDEAS

    as
    1. Marnie Griffith & Gary Codner & Erwin Weinmann & Sergei Schreider, 2009. "Modelling hydroclimatic uncertainty and short-run irrigator decision making: the Goulburn system ," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 53(4), pages 565-584, October.
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