Towards Tensor Representation of Controlled Coupled Markov Chains

Daniel McInnes, Boris Miller, Gregory Miller and Sergei Schreider
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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
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

Mathematics, 2020, vol. 8, issue 10, 1-17

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.

Keywords: coupled markov chains; stochastic control; optimal control; tensor representation; dynamic programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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