Optimal solutions in weakly coupled multiple decision maker Markov chains with nonclassical information

Research output: Contribution to journalConference article

Abstract

For Markov chains controlled by a team of agents there is no generally applicable method for obtaining the optimal control policy if the delay in information sharing between the agents is more than one-step. The authors consider such a problem for a Markov chain whose transition probability matrix consists of blocks, with the coupling between the blocks being on the order of ε, where ε is a small parameter. It is shown that if each block is controlled by only one agent, then it is possible to obtain policies arbitrarily close to the optimal control policy by making use of the fact that the coupling between the blocks is weak. The authors present a complete set of results for the finite-horizon case and discuss possible extensions to the infinite-horizon case.

Original languageEnglish (US)
Pages (from-to)168-173
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume1
StatePublished - Dec 1 1989
EventProceedings of the 28th IEEE Conference on Decision and Control. Part 1 (of 3) - Tampa, FL, USA
Duration: Dec 13 1989Dec 15 1989

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Markov processes
Markov chain
Optimal Solution
Control Policy
Optimal Policy
Optimal Control
Controlled Markov Chains
Transition Probability Matrix
Finite Horizon
Information Sharing
Infinite Horizon
Small Parameter
Policy

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

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title = "Optimal solutions in weakly coupled multiple decision maker Markov chains with nonclassical information",
abstract = "For Markov chains controlled by a team of agents there is no generally applicable method for obtaining the optimal control policy if the delay in information sharing between the agents is more than one-step. The authors consider such a problem for a Markov chain whose transition probability matrix consists of blocks, with the coupling between the blocks being on the order of ε, where ε is a small parameter. It is shown that if each block is controlled by only one agent, then it is possible to obtain policies arbitrarily close to the optimal control policy by making use of the fact that the coupling between the blocks is weak. The authors present a complete set of results for the finite-horizon case and discuss possible extensions to the infinite-horizon case.",
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AU - Basar, M Tamer

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N2 - For Markov chains controlled by a team of agents there is no generally applicable method for obtaining the optimal control policy if the delay in information sharing between the agents is more than one-step. The authors consider such a problem for a Markov chain whose transition probability matrix consists of blocks, with the coupling between the blocks being on the order of ε, where ε is a small parameter. It is shown that if each block is controlled by only one agent, then it is possible to obtain policies arbitrarily close to the optimal control policy by making use of the fact that the coupling between the blocks is weak. The authors present a complete set of results for the finite-horizon case and discuss possible extensions to the infinite-horizon case.

AB - For Markov chains controlled by a team of agents there is no generally applicable method for obtaining the optimal control policy if the delay in information sharing between the agents is more than one-step. The authors consider such a problem for a Markov chain whose transition probability matrix consists of blocks, with the coupling between the blocks being on the order of ε, where ε is a small parameter. It is shown that if each block is controlled by only one agent, then it is possible to obtain policies arbitrarily close to the optimal control policy by making use of the fact that the coupling between the blocks is weak. The authors present a complete set of results for the finite-horizon case and discuss possible extensions to the infinite-horizon case.

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