Paper: Optimal control of markov chains admitting strong and weak interactions

Authors:
François Delebecque;Jean-Pierre Quadrat
Affiliations:
INRIA-Laboria, Domaine de Voluceau, 78150 Le Chesnay, France;INRIA-Laboria, Domaine de Voluceau, 78150 Le Chesnay, France
Venue:
Automatica (Journal of IFAC)
Year:
1981

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Abstract

This paper is devoted to the study of an optimal control problem for a Markov chain with generator B + @eA, where @e is a small parameter. It is shown that an approximate solution can be calculated by a policy improvement algorithm involving computations relative to an 'aggregated' problem (the dimension of which is given by N, the number of ergodic sets for the B matrix) together with a family of 'decentralized' problems (the dimensions of which are given by the number of elements in each ergodic set for the B matrix).