ANZIAM J.
45 (2003), 49-74
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Control of singularly perturbed Markov chains: A numerical study
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H. Yang
Department of Electrical and Computer Engineering
University of Minnesota
Minneapolis, MN 55455
USA
hyang@ece.umn.edu
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G. Yin
Department of Mathematics
Wayne State University
Detroit, MI 48202
USA
gyin@math.wayne.edu
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K. Yin
Department of Wood and Paper Science
University of Minnesota
St. Paul, MN 55108
USA
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Q. Zhang
Department of Mathematics
University of Georgia
Athens, GA 30602
USA
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Abstract
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This work is devoted to numerical studies of
nearly optimal controls of systems driven by
singularly perturbed Markov chains. Our approach
is based on the ideas of hierarchical controls
applicable to many large-scale systems. A
discrete-time linear quadratic control problem is
examined. Its corresponding limit system is
derived. The associated asymptotic properties and
near optimality are demonstrated by numerical
examples. Numerical experiments for a
continuous-time hybrid linear quadratic regulator
with Gaussian disturbances and a discrete-time
Markov decision process are also presented. The
numerical results have not only supported our
theoretical findings but also provided insights
for further applications.
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