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Lasserre, Jean B. / Onesimo Hernandez-Lerma. Discrete-Time Markov Control Processes - Basic Optimality Criteria. Springer New York, 1995.
eng

Jean B. Lasserre / Onesimo Hernandez-Lerma

Discrete-Time Markov Control Processes

Basic Optimality Criteria
  • Springer New York
  • 1995
  • Gebunden
  • 236 Seiten
  • ISBN 9780387945798

This book presents the first part of a planned two-volume series devoted to a systematic exposition of some recent developments in the theory of discrete- time Markov control processes (MCPs). Interest is mainly confined to MCPs with Borel state and control (or action) spaces, and possibly unbounded costs and noncompact control constraint sets. MCPs are a class of stochastic control problems, also known as Markov decision processes, controlled Markov processes, or stochastic dynamic pro­ grams; sometimes, particularly when the state space is a countable set, they are also called Markov decision (or controlled Markov) chains. Regardless of the name used, MCPs appear in many fields, for

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example, engineering, economics, operations research, statistics, renewable and nonrenewable re­ source management, (control of) epidemics, etc. However, most of the lit­ erature (say, at least 90%) is concentrated on MCPs for which (a) the state space is a countable set, and/or (b) the costs-per- stage are bounded, and/or (c) the control constraint sets are compact. But curiously enough, the most widely used control model in engineering and economics--namely the LQ (Linear system/Quadratic cost) model-satisfies none of these conditions. Moreover, when dealing with "partially observable" systems) a standard approach is to transform them into equivalent "completely observable" sys­ tems in a larger state space (in fact, a space of probability measures), which is uncountable even if the original state process is finite- valued.

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