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Dynamic programming: deterministic and stochastic models. (English) Zbl 0649.93001
Englewood Cliffs, N.J. 07632: Prentice-Hall, Inc. VIII, 376 p.; $ 64.85 (1987).
This book provides a comprehensive and unified treatment of dynamic programming for discrete stochastic systems, which is suitable for an audience from mathematicians and engineers to social scientists. At the beginning a single basic problem is introduced and then all considerations throughout the text are carried out with its help. Let us note that many stochastic control problems, Markovian decision problems and classes of combinatorial problems, popular in computer science, are solved by applying the dynamic programming technique. Moreover, the text provides a large variety of examples, many of them being important on their own. Recent research material such as queueing decision problems, armed bandit problems, stochastic scheduling, heuristic search, self- tuning regulators, and adaptive aggregation is also included.
The book is organized in the following seven chapters: (1) The dynamic programming algorithm; (2) Applications in specific areas; (3) Problems with imperfect state information; (4) Suboptimal and adaptive control; (5) Infinite horizon problems: theory; (6) Infinite horizon problems: applications; (7) Minimization of average cost per stage.
The mathematical prerequisites for reading the text are summarized in four appendices: (A) Review on basic mathematical notions; (B) On optimization theory; (C) On probability theory; (D) On finite state Markov chains.
In fact the reader needs a good knowledge of introductory probability and undergraduate mathematics. Nevertheless the book can even be read with success if one does not go to deeply into details. Those, who have no desire to bypass the mathematically rigorous treatment of the problems, can look for the author’s monograph written jointly with St. Shreve [Stochastic optimal control. The discrete time case (1978; Zbl 0471.93002)].
Reviewer: Sv.Gaidov

93-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory
90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
93E20 Optimal stochastic control
49L20 Dynamic programming in optimal control and differential games
90B22 Queues and service in operations research
90B35 Deterministic scheduling theory in operations research
90B40 Search theory
90B50 Management decision making, including multiple objectives
90C40 Markov and semi-Markov decision processes
90C39 Dynamic programming
93C40 Adaptive control/observation systems
93C55 Discrete-time control/observation systems
93E03 Stochastic systems in control theory (general)