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Deterministic and Stochastic Optimal Control : Stochastic Modelling and Applied Probability - Wendell H. Fleming

Deterministic and Stochastic Optimal Control

Stochastic Modelling and Applied Probability

Hardcover

Published: 18th October 1982
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This book may be regarded as consisting of two parts. In Chapters I-IV we pre­ sent what we regard as essential topics in an introduction to deterministic optimal control theory. This material has been used by the authors for one semester graduate-level courses at Brown University and the University of Kentucky. The simplest problem in calculus of variations is taken as the point of departure, in Chapter I. Chapters II, III, and IV deal with necessary conditions for an opti­ mum, existence and regularity theorems for optimal controls, and the method of dynamic programming. The beginning reader may find it useful first to learn the main results, corollaries, and examples. These tend to be found in the earlier parts of each chapter. We have deliberately postponed some difficult technical proofs to later parts of these chapters. In the second part of the book we give an introduction to stochastic optimal control for Markov diffusion processes. Our treatment follows the dynamic pro­ gramming method, and depends on the intimate relationship between second­ order partial differential equations of parabolic type and stochastic differential equations. This relationship is reviewed in Chapter V, which may be read inde­ pendently of Chapters I-IV. Chapter VI is based to a considerable extent on the authors' work in stochastic control since 1961. It also includes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle.

The Simplest Problem in Calculus of Variations
The Optimal Control Problem
Existence and Continuity Properties of Optimal Controls
Dynamic Programming
Stochastic Differential Equations and Markov Diffusion Processes
Optimal Control of Markov Diffusion Processes
Appendices
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387901558
ISBN-10: 0387901558
Series: Stochastic Modelling and Applied Probability
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 222
Published: 18th October 1982
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.88  x 1.91
Weight (kg): 0.5