Optimal Control

Peter Whittle

Editore: Wiley-Blackwell, 1995
ISBN 10: 0471956791 / ISBN 13: 9780471956792
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Riassunto: The concept of a system as an entity in its own right has emerged with increasing force in the past few decades in, for example, the areas of electrical and control engineering, economics, ecology, urban structures, automaton theory, operational research and industry. The more definite concept of a large-scale system is implicit in these applications, but is particularly evident in fields such as the study of communication networks, computer networks and neural networks. The Wiley-Interscience Series in Systems and Optimization has been established to serve the needs of researchers in these rapidly developing fields. It is intended for works concerned with developments in quantitative systems theory, applications of such theory in areas of interest, or associated methodology.

This is the first book-length treatment of risk-sensitive control, with many new results. The quadratic cost function of the standard LQG (linear/quadratic/Gaussian) treatment is replaced by the exponential of a quadratic, giving the so-called LEQG formulation allowing for a degree of optimism or pessimism on the part of the optimiser. The author is the first to achieve formulation and proof of risk-sensitive versions of the certainty-equivalence and separation principles. Further analysis allows one to formulate the optimization as the extremization of a path integral and to characterize the solution in terms of canonical factorization. It is thus possible to achieve the long-sought goal of an operational stochastic maximum principle, valid for a higher-order model, and in fact only evident when the models are extended to the risk-sensitive class. Additional results include deduction of compact relations between value functions and canonical factors, the exploitation of the equivalence between policy improvement and Newton Raphson methods and the direct relation of LEQG methods to the H??? and minimum-entropy methods. This book will prove essential reading for all graduate students, researchers and practitioners who have an interest in control theory including mathematicians, engineers, economists, physicists and psychologists. 1990 Stochastic Programming Peter Kall, University of Zurich, Switzerland and Stein W. Wallace, University of Trondheim, Norway Stochastic Programming is the first textbook to provide a thorough and self-contained introduction to the subject. Carefully written to cover all necessary background material from both linear and non-linear programming, as well as probability theory, the book draws together the methods and techniques previously described in disparate sources. After introducing the terms and modelling issues when randomness is introduced in a deterministic mathematical programming model, the authors cover decision trees and dynamic programming, recourse problems, probabilistic constraints, preprocessing and network problems. Exercises are provided at the end of each chapter. Throughout, the emphasis is on the appropriate use of the techniques, rather than on the underlying mathematical proofs and theories, making the book ideal for researchers and students in mathematical programming and operations research who wish to develop their skills in stochastic programming. 1994

From the Inside Flap: Optimal Control Basics and Beyond Peter Whittle Statistical Laboratory, University of Cambridge, UK ‘Control theory’ is now understood not merely in the narrow sense of the control of mechanisms but in the wider sense of the control of any dynamic system (e.g. communication, distribution, production, financial, economic), in general stochastic and imperfectly observed. The author takes this wider view and so covers general techniques of optimisation (e.g. dynamic programming and the maximum principle) as well as topics more classically associated with narrow-sense control theory (e.g. stability, feedback, controllability). There is now a great deal of standard material in this area, and it is to this which the ‘basics’ component of the book provides an introduction. However, while the material may be standard, the treatment of the section is shaped considerably by consciousness of the ‘beyond’ component into which it leads. This subsequent section covers risk-sensitive and H??? criteria, time-integral methods, optimal stationary policies, near-determinism and large deviation theory. Covering both standard material and recent results, this book will prove to be essential reading for students and researchers with an interest in control theory. Contents Preface Basics Part 1 Deterministic Models Part 2 Stochastic Models Beyond Part 3 Risk-sensitive and H??? Criteria Part 4 Time-integral Methods and Optimal Stationary Policies Part 5 Non-determinism and Large Deviation Theory Appendices References Index By the same author Optimization Over Time, Volume 2: Dynamic Programming and Stochastic Control Wiley 1983, ISBN 0 471 10496 5 Risk-Sensitive Optimal Control Wiley 1990, ISBN 0 471 92622 1 Of related interest Probability, Statistics and Optimization: A Tribute to Peter Whittle F.P. Kelly (Editor), Statistical Laboratory, University of Cambridge, UK Wiley 1994, ISBN 0 471 94829 2

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Titolo: Optimal Control
Casa editrice: Wiley-Blackwell
Data di pubblicazione: 1995
Legatura: Hardcover
Condizione libro: New

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Peter Whittle
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Descrizione libro John Wiley and Sons Ltd, United Kingdom, 1996. Hardback. Condizione libro: New. Language: English . Brand New Book. The concept of a system as an entity in its own right has emerged with increasing force in the past few decades in, for example, the areas of electrical and control engineering, economics, ecology, urban structures, automaton theory, operational research and industry. The more definite concept of a large--scale system is implicit in these applications, but is particularly evident in fields such as the study of communication networks, computer networks and neural networks. The Wiley--Interscience Series in Systems and Optimization has been established to serve the needs of researchers in these rapidly developing fields. It is intended for works concerned with developments in quantitative systems theory, applications of such theory in areas of interest, or associated methodology. This is the first book--length treatment of risk--sensitive control, with many new results. The quadratic cost function of the standard LQG (linear/quadratic/Gaussian) treatment is replaced by the exponential of a quadratic, giving the so--called LEQG formulation allowing for a degree of optimism or pessimism on the part of the optimiser. The author is the first to achieve formulation and proof of risk--sensitive versions of the certainty--equivalence and separation principles. Further analysis allows one to formulate the optimization as the extremization of a path integral and to characterize the solution in terms of canonical factorization. It is thus possible to achieve the long--sought goal of an operational stochastic maximum principle, valid for a higher--order model, and in fact only evident when the models are extended to the risk--sensitive class. Additional results include deduction of compact relations between value functions and canonical factors, the exploitation of the equivalence between policy improvement and Newton Raphson methods and the direct relation of LEQG methods to the H??? and minimum--entropy methods. This book will prove essential reading for all graduate students, researchers and practitioners who have an interest in control theory including mathematicians, engineers, economists, physicists and psychologists. 1990 Stochastic Programming Peter Kall, University of Zurich, Switzerland and Stein W. Wallace, University of Trondheim, Norway Stochastic Programming is the first textbook to provide a thorough and self--contained introduction to the subject. Carefully written to cover all necessary background material from both linear and non--linear programming, as well as probability theory, the book draws together the methods and techniques previously described in disparate sources. After introducing the terms and modelling issues when randomness is introduced in a deterministic mathematical programming model, the authors cover decision trees and dynamic programming, recourse problems, probabilistic constraints, preprocessing and network problems. Exercises are provided at the end of each chapter. Throughout, the emphasis is on the appropriate use of the techniques, rather than on the underlying mathematical proofs and theories, making the book ideal for researchers and students in mathematical programming and operations research who wish to develop their skills in stochastic programming. 1994. Codice libro della libreria AAH9780471956792

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Descrizione libro John Wiley and Sons Ltd, United Kingdom, 1996. Hardback. Condizione libro: New. Language: English . Brand New Book. The concept of a system as an entity in its own right has emerged with increasing force in the past few decades in, for example, the areas of electrical and control engineering, economics, ecology, urban structures, automaton theory, operational research and industry. The more definite concept of a large--scale system is implicit in these applications, but is particularly evident in fields such as the study of communication networks, computer networks and neural networks. The Wiley--Interscience Series in Systems and Optimization has been established to serve the needs of researchers in these rapidly developing fields. It is intended for works concerned with developments in quantitative systems theory, applications of such theory in areas of interest, or associated methodology. This is the first book--length treatment of risk--sensitive control, with many new results. The quadratic cost function of the standard LQG (linear/quadratic/Gaussian) treatment is replaced by the exponential of a quadratic, giving the so--called LEQG formulation allowing for a degree of optimism or pessimism on the part of the optimiser. The author is the first to achieve formulation and proof of risk--sensitive versions of the certainty--equivalence and separation principles. Further analysis allows one to formulate the optimization as the extremization of a path integral and to characterize the solution in terms of canonical factorization. It is thus possible to achieve the long--sought goal of an operational stochastic maximum principle, valid for a higher--order model, and in fact only evident when the models are extended to the risk--sensitive class. Additional results include deduction of compact relations between value functions and canonical factors, the exploitation of the equivalence between policy improvement and Newton Raphson methods and the direct relation of LEQG methods to the H??? and minimum--entropy methods. This book will prove essential reading for all graduate students, researchers and practitioners who have an interest in control theory including mathematicians, engineers, economists, physicists and psychologists. 1990 Stochastic Programming Peter Kall, University of Zurich, Switzerland and Stein W. Wallace, University of Trondheim, Norway Stochastic Programming is the first textbook to provide a thorough and self--contained introduction to the subject. Carefully written to cover all necessary background material from both linear and non--linear programming, as well as probability theory, the book draws together the methods and techniques previously described in disparate sources. After introducing the terms and modelling issues when randomness is introduced in a deterministic mathematical programming model, the authors cover decision trees and dynamic programming, recourse problems, probabilistic constraints, preprocessing and network problems. Exercises are provided at the end of each chapter. Throughout, the emphasis is on the appropriate use of the techniques, rather than on the underlying mathematical proofs and theories, making the book ideal for researchers and students in mathematical programming and operations research who wish to develop their skills in stochastic programming. 1994. Codice libro della libreria AAH9780471956792

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