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Optimal Control Edition. ed. [Kõva köide]

  • Formaat: Hardback, 520 pages, kõrgus x laius x paksus: 235x155x28 mm, kaal: 2010 g, 13 black & white illustrations
  • Sari: Systems & Control: Foundations and Applications
  • Ilmumisaeg: 19-May-2000
  • Kirjastus: Birkhauser Boston Inc
  • ISBN-10: 0817640754
  • ISBN-13: 9780817640750
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  • Formaat: Hardback, 520 pages, kõrgus x laius x paksus: 235x155x28 mm, kaal: 2010 g, 13 black & white illustrations
  • Sari: Systems & Control: Foundations and Applications
  • Ilmumisaeg: 19-May-2000
  • Kirjastus: Birkhauser Boston Inc
  • ISBN-10: 0817640754
  • ISBN-13: 9780817640750
Teised raamatud teemal:
"Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control." -Mathematical Reviews"Thanks to a great effort to be self-contained, [ this book] renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis)." -Automatica

This new book brings together important new results and advances in optimal control, providing a self-contained analysis and incorporating numerous simplifications and unifying features for the subject's key concepts and foundations.

Arvustused

"The book by R. Vinter is really well written; it goes from the very basic tools in variational analysis, as direct methods and regularity, to the most recent results in dynamic programming. Special attention is devoted to nonsmooth analysis tools!. The book is enriched by many examples: this is a very important point for a reader who wants to approach control theory, and makes the volume suitable not only for specialists but also for students at a Ph.D. level." --Zentralblatt Math "In the book, many major developments in optimal control based on nonsmooth analysis in recent years are brought together in a form accessible to a broader audience!. The book may be an essential resource for potential readers, experts in control and optimization, as well as postgraduates and applied mathematicians, and it will be valued for its accessibility and clear exposition."--Applications of Mathematics "In this self-contained monograph the author brings us right to the frontier of the research on necessary optimality conditions using the methodology of nonsmooth analysis and variational methods. He also presents a new perspective on the regularity of minimizers and discusses some of the recent progress on dynamic programming!. Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control." --Mathematical Reviews "This remarkable book presents Optimal Control seen as a natural development of Calculus of Variations so as to deal with the control of engineering devices. This guideline is followed throughout the book and especially in its first chapter "Overview" that summarizes the philosophy, scope and results of this monograph. The main technical feature is the use of Nonsmooth Analysis and most of the attention is focused on necessary conditions for optimality...The book brings together most of recent developments in Optimal Control via Nonsmooth Analysis methods. Thanks to a great effort to be self-contained, it renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis)." --Automatica

Preface xi
Notation xvii
Overview
1(60)
Optimal Control
1(3)
The Calculus of Variations
4(14)
Existence of Minimizers and Tonelli's Direct Method
18(3)
Sufficient Conditions and the Hamilton-Jacobi Equation
21(4)
The Maximum Principle
25(5)
Dynamic Programming
30(5)
Nonsmoothness
35(4)
Nonsmooth Analysis
39(13)
Nonsmooth Optimal Control
52(4)
Epilogue
56(4)
Notes for
Chapter 1
60(1)
Measurable Multifunctions and Differential Inclusions
61(48)
Introduction
61(1)
Convergence of Sets
62(2)
Measurable Multifunctions
64(11)
Existence and Estimation of F-Trajectories
75(11)
Perturbed Differential Inclusions
86(5)
Existence of Minimizing F-Trajectories
91(3)
Relaxation
94(6)
The Generalized Bolza Problem
100(8)
Notes for
Chapter 2
108(1)
Variational Principles
109(18)
Introduction
109(1)
Exact Penalization
110(1)
Ekeland's Theorem
111(4)
Mini-Max Theorems
115(10)
Notes for
Chapter 3
125(2)
Nonsmooth Analysis
127(52)
Introduction
127(1)
Normal Cones
128(5)
Subdifferentials
133(6)
Difference Quotient Representations
139(5)
Nonsmooth Mean Value Inequalities
144(5)
Characterization of Limiting Subgradients
149(5)
Subgradients of Lipschitz Continuous Functions
154(7)
The Distance Function
161(5)
Criteria for Lipschitz Continuity
166(4)
Relationships Between Normal and Tangent Cones
170(9)
Subdifferential Calculus
179(22)
Introduction
179(2)
A Marginal Function Principle
181(4)
Partial Limiting Subgradients
185(2)
A Sum Rule
187(3)
A Nonsmooth Chain Rule
190(3)
Lagrange Multiplier Rules
193(4)
Notes for
Chapters 4 and 5
197(4)
The Maximum Principle
201(32)
Introduction
201(2)
The Maximum Principle
203(5)
Derivation of the Maximum Principle from the Extended Euler Condition
208(6)
A Smooth Maximum Principle
214(14)
Notes for
Chapter 6
228(5)
The Extended Euler-Lagrange and Hamilton Conditions
233(52)
Introduction
233(4)
Properties of the Distance Function
237(5)
Necessary Conditions for a Finite Lagrangian Problem
242(10)
The Extended Euler-Lagrange Condition: Nonconvex Velocity Sets
252(7)
The Extended Euler-Lagrange Condition: Convex Velocity Sets
259(5)
Dualization of the Extended Euler-Lagrange Condition
264(13)
The Extended Hamilton Condition
277(3)
Notes for
Chapter 7
280(5)
Necessary Conditions for Free End-Time Problems
285(36)
Introduction
285(3)
Lipschitz Time Dependence
288(7)
Essential Values
295(2)
Measurable Time Dependence
297(4)
Proof of Theorem 8.4.1
301(9)
Proof of Theorem 8.4.2
310(3)
A Free End-Time Maximum Principle
313(5)
Notes for
Chapter 8
318(3)
The Maximum Principle for State Constrained Problems
321(40)
Introduction
321(3)
Convergence of Measures
324(5)
The Maximum Principle for Problems with State Constraints
329(5)
Derivation of the Maximum Principle for State Constrained Problems from the Euler-Lagrange Condition
334(5)
A Smooth Maximum Principle for State Constrained Problems
339(20)
Notes for
Chapter 9
359(2)
Differential Inclusions with State Constraints
361(36)
Introduction
361(1)
A Finite Lagrangian Problem
362(6)
The Extended Euler-Lagrange Condition for State Constrained Problems: Nonconvex Velocity Sets
368(7)
Necessary Conditions for State Constrained Problems: Convex Velocity Sets
375(7)
Free Time Problems with State Constraints
382(5)
Nondegenerate Necessary Conditions
387(9)
Notes for
Chapter 10
396(1)
Regularity of Minimizers
397(38)
Introduction
397(6)
Tonelli Regularity
403(5)
Proof of The Generalized Tonelli Regularity Theorem
408(9)
Lipschitz Continuous Minimizers
417(5)
Autonomous Variational Problems with State Constraints
422(3)
Bounded Controls
425(3)
Lipschitz Continuous Controls
428(4)
Notes for
Chapter 11
432(3)
Dynamic Programming
435(58)
Introduction
435(7)
Invariance Theorems
442(10)
The Value Function and Generalized Solutions of the Hamilton-Jacobi Equation
452(13)
Local Verification Theorems
465(9)
Adjoint Arcs and Gradients of the Value Function
474(9)
State Constrained Problems
483(4)
Notes for
Chapter 12
487(6)
References 493(12)
Index 505
Richard Vinter is Head of the Control and Power Research Group at Imperial College London.