Elements of Dynamic Optimization PDF Download

Author: Alpha C. Chiang
Publisher:
ISBN: 9781577660965
Category : Economics, Mathematical
Languages : en
Pages : 0

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INTRODUCTION 1.

Author: Francis Clarke
Publisher: American Mathematical Soc.
ISBN: 9781470404178
Category : Mathematics
Languages : en
Pages : 113

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Book Description
This monograph derives necessary conditions of optimality for a general control problem formulated in terms of a differential inclusion. These conditions constitute a new state of the art, subsuming, unifying, and substantially extending the results in the literature. The Euler, Weierstrass and transversality conditions are expressed in their sharpest known forms. No assumptions of boundedness or convexity are made, no constraint qualifications imposed, and only weak pseudo-Lipschitz behavior is postulated on the underlying multifunction. The conditions also incorporate a 'stratified' feature of a novel nature, in which both the hypotheses and the conclusion are formulated relative to a given radius function.When specialized to the calculus of variations, the results yield necessary conditions and regularity theorems that go significantly beyond the previous standard. They also apply to parametrized control systems, giving rise to new and stronger maximum principles of Pontryagin type. The final chapter is devoted to a different issue, that of the Hamiltonian necessary condition. It is obtained here, for the first time, in the case of nonconvex values and in the absence of any constraint qualification; this has been a longstanding open question in the subject. Apart from the final chapter, the treatment is self-contained, and calls upon only standard results in functional and nonsmooth analysis.

Author: Morton I. Kamien
Publisher: Courier Corporation
ISBN: 0486310280
Category : Mathematics
Languages : en
Pages : 402

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Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.

Author: Francis Clarke
Publisher: American Mathematical Soc.
ISBN: 0821835912
Category : Mathematics
Languages : en
Pages : 113

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Book Description
This monograph derives necessary conditions of optimality for a general control problem formulated in terms of a differential inclusion. These conditions constitute a new state of the art, subsuming, unifying, and substantially extending the results in the literature. The Euler, Weierstrass and transversality conditions are expressed in their sharpest known forms. No assumptions of boundedness or convexity are made, no constraint qualifications imposed, and only weak pseudo-Lipschitz behavior is postulated on the underlying multifunction. The conditions also incorporate a `stratified' feature of a novel nature, in which both the hypotheses and the conclusion are formulated relative to a given radius function. When specialized to the calculus of variations, the results yield necessary conditions and regularity theorems that go significantly beyond the previous standard. They also apply to parametrized control systems, giving rise to new and stronger maximum principles of Pontryagin type. The final chapter is devoted to a different issue, that of the Hamiltonian necessary condition. It is obtained here, for the first time, in the case of nonconvex values and in the absence of any constraint qualification; this has been a longstanding open question in the subject. Apart from the final chapter, the treatment is self-contained, and calls upon only standard results in functional and nonsmooth analysis.

Author: Alpha C. Chiang
Publisher: McGraw-Hill Companies
ISBN:
Category : Business & Economics
Languages : en
Pages : 358

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Designed to be used with Chiang's "Fundamental Methods of Mathematical Economics", or independently at advanced undergraduate or graduate level, this text presents an in-depth exploration of dynamic optimization in economics.

Author: Ronald E. Miller
Publisher:
ISBN:
Category : Business & Economics
Languages : en
Pages : 352

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Author: Piernicola Bettiol
Publisher: Springer Nature
ISBN: 303150089X
Category :
Languages : en
Pages : 789

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Author: Arthur Earl Bryson
Publisher: Prentice Hall
ISBN:
Category : Computers
Languages : en
Pages : 458

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Book Description
"Dynamic Optimization" takes an applied approach to its subject, offering many examples and solved problems that draw from aerospace, robotics, and mechanics. The abundance of thoroughly tested general algorithms and Matlab codes provide the reader with the practice necessary to master this inherently difficult subject, while the realistic engineering problems and examples keep the material interesting and relevant. FEATURES/BENEFITS Covers dynamic programming, relating it to the calculus of variations and optimal control, and neighboring optimum control (differential dynamic programming), a practical method for nonlinear feedback control. Includes a disk that contains 40 gradient and shooting codes, as well as codes that solve the time-varying Riccati equation (the DYNOPT Toolbox). These codes have been thoroughly tested on hundreds of problems. Contains many realistic examples and problems. Solutions to the examples and problems, as well as the codes that produce the figures, are included on the accompanying disk. Covers dynamic optimization with inequality constraints and singular arcs using inverse dynamic optimization (differential inclusion).

Author: S. K. Agrawal
Publisher: Springer Science & Business Media
ISBN: 9401591490
Category : Technology & Engineering
Languages : en
Pages : 228

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Book Description
This textbook deals with optimization of dynamic systems. The motivation for undertaking this task is as follows: There is an ever increasing need to produce more efficient, accurate, and lightweight mechanical and electromechanical de vices. Thus, the typical graduating B.S. and M.S. candidate is required to have some familiarity with techniques for improving the performance of dynamic systems. Unfortunately, existing texts dealing with system improvement via optimization remain inaccessible to many of these students and practicing en gineers. It is our goal to alleviate this difficulty by presenting to seniors and beginning graduate students practical efficient techniques for solving engineer ing system optimization problems. The text has been used in optimal control and dynamic system optimization courses at the University of Deleware, the University of Washington and Ohio University over the past four years. The text covers the following material in a straightforward detailed manner: • Static Optimization: The problem of optimizing a function that depends on static variables (i.e., parameters) is considered. Problems with equality and inequality constraints are addressed. • Numerical Methods: Static Optimization: Numerical algorithms for the solution of static optimization problems are presented here. The methods presented can accommodate both the unconstrained and constrained static optimization problems. • Calculus of Variation: The necessary and sufficient conditions for the ex tremum of functionals are presented. Both the fixed final time and free final time problems are considered.

Author: Michael D. Intriligator
Publisher: SIAM
ISBN: 0898715113
Category : Mathematics
Languages : en
Pages : 515

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Book Description
A classic account of mathematical programming and control techniques and their applications to static and dynamic problems in economics.