This book describes the mathematical theory inspired by the irreversible nature of time-evolving events. The first part of the book deals with the ability to steer a system from any point of departure to any desired destination. The second part deals with optimal control--the problem of finding the best possible course. The author demonstrates an overlap with mathematical physics using the maximum principle, a fundamental concept of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. He draws applications from geometry, mechanics, and control of dynamical systems. The geometric language in which the author expresses the results allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians.
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Editorial Reviews
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"...remarkably well-written...I strongly recommend GCT for the use of teachers and graduate students of control theory, mechanics and mathematics (especially dynamical systems and differential geometry), as well as for the mathematician new to control theory. It is a helpful guide for anyone engaged in research or applications of optimal control." IEEE Transactions on Automatic Control
Book Description
Geometric control theory concerns the differential equations described by non-commuting vector fields. It builds ideas from the theory of differential systems and the calculus of variations into a cohesive mathematical framework applicable to a wide range of problems from differential geometry, applied mathematics, physics and engineering.
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0 of 2 people found the following review helpful:
1.0 out of 5 stars
a worst book on optimal control theory,
This review is from: Geometric Control Theory (Cambridge Studies in Advanced Mathematics) (Paperback)
This book is a typical one that misleads readers. The way this book handles Hamiltonian reduction theory in the context of optimal control is very clumsy. Hamiltonian reduction theory has been well established since sixties. This book only reflects the author's stubbornness against learning the elementary reduction theory. Jurdjevic pretends to create a reduction theory without citing tons of relevant books and papers. What's worse is that he does it very poorly.
1 of 4 people found the following review helpful:
5.0 out of 5 stars
The Best book on the topic,
By A Customer
This review is from: Geometric Control Theory (Cambridge Studies in Advanced Mathematics) (Hardcover)
This is realy the best book on the topic. In some sense it is the only modern book. If you work on Control Theory and you want to lern some modern geometric tecniques you have to read it !!!
4 of 10 people found the following review helpful:
5.0 out of 5 stars
Quite simply, the most penetrating text in the field.,
By A Customer
This review is from: Geometric Control Theory (Cambridge Studies in Advanced Mathematics) (Hardcover)
This outstanding monograph relates optimal control theory to the calculus of variations. The field has been sorely lacking a comprehensive and unifying text to bring together mathematics' most challenging and important legacies. Finally, Velimir Jurdjevic has closed that gap, in an impossibly brilliant yet gripping and thorough series of proofs that promise to define the burden of future research.
Velimir Jurdjevic, what can't he do?
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Inside This Book
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First Sentence:
Although differentiable manifolds have become familiar subjects to modern mathematicians, it still seems appropriate to begin with an introductory discussion of differentiable manifolds. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
abnormal extremal curves, regular extremal curve, exp tfi, control affine system, abnormal extremals, homogeneous polynomial vector field, extremal triple, extremal equations, absolutely continuous curve, controllable whenever, following differential system, vector field whose value, smallest vector space, reachable sets, elastic problem, lector fields, linear quadratic system, real analytic vector fields, kinetic analogue, regular extremals, linear quadratic problem, orbit theorem, constant vector fields, integrability theory, controllability properties Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Assume, Proof Suppose, Corollary Let New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Although differentiable manifolds have become familiar subjects to modern mathematicians, it still seems appropriate to begin with an introductory discussion of differentiable manifolds. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
abnormal extremal curves, regular extremal curve, exp tfi, control affine system, abnormal extremals, homogeneous polynomial vector field, extremal triple, extremal equations, absolutely continuous curve, controllable whenever, following differential system, vector field whose value, smallest vector space, reachable sets, elastic problem, lector fields, linear quadratic system, real analytic vector fields, kinetic analogue, regular extremals, linear quadratic problem, orbit theorem, constant vector fields, integrability theory, controllability properties Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Assume, Proof Suppose, Corollary Let New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 13
books:
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26
books
cite this book:
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- Calculus of Variations (Carus Monograph) by Gilbert Ames Bliss in Back Matter
- Spaces of Constant Curvature by Joseph A. Wolf in Back Matter
- Mathematical Control Theory: Deterministic Finite Dimensional Systems (Texts in Applied Mathematics, Vol. 6) by Eduardo D. Sontag in Back Matter
- Differential Equations: Dynamical Systems, and Control Science: Lecture Notes in Pure and Applied Mathematics Series/152 by K.D. Elworthy in Back Matter
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John in Back Matter
See all 13 books this book cites
- Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications by F. Monroy-Perez on 5 pages
- Mathematical Control Theory by John B. Baillieul on page 196, page 267, and page 320
- The Dynamics of Control (Systems & Control: Foundations & Applications) by Fritz Colonius in Back Matter (1), Back Matter (2), and Back Matter (3)
- Optimal Syntheses for Control Systems on 2-D Manifolds (Mathématiques et Applications) by Ugo Boscain on page 13, and Back Matter
- Control of Complex Systems by Karl J. Aström on page 410, and Back Matter
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