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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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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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"...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
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- PublisherCambridge University Press
- Publication date1996
- ISBN 10 0521495024
- ISBN 13 9780521495028
- BindingHardcover
- Edition number1
- Number of pages512
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Geometric Control Theory (Cambridge Studies in Advanced Mathematics, Series Number 52)
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