Geometric Control Theory

Geometric Control Theory

by Velimir Jurdjevic, Jurdjevic Velimir
     
 

ISBN-10: 0521058244

ISBN-13: 9780521058247

Pub. Date: 01/28/2008

Publisher: Cambridge University Press

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…  See more details below

Overview

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. The author 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.

Product Details

ISBN-13:
9780521058247
Publisher:
Cambridge University Press
Publication date:
01/28/2008
Series:
Cambridge Studies in Advanced Mathematics Series, #52
Edition description:
New Edition
Pages:
512
Product dimensions:
6.00(w) x 8.80(h) x 1.30(d)

Table of Contents

Introduction
Acknowledgments
Pt. 1Reachable sets and controllability1
1Basic formalism and typical problems3
2Orbits of families of vector fields32
3Reachable sets of Lie-determined systems64
4Control affine systems95
5Linear and polynomial control systems125
6Systems on Lie groups and homogeneous spaces150
Pt. 2Optimal control theory195
7Linear systems with quadratic costs199
8The Riccati equation and quadratic systems228
9Singular linear quadratic problems259
10Time-optimal problems and Fuller's phenomenon300
11The maximum principle332
12Optimal problems on Lie groups368
13Symmetry, integrability, and the Hamilton-Jacobi theory407
14Integrable Hamiltonian systems on Lie groups: the elastic problem, its non-Euclidean analogues, and the rolling-sphere problem444
References483
Index489

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