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Control Theory from the Geometric Viewpoint : Encyclopaedia of Mathematical Sciences - Andrei A. Agrachev

Control Theory from the Geometric Viewpoint

Encyclopaedia of Mathematical Sciences


Published: 15th April 2004
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This book presents some facts and methods of Mathematical Control Theory treated from the geometric viewpoint. It is devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations. The problems of controllability, state and feedback equivalence, and optimal control are studied. Some of the topics treated by the authors are covered in monographic or textbook literature for the first time while others are presented in a more general and flexible setting than elsewhere. Although being fundamentally written for mathematicians, the authors make an attempt to reach both the practitioner and the theoretician by blending the theory with applications. They maintain a good balance between the mathematical integrity of the text and the conceptual simplicity that might be required by engineers. It can be used as a text for graduate courses and will become most valuable as a reference work for graduate students and researchers.

Aus den Rezensionen:

"Der Band ist aus Graduiertenkursen an der International School for Advanced Studies in Triest entstanden ... Mathematisch werden gute Kenntnisse der Analysis, der linearen Algebra und der Funktionalanalysis vorausgesetzt. ... Bekannte und neue Beispiele ... illustrieren hier die Fulle an Aussagen in sehr anschaulicher Weise. Insgesamt ist so ein Band entstanden, der Mathematikern und mathematisch interessierten Anwendern wertvolle Anregungen bei der Auseinandersetzung mit gesteuerten bzw. geregelten nichtlinearen Systemen und deren Optimierung bietet."

(l. Troch, in: IMN - Internationale Mathematische Nachrichten, 2006, Issue 202, S. 44 f.)

Vector fields and control systems on smooth manifoldsp. 1
Elements of chronological calculusp. 21
Linear systemsp. 47
State linearizability of nonlinear systemsp. 53
The orbit theorem and its applicationsp. 63
Rotations of the rigid bodyp. 81
Control of configurationsp. 97
Attainable setsp. 109
Feedback and state equivalence of control systemsp. 121
Optimal control problemp. 137
Elements of exterior calculus and symplectic geometryp. 145
Pontryagin maximum principlep. 167
Examples of optimal control problemsp. 191
Hamiltonian systems with convex Hamiltoniansp. 207
Linear time-optimal problemp. 211
Linear-quadratic problemp. 223
Sufficient optimality conditions, Hamilton-Jocobi equation, and dynamic programmingp. 235
Hamiltonian systems for geometric optimal control problemsp. 247
Examples of optimal control problems on compact Lie groupsp. 265
Second order optimality conditionsp. 293
Jacobi equationp. 333
Reductionp. 355
Curvaturep. 363
Rolling bodiesp. 377
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540210191
ISBN-10: 3540210199
Series: Encyclopaedia of Mathematical Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 412
Published: 15th April 2004
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 3.18
Weight (kg): 1.73