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E-raamat: Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications illustrated edition [World Scientific e-raamat]

Edited by (Univ De Bourgogne, France), Edited by (Univ De Bourgogne, France), Edited by (Univ Autonoma Metropolitana-azcapotzalco, Mexico), Edited by (Univ Autonoma Metropolitana-azcapotzalco, Mexico)
  • Formaat: 496 pages, Illustrations
  • Ilmumisaeg: 30-Jan-2002
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789812778079
Teised raamatud teemal:
  • World Scientific e-raamat
  • Hind: 184,80 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Contemporary Trends in Nonlinear Geometric Control Theory and Its Applications illustrated editionSuurem pilt
  • Formaat: 496 pages, Illustrations
  • Ilmumisaeg: 30-Jan-2002
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789812778079
Teised raamatud teemal:
World Scientific e-raamatudRohkem infot World Scientific e-raamatute kohta
Raamatu kodulehekülg: http://www.worldscientific.com/worldscibooks/10.1142/4879#t=toc
Mathematical control theory has evolved from the study of practical problems in engineering and sciences to the elaboration of deep, important concepts in mathematics and applied sciences. This volume concerns contemporary trends in nonlinear geometric control theory and its applications. It is a fine collection of papers presenting new results, relevant open problems, and important applications regarding academic and real-world problems.The book is dedicated to Velimir Jurdjevic whose scientific activity has been influential in the research of many of the authors. It contains a number of articles specially written by colleagues and friends of Vel Jurdjevic, all of them leading applied mathematicians and control theorists. There is also place for surveys on topics of current research which present the state of the art of modern geometric control theory. Finally, the volume contains several new mathematical ideas generated by geometric control theory techniques, which may initiate new directions of research beyond control theory.
Foreword xiii
Part I Invited Survey
Chapters		 1(166)
Variational Problems on Lie Groups and their Homogeneous Spaces: Elastic Curves, Tops, and Constrained Geodesic Problems
3(50)
V. Jurdjevic
F. Monroy-Perez
Introduction
3(3)
Space forms and their frame bundles
6(13)
Hamiltonians and the extremal curves
19(34)
Controllability of Lie Systems
53(24)
J. D. Lawson
D. Mittenhuber
Introduction
53(1)
Control systems on Lie groups
54(3)
Groups irrelevant for transitivity
57(2)
Exploiting compactness and irrelevancy
59(2)
Irrelevant groups and algebras
61(3)
Irrelevant groups and algebras: the solvable case
64(11)
Irrelevant groups and algebras: the semisimple case
75(2)
Canonical Contact Systems for Curves: A Survey
77(36)
W. Respondek
W. Pasillas-Lepine
Introduction
77(3)
The canonical contact system for curves
80(3)
History
83(5)
Involutive subdistributions of corank one
88(4)
Contact systems, characteristic distributions and involutive subdistributions
92(10)
Flatness of contact systems
102(3)
An example
105(2)
Singular points and extended Kumpera-Ruiz normal forms
107(6)
The Brachistochrone Problem and Modern Control Theory
113(54)
H.J. Sussmann
J. C. Willems
Introduction
113(5)
Johann Bernoulli and the brachistochrone problem
118(5)
The standard formulation and Johann Bernoulli's solution
123(5)
Spurious solutions and the calculus of variations approach
128(3)
The optimal control approach
131(5)
The differential-geometric connection
136(14)
Five modern variations on the theme of the brachistochrone
150(17)
Part II Contributed
Chapters		 167(306)
Symplectic Methods for Strong Local Optimality in the Bangbang Case
169(14)
A. A. Agrachev
G. Stefani
P. L. Zezza
Introduction
169(2)
Main results
171(5)
Sketch of the proof
176(7)
Charges in Magnetic Fields and Sub-Riemannian Geodesics
183(20)
A. Anzaldo-Meneses
F. Monroy-Perez
Introduction
183(1)
Sub-Riemannian geometry and classical particles
184(4)
Polynomial magnetic fields
188(7)
Linear magnetic fields, and Cartan's five dimensional case
195(8)
Topological Versus Smooth Linearization of Control Systems
203(14)
L. Baratchart
J. B. Pomet
M. Chyba
Introduction
203(3)
Preliminaries on equivalence of control systems
206(2)
Main result on topological linearization
208(3)
An open question
211(2)
Implications in control theory
213(4)
Local Approximation of the Reachable Set of Control Processes
217(16)
R. M. Bianchini
Introduction
217(1)
Tangent cones
218(7)
Examples of g-variations
225(3)
Applications
228(2)
Open Problems
230(3)
Geometric Optimal Control of the Atmospheric Arc for a Space Shuttle
233(24)
B. Bonnard
E. Busvelle
G. Launay
Introduction
233(2)
The model
235(3)
The control problem
238(2)
The minimal principle without state constraints-extremal curves
240(9)
Optimal control with state constraints
249(8)
High-Gain and Non-High-Gain Observers for Nonlinear Systems
257(30)
E. Busvelle
J. P. Gauthier
Introduction, systems under consideration
257(4)
Justification of the assumptions and observability
261(3)
Statement and proof of the theoretical result
264(9)
Application: observation of a binary distillation column
273(10)
Appendix: Technical lemmas
283(4)
Lie Systems in Control Theory
287(18)
J.F. Carinena
A. Ramos
Introduction
287(1)
Systems of differential equations admitting a superposition rule
288(2)
Control and controllability of systems on Lie groups
290(1)
The Wei-Norman method
291(1)
Illustrative examples
292(13)
From the Geometry to the Algebra of Nonlinear Observability
305(42)
S. Diop
Introduction
305(3)
The differential algebraic geometric approach
308(11)
Computing
319(28)
Appendix: Basic differential algebraic geometry
328(6)
Appendix: Characteristic sets
334(13)
Existence Theorems in Nonlinear Realization Theory and a Cauchy-Kowalewski Type Theorem
347(12)
B. Jakubczyk
Introduction
347(1)
Existence of analytic realizations
348(3)
Convergence along vector fields and their commutators
351(3)
Existence of analytic solutions of PDE's
354(5)
Normality, Local Controllability and NOC for Multiobjective Optimal Control Problems
359(22)
A. Jourani
Introduction
359(4)
Background
363(5)
Normality implies seminormality
368(4)
Hamiltonian normality implies seminormality
372(1)
Normality implies seminormality for systems of Mayer type
373(2)
NOC for multiobjective optimal control problems
375(6)
Controllability and Coordinates of the First Kind
381(24)
M. Kawski
Introduction
381(2)
Integral manifolds and controllability
383(4)
Separating invariant flows from time-varying functionals
387(4)
Coordinates of the 1st kind
391(4)
Supporting hyperplanes
395(10)
Variational Equations of Lagrangian Systems and Hamilton's Principle
405(18)
H. N. Nunez-Yepez
J. Delgado
A. L. Salas-Brito
Introduction
405(1)
The variational principle
406(3)
Symmetries and constants of motion
409(3)
Intrinsic formulation
412(5)
Examples
417(6)
Control of the Hovercraft Vessel: A Flatness plus Second Order Sliding Mode control Approach
423(18)
H. Sira-Ramirez
Introduction
423(1)
The hovercraft model
424(5)
Trajectory tracking for the hovercraft system
429(4)
Simulation results
433(8)
Optimality of Singular Trajectories and Asymptotics of Accessibility Sets under Generic Assumptions
441(18)
E. Trelat
Introduction
441(2)
Optimality of singular trajectories
443(8)
Asymptotics of the accessibility sets
451(8)
Control Theory and Holomorphic Diffeomorphisms
459(14)
D. Varolin
Introduction
459(1)
Complex analytic considerations
460(2)
Holomorphic vector fields
462(4)
Jets
466(7)
Index 473


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