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Agrachev A.A., Sachkov Yu.L. — Control theory from the geometric viewpoint
Agrachev A.A., Sachkov Yu.L. — Control theory from the geometric viewpoint



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Название: Control theory from the geometric viewpoint

Авторы: Agrachev A.A., Sachkov Yu.L.

Аннотация:

This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are
reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required.


Язык: en

Рубрика: Математика/Оптимизация и управление/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 416

Добавлена в каталог: 21.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Attainable set      13 134
Cartan's formula      150
Cauchy's formula      45
Chronological exponential, left      31
Chronological exponential, right      27
Conjugate point      227
Conjugate time      325 329
Connection      370
Connection, Levi — Civita      370
Control parameter      11
Control system      11
Control system, bilinear      311
Control system, completely controllable      47
Control system, control-affine      45
Control system, left-invariant      251
Control system, linear      45
Control system, linear, Brunovsky normal form      125
Control system, linear, Kronecker indices      123
Control system, right-invariant      251
Control system, single-input      312
Control, bang-bang      197 279
Control, singular      199 283
Controllability, local      311
Convex hull      139
Cost functional      133
Cotangent bundle      142
Cotangent bundle, canonical coordinates      142
Cotangent bundle, canonical symplectic structure      154
Cotangent bundle, trivialization      242
Cotangent space      142
Critical point, corank      289
Curvature, 2-dimensional systems      356
Curvature, 3-dimensional control-affine systems      366
Curvature, Gaussian      363
Derivation of algebra      22
Diffeomorphism      3
Differential      6
Differential form      143 146
Differential form, exterior differential      148
Differential form, integral      143 146
Differential form, interior product      150
Differential form, Lie derivative      149
Differential, second      288
distribution      72
Distribution, 2-generating      311
Distribution, integrable      72
Distribution, integral manifold      72
Dual basis      141
Dual space      141
Dubins car      194
Dubins car, with angular acceleration control      315
Dynamic programming      238
Dynamical system      6
Embedding      4
Endpoint mapping      218 285
Endpoint mapping, differential      297
Endpoint mapping, second differential      299
Equivalence, feedback      118
Equivalence, local state      74
Equivalence, local state-feedback      127
Exponential of vector field      33
Exterior k-form      144
Exterior product      144
Extremal      164
Extremal trajectory      164
Extremal, abnormal      177
Extremal, nice singular      308
Extremal, normal      177
Extremal, regular      302
Extremal, strictly abnormal      310
Extremal, totally singular      304
Family of functionals, regularity properties      25
Family of functions, regularity properties      24
Family of vector fields, bracket-generating      65 105
Family of vector fields, completely nonholonomic      65
Family of vector fields, full-rank      105
Family of vector fields, symmetric      61
Feedback transformation      118
Filippov's theorem      136
Flow      25
Frobenius condition      73
Fuller's phenomenon      322
General Position Condition      205
Group, general linear      249
Group, orthogonal      250
Group, special linear      250
Group, special orthogonal      250
Group, special unitary      250
Group, unitary      250
Hamilton — Jacobi equation      238
Hamiltonian      155
Hamiltonian system      155
hessian      287
Immersion      62
Index of quadratic form      291
Integral invariant of Poincare — Cartan      230
Isotropic space      161
Jacobi equation, in moving frame      362
Jacobi equation, regular case      327
Jacobi equation, singular case      331
Jacobi identity      35
Lagrangian subspace      161
Lebesgue point      170
Lie algebra      36
Lie algebra, structural constants      249
Lie bracket of vector fields      15
Lie bracket, formula in coordinates      15
Lie group      249
Lie group, linear      250
Lie subgroup      252
Lie's theorem      253
Liouville 1-form      153
Manifold      2
Manifold, Riemannian      367
Manifolds, diffeomorphic      3
Mapping, locally open      288
Mapping, proper      4
Mapping, smooth      3
Module      69
Module, finitely generated      69
Module, locally finitely generated      71
Morse's lemma      291
Needle-like variations      171
ODE      6
ODE, nonautonomous      26
Optimal control      134
Optimal control problem      134
Optimal trajectory      134
Optimality condition, Goh      305 309
Optimality condition, Legendre      301 308
Optimality condition, Legendre, generalized      307 309
Optimality condition, Legendre, generalized, strong      307
Optimality condition, Legendre, strong      302
Optimality conditions, necessary      163 309
Optimality conditions, sufficient      232 235 336 344
Optimality, geometric      285
Optimality, local finite-dimensional      289
Optimality, local geometric      289
Optimality, strict strong      336
Optimality, strong      336
Orbit      61
Parallel translation      370
Point, Poisson stable      112
Poisson bracket      157
Pontryagin maximum principle      164 173 176 178 183
Problem, linear time-optimal      205
Problem, linear-quadratic      217
Problem, Riemannian      259
Problem, sub-Riemannian      261 309
Problem, time-optimal      139
Reachable set      13
Reduction      345
Relaxation      139
Relaxed system      140
Riemannian structure      367
Rigid body      79
Rigid body, angular velocity      80
Rigid body, Euler equations      84
Space of control parameters      11
State      11
State space      11
Submanifold      1
Submanifold, immersed      62
Switching function      279
Symplectic manifold      155
Symplectic space      161
Symplectic structure      155
Tangent space      4 5
Tangent vector      4
Tautological      1-form
Topology, $c^\infty(M)$      24
Transversality conditions      178
Variations formula      40
Vector field      5 25
Vector field, autonomous      33
Vector field, compatible      109
Vector field, complete      8 27
Vector field, conservative      113
Vector field, flow      10
Vector field, Hamiltonian      155
Vector field, Hamiltonian lift      159
Vector field, nonautonomous      25
Vector field, parallel      370
Vector field, Poisson stable      112
Vector field, with compact support      27
Vector fields, commutator      15
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