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