Bhaya A., Kaszkurewicz E. — Control Perspectives on Numerical Algorithms and Matrix Problems :: Электронная библиотека попечительского совета мехмата МГУ

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Bhaya A., Kaszkurewicz E. — Control Perspectives on Numerical Algorithms and Matrix Problems

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Название: Control Perspectives on Numerical Algorithms and Matrix Problems

Авторы: Bhaya A., Kaszkurewicz E.

Аннотация:

This book organizes the analysis and design of iterative numerical methods from a control perspective. A variety of applications are discussed, including iterative methods for linear and nonlinear systems of equations, neural networks for linear and quadratic programming problems and integration and shooting methods for ordinary differential equations.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 2006

Количество страниц: 272

Добавлена в каталог: 11.04.2010

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Предметный указатель

$C_{d}$       44
$C_{s}$       44
$\delta$ -iteration      107
$\delta$ -iteration, stabilization of frequency of appearance of      107
$\Gamma$ set of local minimizers      150
$\gamma$ -iteration      107
$\Omega$ feasible set      150
Absolute error      68
Absolute stability theory      68
Abu — Mostafa, Y      174
Adaptive filtering      82
Adaptive stepsize formulas,simplification of      62
Adaptive time-stepping, conceptual description of      180
Akilov, G.      84
Alaghband, G      174
Alber, Ya. I.      65 89 90
Algebraic Riccati equation      208
Algorithm, conjugate gradient as dynamic controller      83
Algorithm, conjugate gradient CLF/LOC version      81
Algorithm, conjugate gradient continuous version of      88
Algorithm, conjugate gradient robustness of      80
Algorithm, conjugate gradient standard form of      81
Algorithm, conjugate gradient “Jacobi” version of      82
Algorithm, continuous Jacobian matrix transpose (CJT)      47 49 50
Algorithm, continuous Newton (CN)      46
Algorithm, Goh’s conceptual      112
Algorithm, Jacobian matrix transpose variable structure (JTV)      48
Algorithm, Krylov subspace      72
Algorithm, Newton variable structure (NV)      47 97
Algorithm, Newton — Raphson      94 96
Algorithm, Orthomin(2)      82
Algorithm, QR as nonlinear discrete dynamical system      228
Algorithm, speed gradient      37
Algorithm, variable structure Jacobian transpose (VJT)      47
Alhanaty, M.      228
Aluffi, F.      56 91
Alvarez, F.      91
Amari, S. I.      141 142 166
Amicucci, G L.      90
Analog computation      xxi 132
Anderson, B. D. O.      229
Anderson, C.      174
ANN learning parameters as control gains      133
Antipin, A. S.      177
Approximation, minimal residual      72
Arc, bang-bang      111
Arc, bang-intermediate      111
Ariyur, K. B      228
Armentano, V. A.      209
Arrow, K. J.      90 177
Artificial neural network (ANN)      132
As reaching phase CLF      148
Ascher, U.      197 224
Ashida, S.      66 68 229
Astrom, K. J.      1 75 196
Asymptotic stability, continuous-time definition of      21
Asymptotic tracking      3
Athans, M.      95
Attouch, H      86 91
Augmented equation      175
Augmented system      158
Axelsson, O.      224
Backpropagation      133
Backpropagation with momentum (BPM)      83
Balakrishnan, V.      229
Bang-bang arc      111
Bang-intermediate arc      111
Bardn, B.      90 109
Barnett, S.      220
Bart, H.      230
Bartlett, P. L.      170
Batterson, S.      228
Bauer, F. L.      200
Bellman, R. E.      119 125 230
Bercovier, M.      228
Bertsekas, D. P.      89 90 128 129 177
Best separating hyperplane problem as QP      169
Bezout number      219 222
Bezout theorem      219
Bhattacharyya, S. P.      75
Bhaya, A.      37 61 66 68 82 90 109 124 136 164 173 174 176 177 205 209—211 219 222
Bilinear system      76
Bloomfield, P.      142
Boggs, P. T.      56 65 66 90 91
Bolte, J.      91
Boltyanskii, V.      10 39 95
Bornemann, F.      181 186 191 224
Bose, N. K.      199 218 219 231
Boundary value problem, two point (TPBVP)      9
Bounded control      96 111
Boyd, S.      xxiv 229
BPM (backpropagation with momentum)      83
BPM (backpropagation with momentum) is equivalent to conjugate gradient      83
BPM (backpropagation with momentum), CG methods, as heavy ball with friction method      84
BPM (backpropagation with momentum), HBF ODE as continuous analog of      86
Braatz, R. D.      200
Brabanter, J. D.      173
Brady, G      174
Branin, F. H      53 54 94 125
Branin’s function      52 62
Brezinski, C      65 66 91 109
Brockett, R. W.      xxiii
Brune, O.      212
Bryson, A. E.      125
Buckingham, N. J.      90
Cain, B. E.      225
Callier, F. M      4 12 39
Calvert, B. D.      174
Campbell, S. L.      xxiii
Campbell’s question      xxiii
Cannon, M. D.      118
Canonical form, Kalman — Gilbert      13
Carey, G F      224
Cauchy — Riemann equations      100
Cauchy’s interlacing theorem      206
Chan, M.      211
Chang, P. S.      82 91
Change of coordinates      45
Chao, K. S.      94 124
Characteristic equation      8
Chen, C. — T.      4 39
Chen, G. — A.      83 91
Chen, H. C      174
Chen, J. D      142
Cheng, S. — X.      91
Cheung, J. Y.      142
Chong, E. K. P      166 177
Chu, M. T.      xxiii 90
Cichocki, A.      133 137 138 141 142 166 177
Clarke, F.H.      31 39 144
CLF (control Liapunov function)      24 42 44 45 50 66 76 82 101 161 163
CLF (control Liapunov function), 1-norm as nonsmooth      47
CLF (control Liapunov function), choice of      84
CLF (control Liapunov function), controller structure determined by      55
CLF (control Liapunov function), definition of      24
CLF (control Liapunov function), nonsmooth      102 104
CLF (control Liapunov function), quadratic      54 55 59
CLF (control Liapunov function), reaching phase      148
CLF (control Liapunov function), relation between continuous- and discrete-time      65
CLF approach      56
CLF approach in Hilbert space setting      84
CLF/LOC approach      46 58 76 83
CLF/LOC approach, design of static controllers by      46
CLF/LOC lemma      58 59 61
CLF/LOC method      37 52
Closed-loop system      44
CN and NV trajectories, comparison of      57
Computational energy function      130
Conceptual iterative method for minimization, optimal control formulation of      112
Condition number geometrical interpretation of      201

Condition number geometrical interpretation of optimal      200
Configuration, standard unity feedback      3 7
Conjugate gradient method      77
Conjugate gradient, as acceleration of Richardson’s method      78
Constraint qualification      151
Constraint set, active      151
Constraint set, violated      151
Continuous algorithms, discrete-time versions of      60
Continuous algorithms, discretization methods for      65
Continuous algorithms, numerical simulation of      56
Continuous Jacobian matrix transpose (CJT)      47—49
Continuous method      xxi
Continuous Newton (CN)      46 48 49 53 57
Continuous Newton method      86
Continuous Newton method, exponential stability of      49
Continuous Newton method, integrated form of      50
Continuous optimization methods      85
Continuous version of      85
Continuous version of nonstationary PD controller interpretation      78
Continuous version of proportional-derivative controller interpretation of      77
Control input, stepsize as      66
Control Liapunov function (CLF)      24 42 44 45 50 66 76 82 101 161 163
Control Liapunov function (CLF) 1-norm as nonsmooth      47
Control Liapunov function (CLF), choice of      84
Control Liapunov function (CLF), controller structure determined by      55
Control Liapunov function (CLF), definition of      24
Control Liapunov function (CLF), nonsmooth      102 104
Control Liapunov function (CLF), quadratic      54 55 59
Control Liapunov function (CLF), reaching phase      148
Control Liapunov function (CLF), relation between continuous- and discrete-time      65
Control system, gradient stabilization of      34
Control system, variable structure      27
Control, deadbeat      7 75
Control, equivalent      31
Control, integral      5
Control, Liapunov optimizing (LOC)      24 45 47
Control, nilpotency of iteration matrix      75
Control, optimal      8
Control, performance index for      8
Control, proportional-integral-derivative (PID)      6
Control, relaxed      117
Control, saturated      111
Control, state space      2
Controllability      3
Controllability subspace      71
Controllable companion form matrix      220
Controllable realization      220
Controllable subspace, noninvariance of      14
Controller      xx 43 58 198
Controller, dynamic      44
Controller, dynamic nonstationary      85
Controller, dynamic time-varying conjugate gradient algorithm as      83
Controller, optimal state feedback      9
Controller, proportional      77
Controller, proportional-derivative (PD)      85
Controller, proportional-integral (PI)      7
Controller, static dynamic, CLF design of      44
Controller, static nonstationary      85
Controller, static state-dependent      44
Controller, static stationary      85
Convergence, global      15
Convergence, local      15
Convergence, used loosely      16
Convex programming problem, GDS for      146
Convolution, discrete-time      7
Coprime polynomials      220
Cortes, C.      172
Cost function      93 95 97
Costate      9
Costate equation      9
Costate in stepsize control problem      188
Costate vector      8
Coupled bilinear systems CLF analysis of      79
Coutinho, A. L. G A.      224
Cox, D. A.      224 225
Cristianini, N.      169 177
Critical point      32
Cullum, C. D.      118
Dahlquist, G.      229
Damping, critical      7
Datta, B. N.      xxiv 199
Davidenko, D.      90
DC1      55
DC2      55
DC3      55 89
DC4      55 89
DDC1      61
DDC2      61
DDC3      61
DDC4      61
DDP (differential dynamic programming)      118
DDP (differential dynamic programming), backward run      123
DDP (differential dynamic programming), brief description of      123
DDP (differential dynamic programming), computational effort of      119
DDP (differential dynamic programming), computational requirements      124
DDP (differential dynamic programming), convergence of      124
DDP (differential dynamic programming), forward run      123
De Figueiredo, R. J. P.      94 124
De Moor, B.      173
De Souza, E.      75
Deadbeat control      83 183 196
Decentralization constraint      208
Decentralized feedback control problem      208
Decentralized integral control      211
Decker, D. W.      53 90
Deficient polynomial equation      219
Delchamps, D. F.      4 39
Demmel, J. W., xxiv      199
Demyanov, V. F      31
Dennis, J. E.      65 90
Derivative action      78
Desoer, C. A.      4 12 39
Deuflhard, P.      181 186 191 224
Deviation      42
Diagonal preconditioning as decentralized feedback      204
Diagonal preconditioning as pole clustering      207
Diagonal-type function      25
Dias, R. J.      219 222
Diene, O., xxiv      82
Diener, I.      53 90
Difference equation      15
Difference equation, autonomous      15
Difference equation, time-invariant      15
Differential dynamic programming (DDP)      118
Differential dynamic programming (DDP), backward run      123
Differential dynamic programming (DDP), brief description of      123
Differential dynamic programming (DDP), computational effort of      119
Differential dynamic programming (DDP), computational requirements      124
Differential dynamic programming (DDP), convergence of      124
Differential dynamic programming (DDP), forward run      123
Differential equation, matrix Riccati      9
Differential inclusion      31 35
Differential inequality      98 102 150 156
disclaimers      xxii 84
Discontinuity set      142
Discontinuity surface      148 150
Discontinuous control      98
Discontinuous Persidskii-type system      101
discrete derivative      79
Discrete dynamical system, nonautonomous      17
Discrete dynamical system, time-varying      17
Discrete probability density, relation to transfer function      229
Discrete-time      17
Discrete-time Jacobian matrix transpose method (DJT)      60—62
Discrete-time Jacobian matrix transpose variable structure method (DJTV)      60—62
Discrete-time Newton method (DN)      60 62
Discrete-time Newton variable structure method (DNV)      60 62
Discrete-time variable structure Jacobian matrix transpose method (DVJT)      60—62
Distance from point to set      18
Dixon, L. C. W.      53 90

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