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Bellman R.E. — Introduction to the mathematical theory of control processes (Volume I: Linear Equations and Quadratic Criteria)
Bellman R.E. — Introduction to the mathematical theory of control processes (Volume I: Linear Equations and Quadratic Criteria)

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Название: Introduction to the mathematical theory of control processes (Volume I: Linear Equations and Quadratic Criteria)

Автор: Bellman R.E.

Аннотация:

A new mathematical discipline has emerged from the bustling scientific activity of the last fifteen years, the theory of control processes. Its mathematical horizons are unlimited and its applications increase in range and importance with each passing year. Consequently, it is reasonable to believe that introductory courses in control theory are essential for training the modern graduate student in pure and applied mathematics, engineering, mathematical physics, economics, biology, operations research, and related fields.
The extremely rapid growth of the theory, associated intimately with the continuing trend toward automation, makes it imperative that courses of this nature rest upon a broad basis. In this first volume, we wish to cover the fundamentals of the calculus of variations, dynamic programming, discrete control processes, use of the digital computer, and functional analysis.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1967

Количество страниц: 145

Добавлена в каталог: 14.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adaptive control      8 214
Additivity      105
Adjoint operator      82 220
Adorno, D.      137 214
Approximation in policy space      185 208
Aris, R.      8
Asymptotic behavior      46 156 170 181
Asymptotic control      57 99
Asymptotic theory      214
Athans, M.      8
Bang-bang control      47 48 124
Bart, A.      47
Beckenbach, E.F.      93 99 216
Beckwith, R.      137 214
Beesack, P.R.      93
Bellman, R.      8 9 26 27 46 47 48 93 94 96 98 99 100 129 130 131 133 135 136 137 164 197 198 209 210 211 213 214 215 216 238 240
Bertram, J.E.      95
Biological systems      8
Brobeck, J.P.      8
Brockett, R.W.      46
Brown, T.A.      94 215
Bucy, R.      99
Buell, J.      47
Bushaw, D.W.      47
Butkovskii, A.G.      216
Calculus of variations      13 49 54 126 135 137 164 165
Calogero, F.      130
Canonical representation      146
Cauchy — Schwarz inequality      219
Cause and effect      136
Cesari, L.      46 47
Characteristic functions      129
Characteristic roots      146
Characteristic vectors      146
Checkers      136
Chemical reactors      8
Chemotherapy      8 47
Chess      136
Coddington, E.      27
Cole, W.J.      93
complexity      5
Computational aspects      173 183
Constraints      76 234
Continued fractions      214
Controllability      177
Cooke, K.L.      26 46
Courant parameter      65
Cox, H.      211
Cremer, H.      27
Cybernetics      102
Dantzig, G.B.      216
Decomposition principles      216
Design      37
Desoer, C.A.      136
Difference equations      23
Differential equations      27
Differential inequality      15
Differential-difference equations      26 46
Discrete control process      116 193
Distributed parameter systems      216
Distributed parameters      204
Dreyfus, S.      100 135 136 137
Duality      99
Duality theory      82
Dynamic programming      8 99 100 101 136 178
Effertz, F.H.      27
Equilibrium      31
Euler equation      52 67 166 208
Euler, L.      51 99
Extrapolation      189 215
Eykhoff, P.      8
Feedback control      5 38 47 95 101
Fredholm integral equation      237
Fredholm resolvent      137 238
Freimer, M.      137 214
Friedrichs, K.O.      99
Friend, M.B.      9
Fundamental lemma      15 54
Gauss method of elimination      210
Geodesic      107
Glicksberg, I.      46 48 137 240
Global constraints      114
Gould, L.A.      95
Governor      47
Green's function      22 27 72 74 100 129 137 209 232
Grodins, F.S.      8 47
Gross, O.      46 48 137 240
Haar's device      54
Haar, A.      99
Hardy, G.H.      92 93
Hilbert space      218 240
Hori, J.      212
Horowitz, I.M.      8
Hurwitz, A.      27
Idealization      31
Identification      3
Ill-conditioned linear systems      195
Ince, E.L.      27 100
Inequalities      87 92 99 191 216
Infinite control process      59
Infinite process      110
information      40 103 127
inhomogeneous equation      12
Initial psychiatric interview      9
Invariant imbedding      159 173 214
Inverse matrix      140
Inverse problem      133
Jacobi matrix      209
Jacobi, K.G.J.      154
Jacobs, O.L.R.      94
Jacquez, J.      8 47
Jordan canonical form      156
Kagiwada, H.      215
Kaiser, J.F.      95
Kalaba, R.      8 46 47 100 131 133 136 197 198 214 215 216
Kalman, R.E.      95 137 214
Kato's lemma      161
Koepcke, R. W.      214
Kramer, J.D.R.Jr.      195 214
Kronecker product      162 197
Kurland, L.      9
Lagrange multiplier      115 198 216 231
Lagrange parameter      77
Lapidus, L.      214
Laplace transform      12
LaSalle, J.P.      48
Lebesgue integral      50
Lehman, S.      129 130 209 210
Levinson, N.      27 211
Limiting behavior      110
Linear chains      212
Linear operators      220
Linear prediction      211
Linear programming      216
Linear systems      22
Liouville — Neumann solution      230
Littlewood, J.E.      92 93
Local constraints      121
Lockett, J.      197 198 216
Mathematical economics      77
Mathematical physics      13
Matrix      140
Matrix exponential      152
Matrix theory      100 138 216
Maxwell, J.C.      47
Merriam, C.W.III      95
Miller, K.S.      129
Min-max operations      130
Minimizing property      56
Minkowski's inequality      93
Minorsky, N.      46 47
Monotone convergence      186
Monotonicity      77
Morgenstern, O.      100
Morse, M.      164
multiple constraints      88
Multipoint boundary-value problems      46
Multistage dynamic programming      101
Multistage linear programming      216
Nagy, B.Sz.      240
Newton, G.C.      95
Noisy dynamic systems      211
Noncummutative      42
Nonlinear boundary-value problems      100
Nonlinear filtering theory      215
Nonlinear oscillations      46
Nonlinear summability      215
Norms      143
Numerical aspects      227
Numerical inversion      216
Numerical solution      33
Optimal control      8
Optimal policy      104 107
Optimality      8
Orthogonal matrix      145
Orthogonality      26
Osborn, H.      137
Oscillation      29
Ostrowski, A.M.      208
Paiewonsky, B.      8
Pappo, H.A.      8
Parseval's theorem      85
Partial differential equation      108
Partitioning      187
Pattern recognition      137
Pearson, J.D.      99
Penalty      65
Pendulum      31
Perturbation      34
Perturbation methods      240
Perturbation series      97 162
Perturbation techniques      47
Phase space      102
Physiological controls      8
Plant adaptive systems      8
Poincare — Lyapunov theory      33 46
Policy      103 136
Positive definite      149 220
Positive definite kernel      74 88
Positivity      130
Prestrud, M.      215
Price      76 115 231
Principle of optimality      107 114 117 179 193
Proportional control      39
Quadrature techniques      34
Quantum mechanical scattering      130
Quasilinearization      98 100 131
Rayleigh — Ritz method      100
Reciprocity      99
Reciprocity relation      22
Recurrence relation      117
Reduction of dimensionality      199 216
Reid, W.T.      164 215
Resolvents      129
Respiratory control      47
Riccati differential equation      211
Riccati equation      15 25 46 93 109 113 118 130 134 159 164 180 184 214
Richardson, J.M.      47 100
Riemann integral      50
Riesz representation theorem      224
Riesz, F.      240
Roberts, S.M.      8
Round-off      34
Schiffer, M.M.      129
Schultz, W.C.      8
Second method of Lyapunov      95
Selberg quadratic form      213
Shapiro, E.      214
Simmons, P.L.      8
Simulation      9 104
Slightly intertwined systems      205
Smoothing      211
Smoothing process      72
Sridhar, R.      215
Stability      28
Stability matrix      161
Stability theory      46
State      103 136
State space      136
Steady state behavior      120
Steady state regime      58
Strong convergence      219
Sturm — Liouville equation      26
Sturm — Liouville theory      68 79 85 100
Successive approximations      65 99 153 184 202
Summation by parts      25
Switching      124 136
symmetric      144
System identification      137
systems      2
Temple, G.      161
Terminal control      63 216
Theory of games      100
Time lags      214
Time-dependent control process      113
Time-optimal control      48
Todd, O.T.      141
Tomastik, E.C.      164
Tou, J.T.      214
Trace      147
Transplantation      135
Trefftz      99
Triangle inequality      144
Two-point boundary condition      13 33
Two-point boundary problems      112
Two-point boundary-value problems      94 164
Twomey, S.      198
Tychonov      198
Uncertainty      7 9
Unknown external forces      90
Unknown influences      125
Variation of parameters      20
Variation-diminishing property      74
Vector      139
Vishnegardskii      47
von Neumann, J.      100
Weak convergence      219
Wiener, N.      211
Wigner, E.P.      160
Wing, G.M.      215
Wirtinger's inequality      93
Wolfe, P.      216
wronskian      18 163
Yamamoto, W.S.      8
Yanase, M.M.      160
Zadeh, L.A.      136
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