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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.
Язык: Рубрика: Computer science /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1 editionГод издания: 1967Количество страниц: 145Добавлена в каталог: 14.04.2010Операции: Положить на полку |
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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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