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| Bhaya A., Kaszkurewicz E. — Control Perspectives on Numerical Algorithms and Matrix Problems |
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| Предметный указатель |
DJT (discrete-time Jacobian matrix transpose method) 60—62
DJTV (discrete-time Jacobian matrix transpose variable structure method) 60—62
DN (discrete-time Newton method) 60 62
DNV (discrete-time Newton variable structure method) 60 62
Dongarra, J. 77
Doyle, J. 5
Dreyfus, S. E. 230
Dual system, unobservable subspace 13
Duane, G 174
DVJT (discrete-time variable structure Jacobian matrix transpose method) 60—62
Dynamic controller as second-order dynamical system 56
Dynamic controller, prototypical stability result for 55
Dynamic programming 119
Dynamic programming, applied to quantum mechanics 230
Dynamic programming, computational effort of 119
Dynamical system, feedback control perspective on 43
Dynamical system, neural-gradient 127
Dynamical system, zero finding 42
Dynamics, second order 7
Edwards, C. 39
Egerstedt, M. B. 227
Eigenvalue shift as control input 228
El Ghaoui, L. 229
Elaydi, S. N 39
Emelin, I. V. 107 124
Energy function 32 128 130 147 160 161 172
Energy function with switching 151
Energy function, Persidskii type 136
Energy function, relation of Liapunov function to 132
EPS (error per step) 181
EPUS (error per unit step) 181
Equilibrium point 15
Equilibrium, asymptotically stable 16
Equilibrium, attractive 16
Equilibrium, exponentially stable 16
Equilibrium, globally asymptotically stable 16
Equilibrium, globally attractive 16
Equilibrium, globally exponentially stable 16
Equilibrium, stable 15
Equilibrium, stable in the sense of Liapunov 15
Equilibrium, unstable 15
Equivalent control 31 36
Erlanson, R 174
Error 42
Error dynamics, state variable description of 186
Error equation 196
Error generating coefficient 186
Error Per Step (EPS) 181
Error Per Unit Step (EPUS) 181
Error, local versus global 180
Euler discretization 65
Evtushenko, Yu. G 90
Exact penalty function 159 160 170
Exponential stability, continuous-time definition of 21
Extraneous singularity 52
Extremum seeking control 228
Factor coprime polynomials 223
Falb, P.L. 95
Fan, M. K. H 211 225
Feasible region, convex polytope 151
Feedback 41
Feedback control system iterative learning control as 198
Feedback gain 44
Feedback law 44
Feron, E. 229
Ferreira, L. V. xxiv 164 173 174 176
Field of values 77
Filippov solution 47 142
Filippov solution, description of 30
Filippov solution, desired properties of 29
Filippov solution, interpretation 30
Filippov solution, nonsmooth analysis 30
Filippov, A. F 29 35
Finite-time convergence 37 98 102 149 150 156 157 176
Finite-time convergence to 149
Fixed point 15
Fletcher and Powell’s function 121
Forsythe, G E. 200
Forward Euler discretization 58 64
Forward Euler Method 95 105 137 186
Fradkov, A. L. 37 38 51
Francis, B. A. 5
Fuhrmann, P. A 229
Function as subdifferential of max  27
Function as subdifferential of |x| 26
Function, control Liapunov (CLF) 24
Function, convex 30
Function, diagonal type 25
Function, half signum (hsgn) 26
Function, Liapunov 16 127
Function, nonconvexity of 115
Function, positive definite 16 22
Function, positive real 212
Function, positive semidefinite 22
Function, Rosenbrock 118
Function, set of zeros of 53
Function, signum (sgn) 26
Function, strictly positive real 212
Function, subdifferential of 30
Function, subgradient of 30
Function, upper half signum (uhsgn) 27
Function, upper half signum, as subdifferential of max 27
Gamkrelidze, R. 10 39 95
Gauss — Seidel method 140
Gavurin, M. K. 90
Gawthrop, P. J. 132
GDS (gradient dynamical system) 31 127 130 140 146 152 172
GDS (gradient dynamical system) as generalized Persidskii-type system 35
GDS (gradient dynamical system) as LP solver 154
GDS (gradient dynamical system) with discontinuous right-hand side 35
GDS (gradient dynamical system), convergence phase analysis 153
GDS (gradient dynamical system), definition of smooth 31
GDS (gradient dynamical system), discontinuous, convergence analysis of 150
GDS (gradient dynamical system), geometrical description of 32
GDS (gradient dynamical system), Liapunov stability of 130
GDS (gradient dynamical system), natural Liapunov function for 32 130
GDS (gradient dynamical system), nonsmooth 35
GDS (gradient dynamical system), stability of equilibria 32
GDS linear programming solver, example of trajectories of 165
GDS quadratic programming solver, sliding mode convergence example 168
Gear, C. W. 181 186
Generalized Persidskii-type system, nonsmooth, definition of 35
Geromel, J. C. 209
Gestel, T. V. 173
Gibson, C. G 219
Glazos, M. P. 177
Global asymptotic stability, continuous-time definition of 21
Globally Lipschitz 21
Goh, B. S. 110 111 117 124
Golub, GH 199 200
Gomulka, J. 53
Goodman, J. W. 137
Goodwin, G C. 212
Gottler, M. 174
Goudou, X. 86 91
Gradient control 34 35 50 51
Gradient descent 99
Gradient dynamical system (GDS) 31 127 130 140 146 152 172
Gradient dynamical system (GDS) as LP solver 154
Gradient dynamical system (GDS) with discontinuous right-hand side 35
Gradient dynamical system (GDS), convergence phase analysis 153
Gradient dynamical system (GDS), definition of smooth 31
Gradient dynamical system (GDS), discontinuous, convergence analysis of 150
Gradient dynamical system (GDS), geometrical description of 32
Gradient dynamical system (GDS), Liapunov stability of 130
Gradient dynamical system (GDS), natural Liapunov function for 32 130
Gradient dynamical system (GDS), nonsmooth 35
Gradient dynamical system (GDS), nonsmooth as generalized Persidskii-type system 35
Gradient dynamical system (GDS), stability of equilibria 32
Gradient dynamics 37
| Gradient method 228
Gradient stabilization 34
Gradient system 103
Gradient system, extension of 33
Gradient vector field 32
Gradient, Sobolev 34
Graebe, S. F 212
Grantham, W. J. 90
Greenbaum, A. 71 72 77 82 224
Grime, L. 91
Guo, J. I. 174
Gustafsson, K. 182 184
Guttalu, R. S. 53 90 125
Hadamard’s inequality 202
Hagan, M. T. 83 91
Hagiwara, M. 91
Hahn, W. 39
Hairer, E. 181 186 224
Half signum (hsgn) 26
Hall, G 182
Hamiltonian function 8
Hamiltonian, in stepsize control problem 188
Hanzon, B. 229
Hasselblatt, B. 39
Hauser, R. 50 90 91
Haykin, S. 174
HBF (heavy ball with friction) 86
HBF (heavy ball with friction), ODE, classical mechanics analogy for 86
Heavy ball with friction (HBF) 86
Heavy ball with friction (HBF), ODE, classical mechanics analogy for 86
Helical valley function 121
Helmke, U. xxiii 229
Hershkowitz, D 210
Higham, D 182
Hirsch, M. W 39 90 125
Hlavacek, V. 192 224
Ho, Y. C. 125
Hopfield, J. J. 133
Horn, R. A. 201
Hsgn (half signum) 26
Hsu, L. 37 211
Hui, S. 166 177
Humphries, A. R. xxiii 91
Hunt, K. J. 132
Hurt, J. 39 68 70 90
Hurwicz, L. 90 177
ILC (iterative learning control) 124 197—199
Impulse response 7 11
In conjugate gradient algorithm 83
Incerti, S. 56 65 91
Influence function 140
Initial value problem (IVP) 179 191 193
Instability, continuous-time definition of 21
Integral action 5
Integral control 5
Integral controller 183 195 212
Integral squared error criterion 191
Integrator, discrete 4 6
Internal model principle 43
Internal stability 213
Invariant set 19 23 33
Inverse function theorem 45
Inverse Liapunov function problem 114
Ipsen, I. C. F 75
Iserles, A. 224
Iterative learning control (ILC) 124 197—199
Iterative learning control as 198
Iterative learning control as optimal 96
Iterative learning control as variable structure 107
Iterative method as feedback control system xx 43 56 58
Iterative method, continuous realization of xx 43 58
Iterative methods, variable structure 96
Itkis, U. 30
IVP(initial value problem) 179 191 193
Jacobi method 140
Jacobian 45
Jacobian matrix transpose structure (JTV) 48—49
Jacobson, D. H., Ill 118 123 125
Johnson, C. R. 201 210 211 225
Jourdain, M. 24
K-winners-take-all 174
K-winners-take-all as linear programming problem 174
K-winners-take-all, GDS for 175
K-winners-take-all, problem as integer programming problem 174
Kailath, T 4 39 74 196
Kalman-Gilbert canonical form as block triangular matrix 14
Kamarthi, S. V. 91
Kantorovich, L. V. 84
Karpinskaya, N. N 90
Karush — Kuhn — Tucker (KKT) 151 173
Karush — Kuhn — Tucker (KKT), conditions 151 154 160
Kashima, K. 66 68 229
Kaski, S. 174
Kaszkurewicz, E. 37 66 68 74 90 109 124 136 164 173 174 176 177 197 209 210
Katok, A. 39
Kawai, T. 185
Kelley, C. T. 53 83 84 90
Kendig, K 219
Khalil, H. K 25 39
KKT (Karush — Kuhn — Tucker) 151 173
KKT (Karush — Kuhn — Tucker), conditions 151 154 160
Kohonen, T 174
Kokotovtf, P. 99 100 105
Korovin, S. K. 228
Kozlov, K. N. 228
Kozyakin, V. S. 137
Krasnosel’skn, M. A. xxii 84 90 107 124
Kroon, L. 230
Krstid, M 228
Kryazhimskii, A. V. 177
Krylov subspace 71
Krylov subspace method, CLF/LOC derivation of 75
KubiCek, M. 192 224
Kurek, J. E 199
Kwakernaak, H. 208
LAD (least absolute deviation) 132 141
Lagrange multiplier 8 95
Lang, R. xxiv
Lapidus, L. 224
Laplace transform  11 204
Largest 19
LaSalle’s theorem, discrete-time version 18
Learning matrix 129 132
Learning matrix as controller gain 129
Learning matrix as preconditioner 132
Learning rate for BPM 83
Learning rate for BPM, optimal, in terms of CG parameters 84
Learning rate for BPM, optimally tuned 83
Least absolute deviation (LAD) 132 141
Least squares support vector machine (LS — SVM) 173
Ledyaev, Yu. S. 31 39
Leigh, J. R. xix
Lemmon, M. 174
Level set, nested, closed, bounded 115
Level set, nested, closed, bounded, nonconvex 117
Li, W 39
Liao, L. Z. 128 177
Liapunov equation 23
Liapunov function 22
Liapunov function, decrement of 16
Liapunov function, Lur’e — Persidskii type 36
Liapunov function, nonsmooth 27
Liapunov function, Persidskii diagonal type 26
Liapunov optimizing control (LOC) 24 45
Liapunov optimizing control (LOC), choice 59 60 75 79 80 83
Liapunov, A. M. 16 127
Lifshits, Je. A. xxii 84 90
Lim, J. S. 219
Limit set, invariance of 33
Limiting porosity 108
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