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| Bhaya A., Kaszkurewicz E. — Control Perspectives on Numerical Algorithms and Matrix Problems |
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| Предметный указатель |
Pole assignment, state feedback for 74
Pole assignment, transfer function realization 11
Pole placement 8
Pole-zero cancellation 12 207 222
Polya, G 231
Polyak, B. T 56 86 90 91 127 129 177
Polynomial equation, finite solutions of 221
Polynomial matrix theory 230
Polynomial zero finding problem 99
Polynomial zero finding problem, neural network for 101
Polynomial zero finding, numerical examples of 105
Polynomial, denominator 11
Polynomial, numerator 11
Pontryagin //-function 8
Pontryagin minimum principle (PMP) 8
Pontryagin, L. 10 39 95
Positive limit point 18
Positive limit set 18
Positive real lemma 229
Potential function 32 86
Powell’s function 121
Practical stability 19
Preconditioner 72
Preconditioner, optimal 200
Prefect conditioning problem 204
Prerequisites xxiii
Prescribed error tolerance (tol) 180
Principle, derivation of 4
Principle, internal model 4 6
Principle, LaSalle’s invariance 22
Problem, absolute stability 25
Problem, asymptotic tracking 3
Problem, inverse eigenvalue 74
Problem, Lur’e 25
Pronzato, L. xxiii
Proportional controller 78
Proportional controller, interpretation 77
Proportional-derivative (PD) 77
Proportional-integral (PI) 7 184
Proportional-integral (PI) controller 184
Proportional-integral-derivative (PID) 6 184
Pyne, I. B 90 177
Qi, H. D 128 177
Qi, L. Q 128 177
Qian, N. 86 91
QP (quadratic programming) 167 172
Quillen, D. 231
Quillen-Suslin theorem from polynomial matrix theory 230
Quinn, J. P. 90
Ramos, P. R. V. 209
Reachability set 112
Reaching phase 103
Reaching phase analysis 156
Reaching phase CLF 148 149 158
Reaching phase CLF as Persidskii-type function 150
Reaching phase conditions 175
Reaching time 31
Real time optimization, without derivative information 228
Realization, minimal 12
Redivo — Zaglia, M. 109
Redont, P. 86 91
Region of convergence 19
Regular point 32
Regular zero 53
Regularization parameter 173
Regulation 3 4 41 42
Regulation problem 98
Regulator problem 73
Relation, signum (sgn) 26
Residue 42
Reynolds, J. 227
Rheinboldt, W.C. 66 91 135
Riaza, R 53 90
Richardson method 139
Richardson method from CLF/LOC approach 77
Robustness of numerical method, control approach to 66
Root-locus properties 207
Rosenbrock function 52 57
Rosenbrock function, extended 119
Rosenbrock, H. H. 230
Rothman, J. 174
Roundoff error as state-dependent disturbance 70
Runge — Kutta method 65 96 186
Runge — Kutta method, A-stability of 229
Russell, R. D. 197 224
Ryan, E. P. 90
Rybashov, M. V. 39 90 91 129 177
S(P, C) 3
Saad, Y 77 81 84
Salgado, M. E 212
Samsonov, A. M. 228
Sastry, P. S. 83 91
Sato, A. 91
Sbarbaro, D. 132
Schaerer, C. E. 74 197
Schenk, C. xxiv
Scherer, R 229
Scholkopf, B 169 177
Schonauer, W. 91
Schrodinger’s equation, as closed loop solution 230
Schur stability 196
Search direction, as control input 112
Sector condition 68
Sector nonlinearity 175
Separating hyperplane 169
Separating surface 169
Serre’s conjecture 231
Servomechanism problem 73
set of 53
Set of points, linearly separable 169
Set of zeros 53
Sgn (signum) 26
Shapiro, A. 200
Shawe Taylor, J. 169 177
Shevitz, D 31 39
Shewchuk, J. R. 91
Shooting iteration 194
Shooting method 191
Shooting method as multidimensional system 199
Shooting method, connection to iterative learning control (ILC) 197
Shooting method, equivalent linear system for linear ODE 196
Shooting method, error dynamics 195
Shooting method, feedback gain matrix of 195
Shub, M 228
Signum (sgn) function, as optimizing control 45
Siili, E. xxiv
Siljak polynomials 101
Siljak, D. 90 105 109 218 224
Silveira, H. M. 90
Simonic, A. xxiv
Simple iterative method, static controller representation of 72
Singular point 53
Singular zero 53
Singularity, essential 53
Singularity, extraneous 52 53
Singularity, nonessential 53
Sivan, R. 208
Sliding mode 29 101 148 150 156
Sliding mode equilibrium 158
Sliding mode equilibrium, description of 160
Sliding phase 29
Slotine, J. — J. E. 39
Smale, S. 39 90 125
smallest 13
Smallest, controllable 13 14
Smallest, unobservable 13
Smillie, J. 228
Smola, A. J. 169 177
Sobolev gradient 34
Sobolev, A. V. xxii 84 90
| Soderlind, G 179 181 184
Soft margin classifier 172
Solution of linear system of equations as quadratic optimization problem 131
Solution of linear system of equations, least absolute deviation (LAD) 132
Sontag, E. D. 4 5 39 74 90
Sophisticated methods, adequacy of 89
SOR (successive overrelaxation) 74 85
Speed gradient algorithms 37
Speed gradient approach 52
Speed gradient method 45
Spurgeon, S. K. 39
Spurt method 107
Spurt method as Richardson method 107
Stability theorems, continuous-time systems 20
Stability, continuous-time definition of 21
Stabilization 3
Stabilization, closed loop 3
Stark, M. 219
State equation 42
State space control 2
static 3
Stationary point 148
Steepest descent algorithm, piecewise smooth 148
Steiger, W. L. 142
Stein equation 17
Stepsize as control 180
Stepsize, LOC choice of 60
Stern, R. J. 31 39
Stolan, J. A. 101 105
Strang, G 200 203
Straus, E. G 200
Stuart, A. M. xxiii 91
Sturmfels, B 231
Subspace, F-invariant largest 13
Successive overrelaxation (SOR) 74 85
Sugie, T. 197 198
Sullivan, F. 77
Support vector classifier (SVC) 172
Support vector machine (SVM) 167
Suslin, A. A. 231
Suykens, J. A. 173
SVC (support vector classifier) 172
SVM (support vector machine) 167
System, autonomous 3
System, basic stability result 26
System, closed loop 2
System, continuous time 2
System, coupled bilinear 79
System, decoupled 3
System, diagonal stability 26
System, dual 12
System, dynamic 3
System, gradient dynamical 127
System, linear 2
System, linear gradient 34
System, nonautonomous 3
System, nonstationary 3
System, Persidskii-type 25 104
System, quasi-gradient 34
Szego, G P. 53 90 231
Szyld, D. B., xxiv 228
Takaki, R. 185
Takeda, M 137
Tanabe, K. 90
Tank, D. W 133
Taxonomy 84
Teixeira, M. C. M 228
Terminology, feedback control 2
Terrell, W. J. 4 39
Theorem, Barbashin — Krasovskii 23
Theorem, common use of 19
Theorem, Krasovskii — LaSalle 19
Theorem, Kuhn — Tucker 113
Theorem, LaSalle 19 23 55 88
Theorem, Quillen — Suslin 230
Threshold parameter, in spurt method 107
Tol (prescribed error tolerance) 180
Tomlinson, J. 227
Torii, M 83 91
TPBVP (two point boundary value problem) 9 95 191—193
Trajectories, comparison of DJT, DVJT, DDC 1
Trajectories, DDC 2 63 64
Transfer function 11 204
Transfer function, poles of 11
Transfer function, realization of 11
Transfer function, zeros of 11
Transmission zero 204
Transmission zero, interlacing theorem for 204
Trefethen, L. N. 56 78
Triple, {F, G, H) 3 12
Truxal, J. G. 207
Tsitsiklis, J. N. 128
Tsypkin, Ya. Z. xxii 90 91 124 129
Tsypkin, Ya. Z. on best algorithms 93
Two point boundary value problem (TPBVP) 9 95 191—193
Unbehauen, R 133 137 138 142 166 177
Unconstrained minimization problem, optimal control formulation of 110
Unconstrained optimization problem, transcription into multistage optimal control problem 119
Upper half signum (uhsgn) 26
Urahama, K. 174
Utkin, V. I. 27 30 31 36 39 47 107 142 146 149 177 228
Utumi, M. 185
Uzawa, H. 90 177
Valli, A. M. P. 224
van der Sluis, A. 200
van der Vorst, H. A. 77 84
van der Waerden, B. L. 219
van Loan, C. F. 199
van Valkenburg, M. E. 212
Vandenberghe, L. xxiv
Vandewalle, J. 173
Vapnik, V. 169 170 172
Varga, R. S. 77 139
Varh, J. M. 200
Variable structure Jacobian transpose (VJT) 47—49 51 56
Variable structure methods 50 109
Variable structure systems 27 107
Vasilev, L. V. 31
Vector field, gradient 32
Vector field, Newton 52
Venets, V. I. 90
Vichnevetsky, R. 224
Vidyasagar, M 25 39 68 166
Vijayakumar, B. V. K. 174
Vincent, T. L. 90
VJT (variable structure Jacobian transpose) 47—49 51 56
von Neumann, J. 1
Vongpanitlerd, S. 229
Wah, B. W 132
Walker, R 174
Wang, Z. 142
Wanner, G 181 186 224
Ward, R. K 142 145
Weighting matrices, final state 8
Weighting matrices, input 8
Weighting matrices, state 8
Weiss, R 91
Wendler, W. 229
Wielandt’s inequality 201
Wielandt’s inequality, geometrical interpretation of 201
Williamson, R. C 170
Willson, A. N 82 91
Wirth, F 229
Wittenmark, B. 75 196
Wolenski, PR. 31 39
Wolfe, W. J. 174
Wonham, W. M. 5
Wood’s function 120
Wright, S. J. xxiv 84 151
Wynn, H. P. xxiii
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