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Sima V. — Algorithms for Linear-Quadratic Optimization
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Название: Algorithms for Linear-Quadratic OptimizationАвтор: Sima V. Аннотация: This up-to-date reference offers valuable theoretical, algorithmic, and computational guidelines for solving the most frequently encountered linear-quadratic optimization problems - providing an overview of recent advances in control and systems theory, numerical linear algebra, numerical optimization, scientific computations, and software engineering. Examining state-of-the-art linear algebra algorithms and associated software, Algorithms for Linear-Quadratic Optimization presents algorithms in a concise, informal language that facilitates computer implementation...discusses the mathematical description, applicability, and limitations of particular solvers...summarizes numerical comparisons of various algorithms...highlights topics of current interest, including H[subscript infinity] and H[subscript 2] optimization, defect correction, and Schur and generalized-Schur vector methods...emphasizes structure-preserving techniques...contains many worked examples based on industrial models...covers fundamental issues in control and systems theory such as regulator and estimator design, state estimation, and robust control...and more. Furnishing valuable references to key sources in the literature, Algorithms for Linear-Quadratic Optimization is an incomparable reference for applied and industrial mathematicians, control engineers, computer programmers, electrical and electronics engineers, systems analysts, operations research specialists, researchers in automatic control and dynamic optimization, and graduate students in these disciplines.
Язык: Рубрика: Математика /Оптимизация и управление /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1996Количество страниц: 366Добавлена в каталог: 23.04.2005Операции: Положить на полку |
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Accessibility 15 Accessibility, subspace 15 Asymptotically stable 13 14 16 17 22 23 31 103 104 Backward error analysis 108 216 Bartels — Stewart algorithm 97 Bartels — Stewart method 145 155—157 Boundary value problem 87 202 209 Characteristic equation 106 222 229 Characteristic equation, generalized 212 215 Characteristic polynomial 106 108 254 Characteristic polynomial, generalized 213 chol 67 CholB 67 Cholesky factor 66 162—164 166 169—173 Cholesky factorization 56 66 67 73 164 170 179 180 183 250 251 Closed-loop 18 22 24 37—39 41 45 47—49 57 58 86 104 183 186 189 200 208 209 245 251 255 258 260 267 271 274 306 328 329 336 338 339 Co-state 202 colred 331 Condition number 57 104 111—113 156 158 170 183 242 245 247—250 252 255 260 267 274 286 303 309 314 322 324 326 330 338 347 Conditioning 2 53 56 69 74 111 183 215 243 248 252 284 286 301 308 Controllability 15 Controllability, matrix 15 28 Controllability, subspace 15 16 Controllable 9 15 101 103 104 174 178 179 Controllable, completely 15 16 177 Cost functional 1 3 4 8 9 18 20 21 29 100 101 Deadbeat control 211 242 268 Defect correction 2 85—87 186 187 245 248 252 257 260 271 274 275 282 293 301 303—305 322 326 327 334-336 338 339 347—349 Deflating subspace 197 198 203 205 208 211 233 234 237 239—242 248 260 262 263 281 284 287 323 Deflation 109 323 325 334 336 347 Descriptor system 27 100 209 210 266 323 Detectability 22 23 86 186 200 250 260 Detectable 17 20 22 50 186 200 207 253 Dynamical systems 1—3 5 6 8 10 12 17 37 44 97 143 144 186 210 242 267 354 Eigenvalue decomposition 51 Eigenvalue dominant 120 Eigenvalue problem 314 Eigenvalue problem, generalized 198 203 204 209 211—214 219 241 264 267 287 Eigenvalue problem, inverse 104 Eigenvalue problem, standard 108 203 211 234 Eigenvalue problem, structured 295 Eigenvalue, defective 107 111 Eigenvalues 14 28 31 104—114 119—125 127—133 135-139 141—143 148 149 156 158 162 171 174 178 179 184 186 189 200—205 208 211—217 220 221 224 227—235 237 239—241 244 251 254 255 258 260 261 265 271 282—291 293 295 296 302 313 315—320 322—326 328 329 333 334 336 338 339 349 355 356 Eigenvalues, multiple 69 106 111 314 325 336 Eigenvalues, simple 106 110 111 Eigenvalues, stable 14 24 26 69 113 197 202 206 242 253 255 261 285 317 319 320 322 324—326 330 349 Eigenvalues, unstable 14 102 113 255 261 305 318 333 335 EISPACK 53—55 57 111 114 116 124 135 197 219 224 229 240 345 Elementary eliminator 64 Elementary Jordan block 107 110 137 Elementary reflector 61 108 109 116 126 139 Elementary transformation 148 326 Elementary, stabilized 65 219 227 Elementary, symplectic 306 308 309 314 318 319 eQRs 121 Equivalence transformation 215 217 Error estimate 86 301 Error integrators 21 22 78 190 259 270 271 328 337 Estimation error 329 Feedback 9 22 26 Filter 12 78 329 Filter, optimal 11 Filter, square-root 78 flops 69 72 74 75 77 80 81 83—85 114 116 121 122 128 129 137 144 145 152—155 159 161 170 175 179—182 219 223 224 227 240 251 261 303 309-311 322 356 Gain 2 18 38—40 42 47 304 Gain, Kalman 11 83 Gain, optimal 21 71 98 183 189 198 242 251 255 256 261 268 272—274 282 303 304 327 328 338 Gain, stabilizing 72 347 Generalized eigenvalues 212 213 216 224 225 228 233 234 239 240 242 260—262 Generalized eigenvalues, finite 204 210 217 229 Generalized eigenvalues, infinite 204 205 213 216 228 233 241 265 Generalized eigenvalues, multiple 260 Generalized eigenvalues, sensitivity of 216 Generalized eigenvalues, simple 216 233 Generalized eigenvalues, stable 242 263 267 268 Generalized eigenvalues, undetermined 216 265 Generalized eigenvalues, unstable 262 269 Generalized eigenvectors 206 219 223 260 Generalized inverse 18 Generalized inverse, Moore — Penrose 9 354 Generalized principal eigenvectors 206 260 Generalized Schur vectors 211 219 223 253 260 261 268 gext 265 Givens transformation 309 336 Givens transformation, symplectic 288 323 gSch 268 gSchv 261 gSchvQ 262 gswap2 238 Hamilton — Jacobi equation 3—6 Hamiltonian quasi-triangular form 288 289 Hamiltonian — Hessenberg form 291—293 297 320 321 Hamiltonian — Hessenberg form, unreduced 291 292 296 Hamiltonian — Schur form see "Hamiltonian quasi-triangular form" Hamiltonian-triangular form 291 HamSR 312 hess 115 Hessenberg-Schur method 152 155—157 Hessenberg-triangular form 158 217 219 220 Hous 62 Householder transformation 61—63 68 74 80 115—117 125 126 129 132—134 156 166 168 170 171 217 220 225 241 265 266 289 309 324 336 Householder transformation, modified 61 116 127 130 166 171—173 219 228 231 236 240 Householder transformation, symplectic 288 323 331 Householder transformation, unitary 61 Hous_n 61 hupptri 62 H_2-control 51 i4SR 314 idQRs 127 idQZs 222 Innovations 11 Iterative refinement 87 304 J-Hessenberg form 294 295 309 313 J-triangular form 306 J-tridiagonal form 295 309 312—314 322—325 349 Jacobi transformation symplectic see "Givens transformation symplectic" Jordan canonical form 110 112 215 283 356 Jtrid 308 Kalman filter 78 329 Kronecker canonical form 215 216 Kronecker product 146 249 Lagran 333 LAPACK 2 54 56—59 64 68 105 107 111—114 116—118 123 129 130 135 147 149 150 152 176 187 197 301 336 346 351 Linear-quadratic control problem 3 8 18 Linear-quadratic optimization 1 2 53 85 Linear-quadratic optimization problem 2 3 5 18 20 105 202 241 306 Linear-quadratic-Gaussian problem 1 12 19 LINPACK 53—56 176 301 303 346 lu 65 LUsol 65 Lyac 160 LyacC 166 Lyad 161 LyadC 169 Lyapunov equation 14 69 97—99 101—103 143 144 147 156 159—161 163 166 170 171 173—183 187 207 208 249 250 299 Lyapunov equation, discrete-time 144 161 162 168 169 173 Lyapunov operator 249 Lyapunov theorem 99 LyaSch 159 Matrix, bidiagonal 58 107 Matrix, block-bidiagonal 176 Matrix, block-diagonal 215 283 356 Matrix, block-triangular 107 356 Matrix, defective 107 110 111 Matrix, derogatory 110 Matrix, diagonal 58 81 84 111 1 73 174 201 231 293 297 330 346 354 Matrix, diagonalizable 110 Matrix, dichotomic 20 113 200 210 247 253 254 267 296 325 Matrix, Hamiltonian 132 186 187 199 248 282 288-291 293 295—300 302 306 308 309 312—314 319—323 325 326 330—336 339 349 Matrix, hermitian 55 106 110 120 162 172 213 Matrix, J-Hessenberg 293 294 312 Matrix, J-triangular 293—295 313 Matrix, J-tridiagonal 293 308 312—315 317 319 Matrix, nondefective 107 110 Matrix, nonderogatory 110 137 295 Matrix, orthogonal 51 61 63 64 73 76 77 108—110 117 126 128 137 138 143 145 155 174—176 180 184 200 213 217 220 227 246—248 253 260 285 288—292 295 296 306 320 331 Matrix, quasi-triangular 142 Matrix, stable 40 41 44 162 164 170 Matrix, symmetric 2 14 18 19 55 61 66 68 72 98 99 110 115 124 174 176 183 186 198 200 208 213 215 247 253 254 267 281—283 287 289 292 293 300—303 307 310 326 330 336 Matrix, symplectic 199 241 246 287—292 295 307 309 310 314 317 320 324 331 Matrix, triangular 54 58 60 62—68 72 73 76 77 79—82 107—109 111 114 115 117—119 121 123 125 126 128 138 153 155 159 162 163 166 169—173 176 181 182 205 216—221 223 225 227—230 232 234—236 239 250 260 265 284 289 293 294 296 302 313 346 356 Matrix, tridiagonal 58 115 293 Matrix, unit triangular 81 82 118 Matrix, unitary 61 106 108 109 111 116 118 120 124—126 162 165 172 173 213 216 233 234 Matrix, unreduced Hessenberg 220—222 224 291 Matrix, unreduced upper Hessenberg 124 126 Matrix, upper Hessenberg 115 121 126 128 152 293 322 Minimal realization 44 Modelling error 38 47 mSchur 133 Multishift algorithm 330 334 345 346 349 Newton's method 87 98 101 105 144 181 186—188 251—254 283 322 Newton_k 180 NTN 188 Ntnc 181 Ntnd 181 Numerically stable 56 69 80 116 123 125 157 163 171 174 179 183 197 214 217 227 235 291 Observability 17 22 23 Observability, matrix 17 28 Observable 16 17 Optimal control 3—8 12 18 24 27 49 50 72 158 188 251 255 268 296 304 327 Optimal estimation 3 10 12 70 77 Optimal stabilizing matrix 18 26 70 186—188 191 Orthogonal basis 69 97 137 138 143 202 234 241 242 Orthogonal complement 63 Orthogonal equivalence transformation 217 218 220 Orthogonal projection 63 Orthogonal symplectic transformation 281 292 293 295 306 321 323 326 331—335 Orthogonal transformation 69 81 115 124 135 138 142 173 182 218 223 224 264 281 282 293 306 320 323 345 347 Paige — Van Loan form 296 297 330 331 Pardcov 83 Pardcovs 83 Pardinf 79 Pardinfs 80 Pencil 197 198 205 209—213 215 216 228 229 235 237 241 242 260 267 281 295 323 355 356 Pencil, Hamiltonian 210 Pencil, Hessenberg-triangular 223 Pencil, regular 205 210 211 213 216 233 284 Pencil, singular 213 215—217 Pencil, symplectic 203 210 295 323 Performance index 2 3 5 7 12 18 20 22 26 188—190 199 210 251 255 257 259 268 270 271 273 304 327-329 337 346 Plane rotation 121 122 125 127 128 130 135 136 138 173 217 219 235 236 240 241 289 324 Plane rotation, complex 164 165 172 173 Pontryagin maximum principle 3 209 psqred 320 PVL 332 qr 63 QR factorization 63 64 68 119 121 125 126 163 165 171-173 244 284 285 287 293 300 301 336 QR iteration 121 123 129-133 137 QR iteration, generalized 219 QR step 121 122 124 125 139 QR step, double 127 129—131 220 221 QR step, multiple 132—134 QR-algorithm 69 105 114 118—125 127—129 131 135 137 157 197 211 217 223 227 233 244 281 282 287 291 295 297 306 312—314 322 324 326 331 336 QR-algorithm, Hamiltonian 291 331 Quadratic convergence 69 97 99 120 122 186 187 284 287 Quasi-triangular form 107 110 114 118 124 125 132 144 145 356 Quasi-triangular-triangular form 219 QZ iteration 219 225 227 QZ step 219 220 223 227 237 238 QZ step, double 222 227 QZ-algorithm 69 157 158 197 211 215 217 219 225 227 233 237 241 261 262 281 287 323 QZHess 218 QZSch 225 QZSch2 232 QZSchord 239 Real Schur form 27 69 97 105 107 110 114 135 144 163 164 166 197 217 356 Real Schur form, generalized 211 217 233 239 356 Reconstructibility 17 Reconstructibility, complete 20 Regulation error 21 Regulator 12 29 32 37 40 43—48 Regulator, stabilizing 42 44 reig2 230 Relative error 56 57 144 157 214 233 245 246 248 300 347 Residual 63 79 80 85—87 109 119 120 157 159 183 189 242 249 252—254 257 260 271 274 275 301 303—306 322 326 328—330 334 335 338 339 Residual, absolute 245 255 Residual, relative 86 245 255 257 260 271 274 275 305 328 329 338 Riccati equation 7 9 18 21 22 24 51 53 56 68 70 85 86 98 104 129 158 183 186—188 197 198 200 201 203 206 208 211 212 241—245 247—250 252 256 260—264 267 268 284 285 287 298 301 303-305 310 311 326-328 335 338 346 349 Riccati equation, algebraic 2 18 19 25 29 49 56 57 69 70 74 77 85—87 97 98 100 144 179 184 186 191 197 198 202 209 211 241—243 247 254 255 260 267 268 281—283 287 292 295 298 304 312 327 330 331 334 336 345 Riccati equation, continuous-time 19 98 187 198 241 243 246 260 267 282 283 287 295 298 303 306 312 330 331 336 345 Riccati equation, difference 2 8 9 68 70 Riccati equation, differential 6 7 68 Riccati equation, discrete-time 19 29 77 98 198 202 241—244 246 260 267 323 Riccati equation, singular 211 264 Riccati solver 68 69 113 179 243 260 284 298 325 347 RicCorr 86 Ricdit 70 Ricditd 75 Ricditds 76 Ricditsr 73 Ricmsh 335 RicSR 322 Robust control 36 37 42 45 Robustness 49 50 ROT 60 Scaling 114—116 139 148 149 174 185 198 243 245—248 251 252 284 305 346 349 SCH 255 Schord 142 schur 131 Schur decomposition 109 Schur decomposition, generalized 216 217 234 Schur decomposition, generalized real 217 234 Schur decomposition, real 110 174 Schur factorization 135 159 187 Schur factorization, real 141 142 Schur form 123 130 132 139 146 162 Schur form, canonical 107 130 135 136 141 Schur-triangular decomposition 217 Schur-triangular form 158 197 227 234 238 240 241 261 262 266—269 Schur2 136 Schv 243 Schvd 244 SclSch 248 Sensitivity 38—40 42 50 111 156 170 Sensitivity, complementary 38 39 Separation theorem 12 sgn 304 Shift 119 121—128 130—134 221—224 226 227 237 314 334 336 349 Shift, double 127 131 135 225 226 231 237 320 326 Shift, multiple 132—134 Shift, quadruple 320 325 326 Shift, single 222 224 226 Sign function 69 174 281—284 286 287 298 300 304 306 345 349 signm 300 Similarity transformation 15 26 106 108—111 114 115 118 124 126 138 142 175 287 291 297 309 315 321 330 332 Singular value decomposition 51 246 265 285 Singular values 37 40-42 48 51 112 286 356 Solve 66 Spectrum 13 105 139 170 171 183 186 189 200 208 209 234 264 282 284 287 313 315 326 spl4x4 317 sqred 321 SR 327 SR algorithm 293 306 310 312 313 319 320 322 324—326 334 SR decomposition 294 295 312 313 SR step 325 SR step, double 315 SR step, quadruple 314 SRiter 319 Stability 40 164 177 182 184 185 198 246 265
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