Assessment and Future Directions of Nonlinear Model Predictive ...

More documents

Recommendations

Info

A Low Dimensional Contractive NMPC Scheme 529But one clearly has by definition of p cand (k + ):‖Fˆq(k)−1 (·,x cl (k + ),p cand (k + ))‖ 2 ∞ ≤‖Fˆq(k) (·,x cl (k), ˆp(k))‖ 2 ∞.Using the last equation in (13) givesV (x cl (k + )) ≤ V (x cl (k)) − α N min{ε, ‖Fˆq(k)(·,x cl (k), ˆp(k))‖ 2 ∞ }. (14)Case where ˆq(k) =1We shall first prove that each time this situation occurs, one necessarily has :x cl (k + ) ∈ ¯B(0,ρ(X)). (15)Proof of (15) Consider a sequence of instant 0 = t 0
530 M. AlamirBut according to the strong contraction assumption, one has :‖F N (·,x cl (k + ),p c (x cl (k + )))‖ 2 ∞ ≤ ϕ(x cl(k + )) ·‖x cl (k + )‖ 2 .]therefore (20) becomes (λ := sup ξ∈ ¯B(0,ρ(X))[ϕ(ξ) ):V (x cl (k + )) ≤ γ‖x cl (k + )‖ 2 + α N min{ε, ϕ(x cl(k + )) ·‖x cl (k + )‖ 2 },≤ γ‖x cl (k + )‖ 2 + α N min{ε, λ ·‖x cl(k + )‖ 2 }. (21)On the other hand, since ˆq(k) = 1 by assumption, one clearly has :‖x cl (k + )‖ 2 ≤ V (x cl (k)) − α N min{ε, ‖x cl(k + )‖ 2 }≤V (x cl (k)). (22)Therefore, using (22) in (21) gives V (x cl (k + )) ≤ γV (x cl (k)) + α min{ε, λ ·V (x cl (k))} andonecanwriteV (x cl (k + )) ≤ (γ + αλ)V (x cl (k)) which, for sufficientlysmall α gives V (x cl (k + )) ≤ θ · V (x cl (k)) for θ1θ · V (x cl (k)) ; θ
Page 2 and 3:
Lecture Notesin Control and Informa
Page 4 and 5:
Series Advisory BoardF. Allgöwer,
Page 7 and 8:
ContentsFoundations and History of
Page 9 and 10:
ContentsIXRobustness, Robust Design
Page 11 and 12:
ContentsXIHybrid NMPC Control of a
Page 13 and 14:
Nonlinear Model Predictive Control:
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Hybrid MPC: Open-Minded but Not Eas
Page 31 and 32:
Hybrid MPC: Open-Minded but Not Eas
Page 34 and 35:
22 S.E. Tuna et al.this says that i
Page 36 and 37:
24 S.E. Tuna et al.In particular, f
Page 38 and 39:
26 S.E. Tuna et al.W N (f(x, ¯κ N
Page 40 and 41:
28 S.E. Tuna et al.where ᾱ := max
Page 42 and 43:
30 S.E. Tuna et al.21.521.5µ=51
Page 44 and 45:
32 S.E. Tuna et al.obstacle and gra
Page 46 and 47:
34 S.E. Tuna et al.[19] C. Prieur.
Page 48 and 49:
36 É. Gyurkovics and A.M. Elaiw[8]
Page 50 and 51:
38 É. Gyurkovics and A.M. ElaiwWe
Page 52:
40 É. Gyurkovics and A.M. ElaiwWe
Page 55 and 56:
Conditions for MPC Based Stabilizat
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
A Computationally Efficient Schedul
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
The Potential of Interpolation for
Page 77 and 78:
The Potential of Interpolation 65De
Page 79 and 80:
The Potential of Interpolation 67Al
Page 81 and 82:
The Potential of Interpolation 693.
Page 83 and 84:
The Potential of Interpolation 71Pr
Page 85 and 86:
The Potential of Interpolation 73Th
Page 87 and 88:
The Potential of Interpolation 75de
Page 89 and 90:
Techniques for Uniting Lyapunov-Bas
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
94 M. Lazar et al.Lipschitz continu
Page 107 and 108:
96 M. Lazar et al.let X T ⊆ X den
Page 109 and 110:
98 M. Lazar et al.S 0 {j ∈S|0
Page 111 and 112:
100 M. Lazar et al.Fig. 1. State-sp
Page 113 and 114:
102 M. Lazar et al.[11] Grimm, G.,
Page 115 and 116:
Model Predictive Control for Nonlin
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
ReferencesModel Predictive Control
Page 125 and 126:
116 F.A.C.C. Fontes, L. Magni, and
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
On the Computation of Robust Contro
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
142 M. Srinivasarao, S.C. Patwardha
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Numerical Methods for Efficient and
Page 171 and 172:
Page 173 and 174:
L i (s i ,u i ):=Numerical Methods
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
182 A. Grancharova, T.A. Johansen,
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
194 V. Sakizlis et al.presented her
Page 201 and 202:
196 V. Sakizlis et al.linear PWA fu
Page 203 and 204:
198 V. Sakizlis et al.non-linear sy
Page 205 and 206:
200 V. Sakizlis et al.Remark 1. For
Page 207 and 208:
202 V. Sakizlis et al.One should no
Page 209 and 210:
204 V. Sakizlis et al.g0.050.10.15x
Page 211 and 212:
Interior-Point Algorithms for Nonli
Page 213 and 214:
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
n p,2 ≤Interior-Point Algorithms
Page 221 and 222:
Hard Constraints for Prioritized Ob
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
A Nonlinear Model Predictive Contro
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Robustness and Robust Design of MPC
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
MPC for Stochastic SystemsMark Cann
Page 261 and 262:
y i (k) =∑n um=1MPC for Stochasti
Page 263 and 264:
MPC for Stochastic Systems 259we ha
Page 265 and 266:
MPC for Stochastic Systems 261form
Page 267 and 268:
MPC for Stochastic Systems 263( )κ
Page 269 and 270:
MPC for Stochastic Systems 265Fig.
Page 271 and 272:
MPC for Stochastic Systems 267⎡
Page 273 and 274:
NMPC for Complex Stochastic Systems
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
Page 287 and 288:
284 H. Chen et al.of the moving hor
Page 289 and 290:
286 H. Chen et al.Hence, at each sa
Page 291 and 292:
288 H. Chen et al.control inputs in
Page 293 and 294:
290 H. Chen et al.Corollary 1. The
Page 295 and 296:
292 H. Chen et al.c A[mol/l]10−10
Page 297 and 298:
294 H. Chen et al.[CSA97] H.Chen,C.
Page 299 and 300:
296 L. Xie, P. Li, and G. Woznyand
Page 301 and 302:
298 L. Xie, P. Li, and G. WoznyDeta
Page 303 and 304:
300 L. Xie, P. Li, and G. Wozny3.2
Page 305 and 306:
302 L. Xie, P. Li, and G. WoznyFig.
Page 307 and 308:
304 L. Xie, P. Li, and G. Wozny[3]
Page 309 and 310:
306 H. Arellano-Garcia et al.applic
Page 311 and 312:
308 H. Arellano-Garcia et al.Fig. 1
Page 313 and 314:
310 H. Arellano-Garcia et al.RECIPE
Page 315 and 316:
312 H. Arellano-Garcia et al.optimi
Page 317 and 318:
314 H. Arellano-Garcia et al.The re
Page 319 and 320:
Interval Arithmetic in Robust Nonli
Page 321 and 322:
Page 323 and 324:
Page 325 and 326:
Page 327 and 328:
Page 329 and 330:
Optimal Online Control of Dynamical
Page 331 and 332:
Page 333 and 334:
Page 335 and 336:
Page 337 and 338:
State Estimation Analysed as Invers
Page 339 and 340:
Page 341 and 342:
Page 343 and 344:
Page 345 and 346:
Page 347 and 348:
Page 349 and 350:
Minimum-Distance Receding-Horizon S
Page 351 and 352:
Page 353 and 354:
Page 355 and 356:
Page 357 and 358:
Page 359 and 360:
Page 361 and 362:
New Extended Kalman Filter Algorith
Page 363 and 364:
Page 365 and 366:
Page 367 and 368:
Page 369 and 370:
NLMPC: A Platform for Optimal Contr
Page 371 and 372:
Page 373 and 374:
Page 375 and 376:
Page 377 and 378:
Page 379 and 380:
Page 381 and 382:
Page 383 and 384:
Page 385 and 386:
384 K. Naidoo et al.polymer control
Page 387 and 388:
386 K. Naidoo et al.are two key qua
Page 389 and 390:
388 K. Naidoo et al.1. It greatly s
Page 391 and 392:
390 K. Naidoo et al.However, with t
Page 393 and 394:
392 K. Naidoo et al.Fig. 4. Bounded
Page 395 and 396:
394 K. Naidoo et al.1. Maintain pro
Page 397 and 398:
396 K. Naidoo et al.7 Commissioning
Page 399 and 400:
398 K. Naidoo et al.[3] N.M.C. Oliv
Page 401 and 402:
400 R. Franke and J. DoppelhamerImp
Page 403 and 404:
402 R. Franke and J. DoppelhamerFig
Page 405 and 406:
404 R. Franke and J. DoppelhamerFig
Page 407 and 408:
406 R. Franke and J. Doppelhamer[3]
Page 409 and 410:
408 B.A. Foss and T.S. Scheicritica
Page 411 and 412:
410 B.A. Foss and T.S. ScheiFig. 2.
Page 413 and 414:
412 B.A. Foss and T.S. Scheidiscuss
Page 415 and 416:
414 B.A. Foss and T.S. ScheiOther a
Page 417 and 418:
416 B.A. Foss and T.S. ScheiIn the
Page 419 and 420:
Integration of Economical Optimizat
Page 421 and 422:
Page 423 and 424:
Page 425 and 426:
Page 427 and 428:
Page 429 and 430:
Page 431 and 432:
Page 433 and 434:
Page 435 and 436:
Controlling Distributed Hyperbolic
Page 437 and 438:
Page 439 and 440:
Page 441 and 442:
Page 443 and 444:
444 K.R. Muske, A.E. Witmer, and R.
Page 445 and 446:
Page 447 and 448:
Page 449 and 450:
Page 451 and 452:
Page 453 and 454:
Robust NMPC for a Benchmark Fed-Bat
Page 455 and 456:
Page 457 and 458:
Page 459 and 460:
Page 461 and 462:
Page 463 and 464:
Real-Time Implementation of Nonline
Page 465 and 466:
Page 467 and 468:
Page 469 and 470:
Page 471 and 472:
Non-linear Model Predictive Control
Page 473 and 474: NMPC of the Hashimoto Simulated Mov
Page 483 and 484: 486 R. Lepore et al.In this study,
Page 485 and 486: 488 R. Lepore et al.3 Control Strat
Page 487 and 488: 490 R. Lepore et al.400.80.6|x−x
Page 489 and 490: 492 R. Lepore et al.0.950.9w P;30.8
Page 491 and 492: Hybrid NMPC Control of a Sugar Hous
Page 499 and 500: Application of the NEPSAC Nonlinear
Page 509 and 510: Integrating Fault Diagnosis with No
Page 519 and 520: 524 M. Alamirmin V (x u(·,x),T) un
Page 521 and 522: 526 M. AlamirDefinition 4. The syst
Page 523: 528 M. Alamir♭V is radially unbou
Page 527 and 528: 532 M. AlamirFig. 2. Stabilization
Page 529 and 530: 534 M. AlamirFig. 3. Closed loop be
Page 531 and 532: A New Real-Time Method for Nonlinea
Page 545 and 546: A Two-Time-Scale Control Scheme for
Page 559 and 560: 566 X.-B. Hu and W.-H. Chen2 Online
Page 561 and 562: 568 X.-B. Hu and W.-H. Chentime alo
Page 563 and 564: 570 X.-B. Hu and W.-H. ChenFig. 3.
Page 565 and 566: 572 X.-B. Hu and W.-H. ChenTable 4.
Page 567 and 568: 574 M. Fujita et al. CameraCameraTa
Page 569 and 570: 576 M. Fujita et al.J(u, t) =∫t+T
Page 571 and 572: 578 M. Fujita et al.ξ 2[rad/s]6420
Page 573 and 574: 580 M. Fujita et al.Acknowledgement
Page 575 and 576:
582 A. Casavola, D. Famularo, and G
Page 577 and 578:
Page 579 and 580:
4. c(t) ∈Cfor all t ∈ Z + ;5. T
Page 581 and 582:
Page 583 and 584:
Distributed Model Predictive Contro
Page 585 and 586:
Page 587 and 588:
Page 589 and 590:
Page 591 and 592:
Page 593 and 594:
Page 595 and 596:
Page 597 and 598:
Page 599 and 600:
608 W.B. Dunbar and S. Desaand sequ
Page 601 and 602:
610 W.B. Dunbar and S. Desademand r
Page 603 and 604:
612 W.B. Dunbar and S. Desabacklog
Page 605 and 606:
614 W.B. Dunbar and S. Desacasescas
Page 607 and 608:
Robust Model Predictive Control for
Page 609 and 610:
Page 611 and 612:
Page 613 and 614:
Page 615 and 616:
Page 617 and 618:
Page 619 and 620:
630 J.J. Arrieta-Camacho, L.T. Bieg
Page 621 and 622:
Page 623 and 624:
Page 625 and 626:
Page 627 and 628:
Page 629 and 630:
Author IndexAlamir, Mazen 523Alamo,
Page 631 and 632:
Lecture Notes in Control and Inform
show all

Assessment and Future Directions of Nonlinear Model Predictive ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?