Assessment and Future Directions of Nonlinear Model Predictive ...

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Chance Constrained Nonlinear Model Predictive Control 303Fig. 5. Inlet and outlet concentration C(k)Fig. 6. Max reachable probabilities of the C(k) chance constraint5 ConclusionsIn this work, a robust nonlinear model predictive controller, chance constrainedNMPC, is proposed. To compute the probability and derivatives of holding inequalityconstraints inverse mapping approach is extended to dynamic nonlinearsituations. To find a monotone relation between the uncertain variable and theoutput which is necessary for the inverse mapping approach, truncated normaldistribution is considered to describe uncertainty variables. CNMPC is illustratedto be effective by controlling a mixing process with both uncertain feedflow rate and feed concentration.Acknowledgements. Lei Xie is grateful for the financial support through the SandwichProgram from the Berlin University of Technology. Financial Support fromthe Deutsche Forschungsgemeischaft (DFG) under the contract LI 806/8-1 isalso gratefully acknowledged.References[1] Mayne D Q, Rawlings J B, Rao C V, Scokaert P O M (2000) Constrained modelpredictive control: Stability and optimality. Automatica 36:789-814[2] Lee J H, Yu Z (1997) Worst-case formulations of model predictive control forsystems with bounded parameters. Automatica 33:763-781
304 L. Xie, P. Li, and G. Wozny[3] Li P, Wendt M, Wozny G (2002) A probabilistically constrained model predictivecontroller. Automatica 38:1171-1176[4] Schwarm A T, Nikolaou M (1999) Chance-constrained model predictive control.AIChE Journal 45:1743-1752[5] Wendt M, Li P, Wozny G (2002) Nonlinear chance-constrained process optimizationunder uncertainty. Ind. Eng. Chem. Res. 41:3621-3629[6] Birge J R, Louveaux F (1997) Introduction to Stochastic Programming. Springer,Berlin.[7] Biegler L T, Grossmann I E (2004) Retrospective on optimization. Computersand Chemical Engineering 28:1169-1192[8] Diwekar U M, Kalagnanam J R (1997) Efficient sampling technique for optimizationunder uncertainty. AIChE Journal 43:440-447[9] Horrace W C (2005) Some results on the multivariate truncated normal distribution.Journal of Multivariate Analysis 94:209-221[10] Li P, Wendt M, Wozny G (2000) Robust model predictive control under chanceconstraints. Computers and Chemical Engineering 24:829-834[11] Li P, Wendt M, Arellano-Carcia H, Wozny G (2002) Optimal operation of distillationprocess under uncertain inflows accumulated in a feed tank. AIChE. Journal48:1198-1211[12] Li P, Wendt M, Wozny G (2004) Optimal production planning for chemicalprocesses under uncertain market conditions. Chemical Engineering Technology27:641-651[13] Sahinidis N V (2004) Optimization under uncertainty: state-of-the-art and opportunities.Computers and Chemical Engineering 28: 971-983
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Lecture Notesin Control and Informa
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Series Advisory BoardF. Allgöwer,
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ContentsFoundations and History of
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ContentsIXRobustness, Robust Design
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ContentsXIHybrid NMPC Control of a
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Nonlinear Model Predictive Control:
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Hybrid MPC: Open-Minded but Not Eas
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Hybrid MPC: Open-Minded but Not Eas
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22 S.E. Tuna et al.this says that i
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24 S.E. Tuna et al.In particular, f
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26 S.E. Tuna et al.W N (f(x, ¯κ N
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28 S.E. Tuna et al.where ᾱ := max
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30 S.E. Tuna et al.21.521.5µ=51
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32 S.E. Tuna et al.obstacle and gra
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34 S.E. Tuna et al.[19] C. Prieur.
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36 É. Gyurkovics and A.M. Elaiw[8]
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38 É. Gyurkovics and A.M. ElaiwWe
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40 É. Gyurkovics and A.M. ElaiwWe
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Conditions for MPC Based Stabilizat
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A Computationally Efficient Schedul
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The Potential of Interpolation for
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The Potential of Interpolation 65De
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The Potential of Interpolation 67Al
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The Potential of Interpolation 693.
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The Potential of Interpolation 71Pr
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The Potential of Interpolation 73Th
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The Potential of Interpolation 75de
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Techniques for Uniting Lyapunov-Bas
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94 M. Lazar et al.Lipschitz continu
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96 M. Lazar et al.let X T ⊆ X den
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98 M. Lazar et al.S 0 {j ∈S|0
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100 M. Lazar et al.Fig. 1. State-sp
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102 M. Lazar et al.[11] Grimm, G.,
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Model Predictive Control for Nonlin
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ReferencesModel Predictive Control
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116 F.A.C.C. Fontes, L. Magni, and
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On the Computation of Robust Contro
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142 M. Srinivasarao, S.C. Patwardha
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Numerical Methods for Efficient and
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L i (s i ,u i ):=Numerical Methods
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182 A. Grancharova, T.A. Johansen,
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194 V. Sakizlis et al.presented her
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196 V. Sakizlis et al.linear PWA fu
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198 V. Sakizlis et al.non-linear sy
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200 V. Sakizlis et al.Remark 1. For
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202 V. Sakizlis et al.One should no
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204 V. Sakizlis et al.g0.050.10.15x
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Interior-Point Algorithms for Nonli
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n p,2 ≤Interior-Point Algorithms
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Hard Constraints for Prioritized Ob
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A Nonlinear Model Predictive Contro
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Robustness and Robust Design of MPC
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Page 255 and 256: Robustness and Robust Design of MPC
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Minimum-Distance Receding-Horizon S
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Minimum-Distance Receding-Horizon S
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New Extended Kalman Filter Algorith
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NLMPC: A Platform for Optimal Contr
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384 K. Naidoo et al.polymer control
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386 K. Naidoo et al.are two key qua
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388 K. Naidoo et al.1. It greatly s
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390 K. Naidoo et al.However, with t
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392 K. Naidoo et al.Fig. 4. Bounded
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394 K. Naidoo et al.1. Maintain pro
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396 K. Naidoo et al.7 Commissioning
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398 K. Naidoo et al.[3] N.M.C. Oliv
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400 R. Franke and J. DoppelhamerImp
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402 R. Franke and J. DoppelhamerFig
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404 R. Franke and J. DoppelhamerFig
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406 R. Franke and J. Doppelhamer[3]
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408 B.A. Foss and T.S. Scheicritica
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410 B.A. Foss and T.S. ScheiFig. 2.
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412 B.A. Foss and T.S. Scheidiscuss
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414 B.A. Foss and T.S. ScheiOther a
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416 B.A. Foss and T.S. ScheiIn the
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Integration of Economical Optimizat
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Controlling Distributed Hyperbolic
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444 K.R. Muske, A.E. Witmer, and R.
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Robust NMPC for a Benchmark Fed-Bat
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Real-Time Implementation of Nonline
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Non-linear Model Predictive Control
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NMPC of the Hashimoto Simulated Mov
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486 R. Lepore et al.In this study,
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488 R. Lepore et al.3 Control Strat
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490 R. Lepore et al.400.80.6|x−x
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492 R. Lepore et al.0.950.9w P;30.8
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Hybrid NMPC Control of a Sugar Hous
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Application of the NEPSAC Nonlinear
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Integrating Fault Diagnosis with No
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524 M. Alamirmin V (x u(·,x),T) un
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526 M. AlamirDefinition 4. The syst
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528 M. Alamir♭V is radially unbou
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530 M. AlamirBut according to the s
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532 M. AlamirFig. 2. Stabilization
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534 M. AlamirFig. 3. Closed loop be
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A New Real-Time Method for Nonlinea
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A Two-Time-Scale Control Scheme for
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566 X.-B. Hu and W.-H. Chen2 Online
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568 X.-B. Hu and W.-H. Chentime alo
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570 X.-B. Hu and W.-H. ChenFig. 3.
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572 X.-B. Hu and W.-H. ChenTable 4.
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574 M. Fujita et al. CameraCameraTa
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576 M. Fujita et al.J(u, t) =∫t+T
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578 M. Fujita et al.ξ 2[rad/s]6420
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580 M. Fujita et al.Acknowledgement
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582 A. Casavola, D. Famularo, and G
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4. c(t) ∈Cfor all t ∈ Z + ;5. T
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Distributed Model Predictive Contro
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608 W.B. Dunbar and S. Desaand sequ
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610 W.B. Dunbar and S. Desademand r
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612 W.B. Dunbar and S. Desabacklog
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614 W.B. Dunbar and S. Desacasescas
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Robust Model Predictive Control for
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630 J.J. Arrieta-Camacho, L.T. Bieg
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Author IndexAlamir, Mazen 523Alamo,
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Lecture Notes in Control and Inform
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