Assessment and Future Directions of Nonlinear Model Predictive ...

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5 ConclusionsComputational Aspects of Approximate Explicit NMPC 191In this paper, practical computational methods for constructing approximateexplicit PWL solutions of NMPC problems are developed. They represent anextension of the approximate approach in [11] since they provide some additionalmechanisms to practically handle also the case of non-convexity of the resultingmp-NLP problem. As a case study, the design of an approximate explicit NMPCfor compressor surge control is considered.References[1] Keerthi S S, Gilbert E G (1988) Optimal infinite horizon feedback laws for ageneral class of constrained discrete-time systems: Stability and moving horizonapproximations. Journal of Optimization Theory and Applications 57:265–293[2] Mayne D Q, Michalska H (1990) Receding horizon control of nonlinear systems.IEEE Transactions on Automatic Control 35:814–824[3] Michalska H, Mayne D Q (1993) Robust receding horizon control of constrainednonlinear systems. IEEE Transactions on Automatic Control 38:1623–1633[4] Chen H, Allgöwer F (1998) A quasi-infinite horizon nonlinear model predictivecontrol scheme with guaranteed stability. Automatica 34:1205–1217[5] Magni L, De Nicolao G, Magnani L, Scattolini R (2001) A stabilizing model-basedpredictive control for nonlinear systems. Automatica 37:1351–1362[6] Magni L, Scattolini R (2004) Stabilizing model predictive control of nonlinearcontinuous time systems. Annual Reviews in Control 28:1-11[7] Bemporad A, Morari M, Dua V, Pistikopoulos E N (2002) The explicit linearquadratic regulator for constrained systems. Automatica 38:3-20[8] Chen W H, Ballance D J, Gawthrop P J (2003) Optimal control of nonlinearsystems: a predictive control approach. Automatica 39:633–641[9] Bacic M, Cannon M, Kouvaritakis B (2003) Constrained NMPC via state-spacepartitioning for input-affine non-linear systems. In: Proceedings of American ControlConference, Denver, Colorado[10] Johansen T A (2002) On multi-parametric nonlinear programming and explicitnonlinear model predictive control. In: Proceedings of IEEE Conference on Decisionand Control, Las Vegas, NV[11] Johansen T A (2004) Approximate explicit receding horizon control of constrainednonlinear systems. Automatica 40:293-300[12] Grancharova A, Johansen T A (2005) Explicit min-max model predictive controlof constrained nonlinear systems with model uncertainty. In: Proceedings of 16-thIFAC World Congress, Prague, Czech Republic[13] Fiacco A V (1983) Introduction to sensitivity and stability analysis in nonlinearprogramming. Academic Press, Orlando, Florida[14] Bemporad A, Filippi C (2003) Approximate multiparametric convex programming.In: Proceedings of 42th IEEE Conference on Decision and Control, Maui,Hawaii[15] Mayne D Q, Rawlings J B, Rao C V, Scokaert P O M (2000) Constrained modelpredictive control: Stability and optimality. Automatica 36:789-814
192 A. Grancharova, T.A. Johansen, and P. Tøndel[16] Bentley J L (1975) Multidimensional binary search trees used for associativesearching. Communications of the ACM 18:509–517[17] Grancharova A, Johansen T A (2002) Approximate explicit model predictive controlincorporating heuristics. In: Proceedings of IEEE International Symposiumon Computer Aided Control System Design, Glasgow, Scotland, U.K.[18] Gravdahl J T, Egeland O (1997) Compressor surge control using a close-coupledvalve and backstepping. In: Proceedings of American Control Conference, Albuquerque,NM.
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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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Page 145 and 146: On the Computation of Robust Contro
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Page 149 and 150: 142 M. Srinivasarao, S.C. Patwardha
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Page 169 and 170: Numerical Methods for Efficient and
Page 173 and 174: L i (s i ,u i ):=Numerical Methods
Page 187 and 188: 182 A. Grancharova, T.A. Johansen,
Page 195: 190 A. Grancharova, T.A. Johansen,
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
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Page 209 and 210: 204 V. Sakizlis et al.g0.050.10.15x
Page 211 and 212: Interior-Point Algorithms for Nonli
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Page 221 and 222: Hard Constraints for Prioritized Ob
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Page 243 and 244: Robustness and Robust Design of MPC
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Robustness and Robust Design of MPC
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MPC for Stochastic SystemsMark Cann
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y i (k) =∑n um=1MPC for Stochasti
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MPC for Stochastic Systems 259we ha
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MPC for Stochastic Systems 261form
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MPC for Stochastic Systems 263( )κ
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MPC for Stochastic Systems 265Fig.
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MPC for Stochastic Systems 267⎡
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NMPC for Complex Stochastic Systems
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284 H. Chen et al.of the moving hor
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286 H. Chen et al.Hence, at each sa
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288 H. Chen et al.control inputs in
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290 H. Chen et al.Corollary 1. The
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292 H. Chen et al.c A[mol/l]10−10
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294 H. Chen et al.[CSA97] H.Chen,C.
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296 L. Xie, P. Li, and G. Woznyand
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298 L. Xie, P. Li, and G. WoznyDeta
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300 L. Xie, P. Li, and G. Wozny3.2
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302 L. Xie, P. Li, and G. WoznyFig.
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304 L. Xie, P. Li, and G. Wozny[3]
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306 H. Arellano-Garcia et al.applic
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308 H. Arellano-Garcia et al.Fig. 1
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310 H. Arellano-Garcia et al.RECIPE
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312 H. Arellano-Garcia et al.optimi
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314 H. Arellano-Garcia et al.The re
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Interval Arithmetic in Robust Nonli
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Optimal Online Control of Dynamical
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State Estimation Analysed as Invers
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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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