Assessment and Future Directions of Nonlinear Model Predictive ...

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550 D. DeHaan and M. Guayand the boundedness of the sets X, U, Θ and Ξ (which ensures that trajectoriesremain in a compact subset of S F ∪ S H ). Thus, z π asymptotically converge toM, the largest invariant subset of {z π | J ˙ = 0 under (12a)}∪{z π : J + − J =0 under (14) }. SinceH maps into the interior of S F (strictly away from S H ),zeno solutions are not possible. This implies M ⊂{z π | J ˙ =0}, and thus fromthe proof of Lemma 2 it follows that M = { z π : (x, u φ ) ∈ Σ }. Feasibilityholds from Lemmas 2 and 3, while the last claim follows from Lemma 1 and thecompactness of X 0 .
A Two-Time-Scale Control Scheme for FastUnconstrained SystemsSebastien Gros, Davide Buccieri, Philippe Mullhaupt, and Dominique BonvinLaboratoire d’Automatique, École Polytechnique Fédérale de Lausanne, CH-1015Lausanne, SwitzerlandSummary. Model predictive control (MPC) is a very effective approach to controlnonlinear systems, especially when the systems are high dimensional and/orconstrained. MPC formulates the problem of input trajectory generation as an optimizationproblem. However, due to model mismatch and disturbances, frequentre-calculation of the trajectories is typically called for. This paper proposes a twotime-scalecontrol scheme that uses less frequent repeated trajectory generation in aslow loop and time-varying linear feedback in a faster loop. Since the fast loop reducesconsiderably the effect of uncertainty, trajectory generation can be done much less frequently.The problem of trajectory generation can be treated using either optimizationbasedMPC or flatness-based system inversion. As proposed, the method cannot handlehard constraints. Both MPC and the two-time-scale control scheme are tested via thesimulation of a flying robotic structure. It is seen that the MPC scheme is too slowto be considered for real-time implementation on a fast system. In contrast, the twotime-scalecontrol scheme is fast, effective and robust.1 IntroductionModel predictive control (MPC) is an effective approach for tackling problemswith nonlinear dynamics and constraints, especially when analytical computationof the control law is difficult [4, 14, 17]. MPC involves re-calculating atevery sampling instant the inputs that minimize a criterion defined over a horizonwindow in the future, taking into account the current state of the system.A crucial point in MPC is the extensive use of the dynamic model. Since themodel is not always accurate, the predicted state evolution may differ from theactual plant evolution, which requires frequent re-calculation of the inputs. Solutionsto this problem are proposed in the literature. One possibility is to castthe problem into a robust framework, where optimization is performed by takingthe uncertainty into account explicitly. Robust predictive control computes inputtrajectories that represent a compromise solution for the range of uncertaintyconsidered [2, 11, 12]. Such a methodology is widely used in the process industry,where system dynamics are sufficiently slow to permit its implementation.However, due to the complexity of the calculations involved in robust predictivecontrol, its applicability to fast dynamics is rather limited. Several promisingR. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 551–563, 2007.springerlink.com c○ Springer-Verlag Berlin Heidelberg 2007
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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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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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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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Page 521 and 522: 526 M. AlamirDefinition 4. The syst
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Page 565 and 566: 572 X.-B. Hu and W.-H. ChenTable 4.
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Distributed Model Predictive Contro
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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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