Assessment and Future Directions of Nonlinear Model Predictive ...

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Distributed MPC for Dynamic Supply Chain Management 615References[1] Bemporad, A., Morari, M. and Ricker, N. L., “Model Predictive Control Toolbox– for use with MATLAB,” User’s Guide, MathWorks, Inc. (2005).[2] Braun, M. W., Rivera, D. E., Carlyle, W. M. and Kempf, K. G., “Application ofModel Predictive Control to Robust Management of Multiechelon Demand Networksin Semiconductor Manufacturing,” Simulation, 79 (3), pp. 139–156 (2003).[3] Chopra, S. and Meindl, P., Supply Chain Management, Strategy, Planning, andOperations, Second Edition, Pearson Prentice-Hall, New Jersey (2004).[4] Dunbar, W. B., “Distributed Receding Horizon Control of Dynamically CoupledNonlinear Systems,” Submitted to IEEE Transaction on Automatic Control, UCSCBaskin School of Engineering Technical Report ucsc-crl-06-03 (2006).[5] Dunbar, W. B. and Murray, R. M., “Distributed Receding Horizon Control forMulti-Vehicle Formation Stabilization,” Automatica, Vol. 2, No. 4 (2006).[6] Jia, D. and Krogh, B. H., “Min-Max Feedback Model Predictive Control for DistributedControl With Communication,” In Proceedings of the IEEE AmericanControl Conference, Anchorage, AK (2002).[7] Sterman, J. D., Business Dynamics - Systems Thinking and Modelling in a ComplexWorld, McGraw-Hill, New York (2000).
Robust Model Predictive Control for ObstacleAvoidance: Discrete Time CaseSaša V. Raković and David Q. MayneImperial College London, London SW7 2BT, United Kingdomsasa.rakovic@imperial.ac.uk, d.mayne@imperial.ac.uk1 IntroductionThe importance of the obstacle avoidance problem is stressed in [4]. Computationof reachability sets for the obstacle avoidance problem is addressed, for continuoustimesystems in [4, 5] and for discrete-time systems in [12]; further results appear in,for instance [2, 17, 18]. The obstacle avoidance problem is inherently non–convex.Most existing results are developed for the deterministic case when external disturbancesare not present. The main purpose of this paper is to demonstrate thatthe obstacle avoidance problem in the discrete time setup has considerable structureeven when disturbances are present. We extend the robust model predictiveschemes using tubes (sequences of sets of states) [9, 11, 14] to address the robustobstacle avoidance problem and provide a mixed integer programming algorithmfor robust control of constrained linear systems that are required to avoid specifiedobstacles. The resultant robust optimal control problem that is solved on–line hasmarginally increased complexity compared with that required for model predictivecontrol for obstacle avoidance in the deterministic case.This paper is organized as follows. Section 2 discusses the general idea of robustcontrol invariant tubes for the obstacle avoidance problem. Section 3 considersin more detail the case when system being controlled is linear. Section 4 presentsa simple tube controller, establishes its properties and provides an illustrativeexample. Finally, Section 5 gives conclusions and indicates further extensions.Notation: Let N {0, 1, 2,...} and N q {0, 1,...,q} for q ∈ N. Apolyhedronis the (convex) intersection of a finite number of open and/or closedhalf-spaces, a polytope is the closed and bounded polyhedron and a closed(open) polygon is the union of a finite number of polytopes (polyhedra). Giventwo sets U ⊂ R n and V ⊂ R n , the Minkowski set addition is defined byU⊕V {u + v | u ∈U, v ∈V}, the Minkowski/Pontryagin set differenceis: U⊖V {x | x ⊕V ⊆U}. The distance of a point z from a set X is denotedby d(z,X) inf{|z − x| |x ∈ X}.2 Problem FormulationWe consider the following discrete-time, time-invariant system:x + = f(x, u, w) (1)R. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 617–627, 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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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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Page 565 and 566: 572 X.-B. Hu and W.-H. ChenTable 4.
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Page 603 and 604: 612 W.B. Dunbar and S. Desabacklog
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Page 619 and 620: 630 J.J. Arrieta-Camacho, L.T. Bieg
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