Assessment and Future Directions of Nonlinear Model Predictive ...

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162 T. Raff, C. Ebenbauer, and F. Allgöwer[2] C.I. Byrnes and A. Isidori and J.C. Willems, “Passivity, Feedback Equivalence,and the Global Stabilization of Minimum Phase Nonlinear Systems”, IEEE Transactionson Automatic Control, pages 1228-1240, (1991).[3] C. Chen and F. Allgöwer, “A Quasi-Infinite Horizon Nonlinear Model PredictiveControl Scheme with Guaranteed Stability”, Automatica, pages 1205-1217, (1998).[4] C. Ebenbauer, “Control of a Quadruple Tank System”, Institute for Systems Theoryin Engineering Laboratory Lecture Notes, (2004).[5] R.A. Freeman P.V. Kokotovic, “Robust Nonlinear Control Design: State-Spaceand Lyapunov Techniques”, Birkhäuser, (1996).[6] A. Jadbabaie, J. Yu, and J. Hauser, “ Stabilizing receding horizon control ofnonlinear systems: a control Lyapunov function approach”, In Proceedings of theAmerican Control Conference, pages 1535 - 1539, (1999).[7] K.H. Johansson , “The Quadruple-Tank Process: A Multivariable Laboratory Processwith Adjustable Zero”, IEEE Transactions on Control Systems Technology,pages 456-465 (2000).[8] R.E. Kalman, “When is a Linear Control System Optimal”, Transactions of theASME, Journal of Basic Engineering, pages 1-10, (1964).[9] S. Keerthi and E. Gilbert, “Optimal Infinite-Horizon Feeback Laws for a GeneralClass of Constrained Discrete-Time Systems: Stability and Moving-Horizon Approximations”, Journal of Optimiztaion Theory and Applications, pages 265-293(1988).[10] H.K. Khalil, “Nonlinear Systems”, Prentice Hall, (1996).[11] D.Q. Mayne and J.B. Rawlings and C.V. Rao and P.O.M. Scokaert, “ConstrainedModel Predictive Control: Stability and Optimality ”, Automatica, pages 789-814,(2000).[12] P. Moylan, “Implications of Passivity for a Class of Nonlinear Systems”, IEEETransactions on Automatic Control, pages 373-381, (1974).[13] Z.K. Nagy, “Nonlinear model predictive control toolbox”, (2005).[14] G. De Nicolao, L. Magni, and R. Scattolni, “Stabilizing Receding-Horizon Controlof Nonlinear Time-Varying Systems”, IEEE Transactions on Automatic Control,pages 1031-1037,(1998).[15] H. Michalska and D. Q. Mayne, “Robust Receding Horizon Control of ConstrainedNonlinear Systems ”, IEEE Transactions on Automatic Control, pages 1623 - 1633,(1993).[16] J. A. Primbs, V. Nevistic, and J.C. Doyle, “A receding horizon generalization ofpointwise min-norm controllers”, IEEE Transactions on Automatic Control, pages898 - 909, (2000).[17] R. Sepulchre M. Jankovic P. Kokotovic, “Constructive Nonlinear Control”,Springer, (1997).[18] J.C. Willems, “Dissipative Dynamical Systems. Part I: General Theory”, Archivefor Rational Mechanics and Analysis, pages 321-351, (1972).
Numerical Methods for Efficient and FastNonlinear Model Predictive ControlHans Georg Bock, Moritz Diehl, Peter Kühl, Ekaterina Kostina,Johannes P. Schlöder, and Leonard WirschingInterdisciplinary Center for Scientific Computing (IWR), University of Heidelberg,Im Neuenheimer Feld 368, 69120 Heidelberg, Germany{bock,m.diehl}@iwr.uni-heidelberg.deSummary. The paper reports on recent progress in the real-time computation of constrainedclosed-loop optimal control, in particular the special case of nonlinear modelpredictive control, of large differential algebraic equations (DAE) systems arising e.g.from a MoL discretization of instationary PDE. Through a combination of a directmultiple shooting approach and an initial value embedding, a so-called “real-time iteration”approach has been developed in the last few years. One of the basic featuresis that in each iteration of the optimization process, new process data are being used.Through precomputation - as far as possible - of Hessian, gradients and QP factorizationsthe response time to perturbations of states and system parameters is minimized.We present and discuss new real-time algorithms for fast feasibility and optimalityimprovement that do not need to evaluate Jacobians online.1 IntroductionFeedback control based on an online optimization of nonlinear dynamic processmodels subject to constraints, and its special case, nonlinear model predictivecontrol (NMPC) [1], is an emerging optimal control technique, mainly appliedto problems in chemical engineering [17]. Currently, NMPC is also transferredto new fields of application such as automotive engineering, where the principaldynamics are much faster. Among the advantages of NMPC are the capabilityto directly handle equality and inequality constraints as well as the flexibilityprovided in formulating the objective function and the process model. Lately, amajor aim has become to develop algorithms that are able to treat large-scalenonlinear first principle models without further need of re-modeling or modelreduction.In this paper we present and investigate several variants of the “real-time iteration”approach to online computation of constrained optimal feedback controllaws. The present realization of this approach is based on the direct multipleshooting method [5] for DAE models [15]. Some of the ideas in this paper, anddetails on the standard variant of the real-time iteration approach can e.g. befound in [3, 8, 10]. The main contribution of this paper is to bring together threeR. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 163–179, 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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Page 201 and 202: 196 V. Sakizlis et al.linear PWA fu
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Page 205 and 206: 200 V. Sakizlis et al.Remark 1. For
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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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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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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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