Assessment and Future Directions of Nonlinear Model Predictive ...

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358 A. Alessandri, M. Baglietto, and G. Battistelli[8] Mayne D.Q., Rawlings, J.B., Rao, C.V., and Scokaert, P.O.M., “Constrainedmodel predictive control: stability and optimality,” Automatica, 36, pp. 789–814,(2000).[9] Rao, C.V., Rawlings, J.B., and Mayne, D.Q., “Constrained state estimation fornonlinear discrete-time systems: stability and moving horizon approximations,”IEEE Trans. on Automatic Control, 48, pp. 246–257, (2003).[10] Vidal, R., Chiuso, A., and Soatto, S.,“Observability and identifiability of jumplinear systems,” Proc. of the 41st IEEE Conference on Decision and Control, LasVegas, Nevada, pp. 3614–3619, (2002).
New Extended Kalman Filter Algorithms forStochastic Differential Algebraic EquationsJohn Bagterp Jørgensen 1 , Morten Rode Kristensen 2 , Per Grove Thomsen 1 ,and Henrik Madsen 11 Informatics and Mathematical Modelling, Technical University of Denmark,DK-2800 Kgs. Lyngby, Denmark{jbj,pgt,hm}@imm.dtu.dk2 Department of Chemical Engineering, Technical University of Denmark, DK-2800Kgs. Lyngby, Denmarkmrk@kt.dtu.dkSummary. We introduce stochastic differential algebraic equations for physical modellingof equilibrium based process systems and present a continuous-discrete paradigmfor filtering and prediction in such systems. This paradigm is ideally suited for stateestimation in nonlinear predictive control as it allows systematic decomposition of themodel into predictable and non-predictable dynamics. Rigorous filtering and predictionof the continuous-discrete stochastic differential algebraic system requires solutionof Kolmogorov’s forward equation. For non-trivial models, this is mathematically intractable.Instead, a suboptimal approximation for the filtering and prediction problemis presented. This approximation is a modified extended Kalman filter for continuousdiscretesystems. The modified extended Kalman filter for continuous-discrete differentialalgebraic systems is implemented numerically efficient by application of an ESDIRKalgorithm for simultaneous integration of the mean-covariance pair in the extendedKalman filter [1, 2]. The proposed method requires approximately two orders of magnitudeless floating point operations than implementations using standard software.Numerical robustness maintaining symmetry and positive semi-definiteness of the involvedcovariance matrices is assured by propagation of the matrix square root of thesecovariances rather than the covariance matrices themselves.1 IntroductionThe objective of state estimation in nonlinear model predictive control is toreconstruct the current state from past and current measurements. This stateestimate is called the filtered state and is used as initial condition for predictionof the mean evolution in the dynamic optimization part of nonlinear modelpredictive control. While there is little or no difference in the way the predictionsare accomplished, extended Kalman filtering (EKF) and moving horizonestimation (MHE) approaches have been suggested to compute the filtered stateestimate for systems described by index-1 differential algebraic equations. However,mainly discrete-time stochastic systems or deterministic continuous-timesystems with stochastics appended in an ad hoc manner have been applied toindex-1 differential algebraic systems.R. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 359–366, 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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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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