Assessment and Future Directions of Nonlinear Model Predictive ...

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60 M.V. Kothare and Z. Wanwe were able to characterize explicitly an estimated region of stability of thedesigned local output feedback predictive controller, we could expand it by designingmultiple predictive controllers, and on-line switch between the local controllersand achieve nonlinear transitions with guaranteed stability. This algorithmprovides a general framework for the scheduled output feedback MPCdesign. Furthermore, we have shown that this scheduled MPC is easily implementableby applying it to a two tank process.AcknowledgmentsPartial financial support for this research from the American Chemical Society’sPetroleum Research Fund (ACS-PRF) and from the P. C. Rossin AssistantProfessorship at Lehigh University is gratefully acknowledged.References[1] D. Angeli, A. Casavola, and E.Mosca. Constrained predictive control of nonlinearplant via polytopic linear system embedding. International Journal of Robust &Nonlinear Control, 10(13):1091–1103, Nov 2000.[2] N.H. El-Farra, P. Mhaskar, and P.D. Christofides. Uniting bounded control andMPC for stabilization of constraed linear systems. Automatica, 40:101–110, 2004.[3] N.H. El-Farra, P. Mhaskar, and P.D. Christofides. Hybrid predictive control ofnonlinear systems: method and applications to chemical processes. InternationalJournal of Robust and Nonlinear Control, 14:199–225, 2004.[4] R. Findeisen, L. Imsland, F. Allgower, and B.A. Foss. State and output feedbacknonlinear model predictive control: An overview. European Journal of Control, 9(2-3), pages 190-206, 2003.[5] R. Findeisen, H. Chen, and F. Allgower. Nonlinear predictive control for setpointfamilies. Proceedings of the 2000 American Control Conf., volume 1, pages 260-264, Chicago, 2000.[6] R. Findeisen, M. Diehl, T. Burner, F. Allgower, H.G. Bock, and J.P. Schloder.Efficient output feedback nonlinear model predictive control. Proceedings of the2002 American Control Conference, pages 4752–4757, Anchorage, 2002.[7] A. Jadbabaie, J. Yu, and J. Hauser. Unconstrained receding-horizon control ofnonlinear systems. IEEE Transactions on Automatic Control, 46(5):776–783, May2001.[8] H. K. Khalil. Nonlinear systems. Macmillan Publishing Company, 1992.[9] Y. Lu and Y. Arkun. A scheduling quasi-min-max Model Predictive Controlalgorithm for nonlinear systems. Journal of Process Control, 12:589–604, August2002.[10] David L. Ma, Danesh K. Tafti, and Richard D. Braatz. Optimal control andsimulation of multidimensional crystallization processes. Computers & ChemicalEngineering, 26(7-8):1103–1116, 2002.[11] L. Magni, G. De Nicolao, L. Magnani, and R. Scattolini. A stabilizing model-basedpredictive control algorithm for nonlinear systems. Automatica, 37:1351–1362,2001.
A Computationally Efficient Scheduled Model Predictive Control Algorithm 61[12] M. W. McConley, B. D. Appleby, M. A. Dahleh, and E. Feron. A computationallyefficient Lyapunov-based scheduling procedure for control of nonlinear systemswith stability guarantees. IEEE Transactions on Automatic Control, 45(1):33–49,January 2000.[13] P. Mhaskar, N.H. El-Farra, and P.D. Christofides. Hybrid predictive control ofprocess systems. AIChE Journal, 50:1242–1259, 2004.[14] H. Michalska and D. Q. Mayne. Moving horizon observers and observer-basedcontrol. IEEE Transactions on Automatic Control, 40(6):995–1006, June 1995.[15] L. Magni, G. De Nicolao and R. Scattolini. Stability and robustness of nonlinearreceding horizon control. In F. Allgöwer and A. Zheng, editors, Nonlinear ModelPredictive Control, pages 23–44, 2000.[16] S. L. De Oliveira Kothare and M. Morari. Contractive Model Predictive Controlfor constrained nonlinear systems. IEEE Transactions on Automatic Control,45(6):1053–1071, June 2000.[17] D. E. Seborg, T. F. Edgar, and D. A. Mellichamp. Process Dynamics and Control.John Wiley & Sons, New York, 1999.[18] P. O. M. Scokaert, D. Q. Mayne, and J. B. Rawlings. Suboptimal model predictivecontrol (feasibility implies stability). IEEE Transactions on Automatic Control,44(3):648 –654, 1999.[19] Z. Wan and M. V. Kothare. Efficient scheduled stabilizing model predictive controlfor constrained nonlinear systems. International Journal of Robust and NonlinearControl, Volume 13, Issue 3-4, Pages 331-346, Mar-Apr 2003.[20] Z. Wan and M. V. Kothare. Efficient scheduled stabilizing output feedback modelpredictive control for constrained nonlinear systems. IEEE Trans. Aut. Control,49(7): 1172-1177, July 2004.AppendixProof. Proof of Theorem 1: Within a neighborhood (Π x ,Π u ) around (x eq ,u eq ),we locally represent the nonlinear system (1) by a LTV model ¯x(k +1) =A(k)¯x(k) +B(k)ū(k) with [ A(k) B(k) ] ∈ Ω. For all x ∈ Π x and u ∈ Π u ,the Jacobian matrix⎡ ∂f 1∂u 1···⎢ .⎣ . .. .∂f 1⎤∂u m⎥⎦∂u m∂f n∂u 1··· ∂fn[ ]∂f∂x , ∂f∂u∈ Ω with ∂f∂x⎡= ⎢⎣∂f 1∂x 1.∂f n∂x 1··· ∂f1∂x n. .. . ⎥⎦⎤··· ∂fn∂x nand∂f∂u =. It is straight forward to establish the closed-loop exponentialstability within S based on the LTV model. Since the LTV model is a representationof a class of nonlinear systems including the given nonlinear system (1)within the neighborhood (Π x ,Π u ), the closed-loop nonlinear system is exponentiallystable within S.Proof. Proof of Theorem 2 and 4: Following the same procedure as in the prooffor Theorem 1, we locally represent the nonlinear error dynamics as a LTV
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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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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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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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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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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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Non-linear Model Predictive Control
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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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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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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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