Assessment and Future Directions of Nonlinear Model Predictive ...

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440 J.M. Igreja, J.M. Lemos, and R.N. da Silva987654320 1 2 3 4 5 6 7Time [h]Fig. 2. Solar field with RHC. Radiation (disturbance – above) (×10 −2 )[W/m 2 ]andoil flow (manipulated variable – below) [l/s].12 x 10−4 Time [h]11109876540 1 2 3 4 5 6 7Fig. 3. Solar field with RHC. Mirror efficiency estimate, ˆα.at the collocation points. The highest temperature at the collocation points correspondsto the oil outlet temperature (variable to be controlled). As it is seen, afteran initial transient corresponding to the start-up of the field in which the temperatureraises progressively (lasting for about 1 hour), the plant output tracks thereference with without static error , with a small overshoot, and with a raise timeof about 10 minutes. When the oil temperature is to be raised to track a positivereference step, the oil flow suddenly decreases. Otherwise, it changes to compensatefor the daily evolution of solar radiation (lower curve in fig. 2). As seen in fig.2), at about 4h30, a strong disturbance caused by a sudden drop of radiation actedon the system. The controller reduced the oil flow so that the energy accumulatedby unit volume of the oil leaving the pipe remains constant, an action that resultedin an almost perfect rejection of the disturbance.
Controlling Distributed Hyperbolic Plants 441Fig. 3 shows the mirror efficiency estimate, ˆα(t) as a function of time. Thisvariable starts from the initial estimate provided by the designer and convergesto an almost constant value after 2 hours. There are only minor changes of ˆα(t)induced by the steps in the reference.5 Discussion and ConclusionsAdaptive nonlinear receding horizon control of plants described by hyperbolicPDEs has been addressed using a novel approach which combines the OrthogonalCollocation Method, Receding Horizon Control and parameter estimation. Theapproach has been tested in a detailed model of a distributed collector solar field.The interest of the work reported is twofold: First, it provides an approachwhich can be used in a class of plants of technological interest. Furthermore, itpresents a case study on adaptive nonlinear receding horizon control, illustratinghow recent algorithms may be applied to distributed parameter plants withtransport phenomena.References[1] Adetola, V. and M. Guay, “Adaptive receding horizon control of nonlinear systems´´,Proc. 6th IFAC Symp. on Nonlinear Control Systems – NOLCOS 2004,Stuttgart Germany, 1055-1060, (2004).[2] Barão M., Lemos J. M. and Silva, R. N., ”Reduced complexity adaptative nonlinearcontrol of a distributed collector solar field”, J. of Process Control, 12, 131-141,(2002).[3] Camacho, E., M. Berenguel and F. Rubio, Advanced Control of Solar Plants, NewYork: Springer Verlag (1997).[4] Christofides, P. D., Nonlinear and Robust Control of PDE Systems, Birkhauser,(2001).[5] Dochain, D., J. P. Babary and Tali-Maamar, “Modeling and adaptive control ofnonlinear distributed parameter bioreactors via orthogonal collocation´´, Automatica,28, 873-883, (1992).[6] Dubljevic, S., P. Mhaskar, N. H. El-Farra and P. D. Christofides, ” PredictiveControl of Transport-Reactioon Processes”, Comp. and Chem. Eng., 29, 2335-2345, (2005).[7] Mhaskar, P., N. H. El-Farra and Pd. D. Christofides (2005). ”Predictive Controlof Switched Nonlinear Systems With Scheduled Mode Transitions”, IEEE Trans.Autom. Control, 50, 1670-1680, (2005).[8] Primbs, J. A., V. Nevistić andJ.Doyle,A Receding Generalization of PointwiseMin-Norm Controllers, citeseer.nj.nec.com, (1998).[9] Shang, H., J. F. Forbes and M. Guay, ”Model Predictive Control for QuasilinearHyperbolic Distributed Parameter Systems”, Ind. Eng. Chem. Res., 43, 2140-2149, (2004).[10] Silva, R. N., J. M. Lemos and L. M. Rato, “Variable sampling adaptive control ofa distributed collector solar field”, IEEE Trans. Control Syst. Tech., 11, 765-772,(2003).[11] Sontag, E., Mathematical Control Theory Springer-Verlag, 2nd Ed., (1998).
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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 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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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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