Assessment and Future Directions of Nonlinear Model Predictive ...

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Close-Loop Stochastic Dynamic Optimization 315[5] P. Li, M. Wendt, and G. Wozny. Robust Model Predictive Control under ChanceConstraints. Computers & Chemical Engineering, 24:829–833, 2000.[6] Z. Nagy and R. D. Braatz. Open-loop and close-loop robust optimal control ofbatch processes using distributional and worst-case analysis. Journal of ProcessControl, 14:411–422, 2004.[7] M. Wendt, P. Li, and G. Wozny. Nonlinear Chance-Constrained Process Optimizationunder Uncertainty. Ind. Eng. Chem. Res., 41:3621–3629, 2002.[8] E. Zafirou. Robust model predictive control of process with hard constraints. Computers& Chemical Engineering, 14:359–371, 1990.
Interval Arithmetic in Robust Nonlinear MPCD. Limon 1 ,T.Alamo 1 ,J.M.Bravo 2 ,E.F.Camacho 1 ,D.R.Ramirez 1 ,D. Muñoz de la Peña 1 ,I.Alvarado 1 , and M.R. Arahal 11 Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla,Sevilla, Spain{limon, alamo, eduardo, danirr, davidmps, alvarado,arahal} @cartuja.us.es2 Departamento de Ingeniería Electrónica, Sistemas Informáticos y Automática.Universidad de Huelva, Huelva, Spaincaro@uhu.esSummary. This paper shows how interval arithmetic can be used to design stabilizingrobust MPC controllers. Interval arithmetic provides a suitable framework to obtaina tractable procedure to calculate an outer bound of the range of a given nonlinearfunction. This can be used to calculate a guaranteed outer bound on the predictedsequence of reachable sets. This allows us to consider the effect of the uncertaintiesin the prediction and to formulate robust dual-mode MPC controllers with ensuredadmissibility and convergence. Interval arithmetic can also be used to estimate thestate when only outputs are measurable. This method provides a guaranteed outerbound on the set of states consistent with the output measurements. Generalizing thecontrollers based on reachable sets, a novel robust output feedback MPC controller isalso proposed.1 IntroductionConsider a process described by an uncertain nonlinear time-invariant discretetime modelx + = f(x, u, w) (1)y = g(x, u, v) (2)where x ∈ R n is the system state, u ∈ R m is the current control vector, y ∈ R pis the measured output, w ∈ R nw is the disturbance input which models theuncertainty, v ∈ R pv is the measurement noise and x + is the successor state. x k ,u k , y k , w k and v k denote the state, input, output, uncertainty and noise of theplant at sampling time k, respectively.It is assumed that the uncertainty is bounded and contained in a compactset,w ∈ W (3)which contains the origin and the noise is bounded in the compact setv ∈ V. (4)R. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 317–326, 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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Page 287 and 288: 284 H. Chen et al.of the moving hor
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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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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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