Assessment and Future Directions of Nonlinear Model Predictive ...

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268 M. Cannon, P. Couchmann, and B. Kouvaritakis[15] M. Cannon, B. Kouvaritakis, and V. Deshmukh. Enlargement of polytopic terminalregion in NMPC by interpolation and partial invariance. Automatica, 40:311–317, 2004.[16] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalitiesin System and Control Theory. SIAM, 1994.[17] M. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret. Applications of second-ordercone programming. Linear Algebra and its Applications, 284:193–228, 1998.[18] B.T. Polyak. Introduction to optimization. Opt. Software Inc., 1987.
NMPC for Complex Stochastic Systems Using aMarkov Chain Monte Carlo ApproachJan M. Maciejowski 1 , Andrea Lecchini Visintini 2 , and John Lygeros 31 Cambridge University Engineering Dept, Cambridge CB2 1PZ, England{jmm,al394}@eng.cam.ac.uk2 Department of Engineering, University of Leicester, Leicester LE1 7RH, UKalvl@leicester.ac.uk3 Automatic Control Laboratory, ETH Zurich, CH-8092, Switzerlandlygeros@ee.upatras.grSummary. Markov chain Monte Carlo methods can be used to make optimal decisionsin very complex situations in which stochastic effects are prominent. We argue thatthese methods can be viewed as providing a class of nonlinear MPC methods. Wediscuss decision taking by maximising expected utility, and give an extension whichallows constraints to be respected. We give a brief account of an application to air trafficcontrol, and point out some other problem areas which appear to be very amenable tosolution by the same approach.1 IntroductionModel Predictive Control (MPC) is characterised by the following features [14]:1. An explicit internal model used to generate predictions,2. Online, real-time optimisation to determine the control signals (manipulatedvariables),3. Use of repeated measurements and re-optimisation to obtain feedback,4. Use of a receding horizon (optional),5. Explicit consideration of constraints (optional).In this chapter we will introduce a control method which appears very differentfrom MPC, as it is usually understood. But it has all the features listed here, sowe claim that it should be considered to be an MPC method. Furthermore, itcan be used with nonlinear models of arbitrary ‘nastiness’, the only requirementbeing that predictions can be generated by simulating the model behaviour. Ourmethod is definitely a nonlinear MPC method. It is even a robust nonlinear MPCmethod, because it can cope with uncertainty in the model.On the other hand, there are some restrictions:1. The uncertainty has to be probabilistic in nature for the method to makesense.2. The criterion of optimality must be the expectation of some utility or performancefunction. We shall argue in section 2 that this is a very mild restriction.R. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 269–281, 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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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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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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