Assessment and Future Directions of Nonlinear Model Predictive ...

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280 J.M. Maciejowski, A. Lecchini Visintini, and J. Lygeros2. Conventional NMPC does not guarantee convergence to the global optimum.MCMC guarantees convergence to a near-optimal solution.3. Conventional NMPC interprets constraints as hard bounds. MCMC gives apre-defined probability of not violating constraints.4. Conventional NMPC uses hill-climbing optimization. MCMC uses stochasticoptimization, which requires much more computational effort and time.5. Satisfactory behaviour of conventional NMPC over time can be achievedusing known techniques. The behaviour of MCMC when used repeatedly ina receding-horizon context has not yet been investigated.The application of the MCMC approach to air traffic control problems hasbeen described. Some speculations on other possible applications have also beengiven. It is expected that many such applications will be found outside traditionalengineering areas, where nonlinear uncertain models are available, and enoughtime is available to complete the required computations ‘on-line’.Research is currently under way to make the MCMC algorithm more suitablefor MPC applications. But some applications can be tackled now, withoutwaiting for the results of further research.References[1] K.J. Arrow. Social Choice and Individual Values. Yale University Press, 2ndedition, 1963.[2] M.B. Beck, editor. Environmental Foresight and Models: a Manifesto. Elsevier,2002.[3] J. Bentham. Principles of Morals and Legislation. Oxford University Press, 1823(originally published 1789).[4] D. Bernoulli. Specimen theoriae novae de mensura sortis, Commentarii AcademiaeScientiarum Imperialis Petropolitanae (5, 175-192, 1738). Econometrica, 22:23–36, 1954. Translated by L. Sommer.[5] H. Blom and J. Lygeros. Stochastic Hybrid Systems: Theory and Safety CriticalApplications. Springer-Verlag, 2006.[6] M.H.A. Davis and M. Zervos. A problem of singular stochastic control withdiscretionary stopping. Annals of Applied Probability, 4:226–240, 1994.[7] A. Doucet, N. de Freitas, and N. Gordon, editors. Sequential Monte Carlo Methodsin Practice. Statistics for Engineering and Information Science. Springer, NewYork, 2001.[8] A. Doucet, S.J. Godsill, and C. Robert. Marginal maximum a posteriori estimationusing Markov chain Monte Carlo. Statistics and Computing, 12:77–84, 2002.[9] W. Glover and J. Lygeros. A stochastic hybrid model for air traffic control simulation.In R. Alur and G. Pappas, editors, Hybrid Systems: Computation andControl, number 2993 in LNCS, pages 372–386. Springr-Verlag, 2004.[10] HYBRIDGE: Distributed Control and Stochastic Analysis of HybridSystems Supporting Safety Critical Real-Time Systems Design.http://www.nlr.nl/public/hosted-sites/hybridge/, 2005. EuropeanCommission FP5 project, contract IST-2001-32460.[11] R.C. Jeffrey. The Logic of Decision. University of Chicago Press, 2nd edition,1983.
NMPC for Complex Stochastic Systems 281[12] B. Kouvaritakis, M. Cannon, and V. Tsachouridis. Recent developments instochastic MPC and sustainable development. In J.J. Gertler, editor, AnnualReviews in Control, volume 28, pages 23–35. Elsevier, 2004.[13] A. Lecchini Visintini, W. Glover, J. Lygeros, and J.M. Maciejowski. Monte Carlooptimization strategies for air traffic control. In Proc. AIAA Guidance, Navigationand Control Conference, San Francisco, August 2005.[14] J.M. Maciejowski. Predictive Control with Constraints. Prentice-Hall, HarlowUK, 2002.[15] H. Markowitz. Portfolio selection. Journal of Finance, 7:77–91, 1952.[16] P. Müller. Simulation based optimal design. In J.M. Bernardo, J.O. Berger, A.P.Dawid, and A.F.M. Smith, editors, Bayesian Statistics 6, pages 459–474. OxfordUniversity Press, 1999.[17] P. Müller, B. Sansó, and M. De Iorio. Optimal Bayesian design by inhomogeneousMarkov chain simulation. J. American Statistical Association, 99(467):788–798,2004.[18] H. Raiffa. Decision Analysis: Introductory Lectures on Choices Under Uncertainty.Addison-Wesley, Reading, MA, 1968.[19] C.P. Robert and G. Casella. Monte Carlo Statistical Methods. Springer-Verlag,New York, 1999.[20] L.J. Savage. The Foundations of Statistics. Wiley, New York, 1954.[21] J. von Neumann and O. Morgenstern. Theory of Games and Economic Behavior.Princeton University Press, 1944.
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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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Page 233 and 234: A Nonlinear Model Predictive Contro
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Page 267 and 268: MPC for Stochastic Systems 263( )κ
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Page 305 and 306: 302 L. Xie, P. Li, and G. WoznyFig.
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Page 315 and 316: 312 H. Arellano-Garcia et al.optimi
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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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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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