Assessment and Future Directions of Nonlinear Model Predictive ...

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16 E.F. Camacho and C. Bordons[44] J. Sjoberg, Q. Zhang, L. Ljung, A. Benveniste, B. Deylon, P. Glorennec, H. Hjalmarsson,and A. Juditsky. Nonlinear black-box modeling in system identification:a unified overview. Automatica, 31(12):1691–1724, 1995.[45] S. Townsend and G.W. Irwin. Nonlinear Predictive Control, chapter NonlinearModel Based Predictive Control Using Multiple Local Models. IEE Control Engineeringseries, 2001.[46] A. Zheng and W. Zhang. Nonlinear Predictive Control, chapter ComputationallyEfficient Nonlinear Model Predictive Control Algorithm for Control of ConstrainedNonlinear Systems. IEE Control Engineering series, 2001.[47] G. Zimmer. State observation by on-line minimization. Int. J. Contr., 60(4):595–606, 1994.
Hybrid MPC: Open-Minded but Not EasilySwayedS. Emre Tuna, Ricardo G. Sanfelice, Michael J. Messina, and Andrew R. TeelDepartment of Electrical and Computer Engineering, University of California, SantaBarbara, CA 93106, USA{emre,rsanfelice,mmessina,teel}@ece.ucsb.eduSummary. The robustness of asymptotic stability with respect to measurement noisefor discrete-time feedback control systems is discussed. It is observed that, when attemptingto achieve obstacle avoidance or regulation to a disconnected set of points fora continuous-time system using sample and hold state feedback, the noise robustnessmargin necessarily vanishes with the sampling period. With this in mind, we proposetwo modifications to standard model predictive control (MPC) to enhance robustnessto measurement noise. The modifications involve the addition of dynamical states thatmake large jumps. Thus, they have a hybrid flavor. The proposed algorithms are wellsuited for the situation where one wants to use a control algorithm that responds quicklyto large changes in operating conditions and is not easily confused by moderately largemeasurement noise and similar disturbances.1 Introduction1.1 ObjectivesThe first objective of this paper is to discuss the robustness of asymptotic stabilityto measurement noise for discrete-time feedback control systems. We focus oncontrol systems that perform tasks such as obstacle avoidance and regulation to adisconnected set of points. We will compare the robustness induced by pure statefeedback algorithms to the robustness induced by dynamic state feedback algorithmsthat have a “hybrid” flavor. Nonlinear model predictive control (MPC),in its standard manifestation, will fall under our purview since 1) it is a methodfor generating a pure state feedback control (see [14] for an excellent survey), 2)it can be used for obstacle avoidance (see [11, 12, 18]) and regulation to a disconnectedset of points (this level of generality is addressed in [9] for example),and 3) dynamic “hybrid” aspects can be incorporated to enhance robustness tomeasurement noise. The second objective of this paper is to demonstrate suchhybrid modifications to MPC. The proposed feedback algorithms are able torespond rapidly to significant changes in operating conditions without gettingconfused by moderately large measurement noise and related disturbances. Thefindings in this paper are preliminary: we present two different hybrid modificationsof MPC, but we have not investigated sufficiently the differences betweenthese modifications, nor have we characterized their drawbacks.R. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 17–34, 2007.springerlink.com c○ Springer-Verlag Berlin Heidelberg 2007
Page 2 and 3: Lecture Notesin Control and Informa
Page 4 and 5: Series Advisory BoardF. Allgöwer,
Page 7 and 8: ContentsFoundations and History of
Page 9 and 10: ContentsIXRobustness, Robust Design
Page 11 and 12: ContentsXIHybrid NMPC Control of a
Page 13 and 14: Nonlinear Model Predictive Control:
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Page 34 and 35: 22 S.E. Tuna et al.this says that i
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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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Nonlinear Model Predictive Control:
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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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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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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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