Assessment and Future Directions of Nonlinear Model Predictive ...

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54 M.V. Kothare and Z. WanAlgorithm 3 (Local output feedback MPC for constrained nonlinearsystems). Consider the nonlinear system (1) and the output map ( 9) withinthe neighborhood (Π x ,Π u ) around (x eq ,u eq ). Given the controller and observerdesign parameters 0
A Computationally Efficient Scheduled Model Predictive Control Algorithm 552.5 Observability Analysis of Output Feedback MPCFor the output feedback MPC in Algorithm 3, the state is not measured, butfrom the output of the system and the estimated state, we can observe theexponential decay of the norm bound of the state estimation error, and thusobserve the real state incrementally.Consider the output feedback MPC in Algorithm 3 which can stabilize anyx(0), ˆx(0) ∈Ssatisfying ‖x(0) − ˆx(0)‖ P≤ η. Let T>0. At time k − T ≥ 0, letx(k − T ), ˆx(k − T ) ∈Ssatisfying ‖x(k −T) − ˆx(k −T)‖ P≤ η. During T steps,an input sequence {u(k − T ), ..., u(k − 1)} ⊂Π u is obtained by the controllerbased on {ˆx(k−T ), ..., ˆx(k−1)} ⊂ S. We know that the state evolution startingfrom x(k − T )drivenby{u(k − T ), ..., u(k − 1)} is inside S⊂Π x . Suppose thatthe state evolution ˜x(k +1)=f(˜x(k),u(k)) starting from ˜x(k − T )=ˆx(k − T )driven by {u(k − T ), ..., u(k − 1)} is also inside Π x , then we can getx(k +1)− ˜x(k +1)=f(x(k),u(k)) − f(˜x(k),u(k))y(k) − ỹ(k) =h(x(k)) − h(˜x(k))Let V T := ∑ k−1j=k−T ‖y(j) − ỹ(j)‖2 . Suppose (x eq ,u eq ) is locally observable, thenthere exist a neighborhood (Π x ,Π u ) around (x eq ,u eq )andT,µ > 0 such thatV T ≥ µ ‖x(k −T) − ˆx(k −T)‖ 2 P ,orequivalently,‖x(k) − ˆx(k)‖2 P ≤ ρT V Tµ.Theorem 4. Consider the nonlinear system (1) and (9). Suppose (x eq ,u eq ) is locallystabilizable and observable, then there exist a neighborhood (Π x ,Π u ) around(x eq ,u eq ) and controller and observer design parameters 0
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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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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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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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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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