Assessment and Future Directions of Nonlinear Model Predictive ...

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Receding Horizon Control for Free-Flight Path Optimization 571Table 1. Six simulation casesDD (nm)No. of UR’sStatic environmentCase 1 Case 2 Case 3500 1000 20001 6 14Dynamic environmentCase 4 Case 5 Case 6500 1000 20001 6 14Ave. OCT(s)Ave. AFT (s)Max.OCT(s)Max. AFT(s)Table 2. Simulation results in static casesCDOCase 1 Case 2 Case 31.2687 8.3675 77.5363965.6 7407.3 148685.3970 37.479 364.923966.9 7435.7 14913RHCCase 1 Case 2 Case 32.5675 4.8498 7.30473966.2 7421.5 149055.7970 7.408 15.5513968.7 7480.4 15052Table 3. Simulation results in dynamic casesAve. OCT(s)Ave. AFT (s)Max.OCT(s)Max. AFT(s)CDOCase 4 Case 5 Case 60.9623 9.448 68.92194222.0 7475 161925.317 38.96 347.9154223.9 8492 16638RHCCase 4 Case 5 Case 62.4930 3.8419 7.87544221.6 7454.3 159325.8990 6.3190 17.6944223.1 7995.8 16118a given performance index when no uncertainties are present. Table 2 showsthat the performance of RHC is very close to that of CDO, which implies thatRHC works very well in static cases. As for OCT’s, RHC is clearly much moreefficient than CDO. Since one time-slice is 10-minutes-long, one can see thatthere is no problem for RHC to run in real-time, while CDO does struggleto complete online computation in some cases. Dynamic cases are our mainconcern, and some corresponding simulation results are given in Table 3. As forperformance, in relatively simple cases like Case 4 and Case 5, CDO and RHChave similar AFT’s, while in complicated cases like Case 6, the performance ofRHC is better than that of CDO. Again, RHC provides reliable and promisingreal-time properties against CDO.Tab. 4 highlights that the horizon length Nshould be properly chosen. If N is too small, the performance is very poor,as is the case of N=1 and N=3 in Tab. 4. However, if N is too large, OCT’sincrease, but the performance is not necessarily improved further. Instead, theperformance could degrade in dynamic cases, as shown for N =9.
572 X.-B. Hu and W.-H. ChenTable 4. Influence of N on RHCN=1 OCT(s)AFT(s)N=3 OCT(s)AFT(s)N=6 OCT(s)AFT(s)N=9 OCT(s)AFT(s)Static environmentCase 1 Case 2 Case 30.8340 0.9365 1.3364006.5 8054.9 178911.3003 1.9507 2.5393965.0 7811.0 156742.5675 4.8498 7.3053966.2 7421.5 149054.6264 10.6017 18.253965.9 7407.6 14894Dynamic environmentCase 4 Case 5 Case 60.7337 0.8465 1.25904225.1 7976.8 169221.2907 1.4612 2.26524226.5 7482.6 162072.4930 3.8419 7.87544221.6 7454.3 159324.0966 8.5754 17.7374221.9 7462.4 160744 ConclusionsThis paper introduces the concept of RHC to the online optimization of flightpaths in a dynamical FF environment. Attention is particularly paid to the horizonlength and terminal penalty to guarantee the success of the proposed algorithm.Simulation results show that, regarding performance, the proposed RHCalgorithm is as good as the existing algorithm in the absence of uncertainties,and achieves better solutions in a dynamic environment. The main advantageof the RHC algorithm is its high efficiency regarding the online computationaltime.References[1] C.D. Wickens, et al (1998). Airspace System Integration-The Concept of FreeFlight. National Academy Press.[2] S. Kahne (2000). Annual reviews in Control, 24:21–29.[3] XB Hu, et al (2004). Eng. Applications of Artificial Intelligence,17:897–907.[4] N. Durand N, et al (1995). Air Traffic Control Quarterly, 3(3).[5] S.F. Wu (1990). Studies on the flight performance management, Ph.D. Thesis,Nanjing University of Aero. and Astro., China.[6] J.A. McDonald and Y. Zhao (2000). Time benefits of free-flight for a commercialaircraft. In The Proc. of the AIAA GNC Conference, Denver,CO,USA, 2000.[7] G. Guastalla, et al (2000). Transportation Sci., 34:394–401.[8] S. Chand et al (2002). Manufacturing and Service Operations Manag., 4:25-43.[9] X.B. Hu (2005). New Results and New Developments in Model Predictive Control.Ph.D. Thesis, Dept. of Aero. and Auto. Eng., Loughborough University.
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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 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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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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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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Controlling Distributed Hyperbolic
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444 K.R. Muske, A.E. Witmer, and R.
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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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Integrating Fault Diagnosis with No
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Robust Model Predictive Control for
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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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