Assessment and Future Directions of Nonlinear Model Predictive ...

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Receding Horizon Control for Free-Flight PathOptimizationXiao-Bing Hu 1 and Wen-Hua Chen 21 Department of Informatics, University of Sussex, UKxiaobing.Hu@Sussex.ac.uk2 Department of Aero. and Auto. Engineering, Loughborough University, UKW.Chen@lboro.ac.ukSummary. This paper presents a Receding Horizon Control (RHC) algorithm to theproblem of on-line flight path optimization for aircraft in a dynamic Free-Flight (FF)environment. The motivation to introduce the concept of RHC is to improve the robustperformance of solutions in a dynamic and uncertain environment, and also to satisfythe restrictive time limit in the real-time optimization of this complicated air trafficcontrol problem. Compared with existing algorithms, the new algorithm proves moreefficient and promising for practical applications.1 Introduction“Free-Flight”(FF) is one of the most promising strategies for future air trafficcontrol (ATC) systems [1, 2]. Within the FF framework, each individual aircrafthas the first responsibility to plan its flight in terms of safety, efficiency andflexibility. One of the key enabling techniques is real-time path planning usingonboard flight management systems. Reference [3] proposes an effective GeneticAlgorithm (GA) for searching optimal flight paths in an FF environment, whereno pre-defined flight routes network exists. However, two questions arise for theGA in [3]: how to cope with unreliable information in a dynamic environment,and how to improve real-time properties.This paper introduces the concept of Receding Horizon Control (RHC) to theGA in [3] and then develops a more efficient algorithm for online optimizingflight paths in a dynamical FF environment. As an N-step-ahead online optimizationstrategy, firstly, RHC provides a promising way to deal with unreliableinformation for far future, and therefore increase the robustness/adoptation ofthe algorithms against environmental uncertainties/changes; secondly, the introductionof RHC can significantly reduce the heavy computational burden of theGA in [3] to an acceptable level. These achievements mainly rely on carefullychoosing horizon length and properly designing terminal penalty in the newlyproposed algorithm.R. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 565–572, 2007.springerlink.com c○ Springer-Verlag Berlin Heidelberg 2007
566 X.-B. Hu and W.-H. Chen2 Online Flight Path Optimization in FF Environment2.1 Optional Free Flight PathsIn contrast to conventional pre-defined flight routes networks, there are numerousoptional free flight paths in an ideal FF environment, as illustrated in Fig.1.Following [4], this paper uses the concept of “time-slice” and a set of discreteoptional headings to transform the non-conflict-airspace into a dynamic flightroutes network, and the optimization problem can be reasonably simplified.Time-slice and discrete optional headings set are two system parameters whichdetermine the complexity of the flight routes network. As discussed in [3], longertime-slice and less optional headings lead to a less flexible network; in the oppositeextreme, the network becomes unnecessarily complicated. Referring tosome papers on air conflict detection and resolution [4], where 5-min-long timeinterval and 10 ◦ discrete angular change for optimizing only local manoeuvresis adopted, this paper, to optimize global flight paths, uses a 10-min time-sliceand a discrete setΩ =[0 ◦ , 10 ◦ , 20 ◦ , ··· , 350 ◦ ,θ dire ] (1)where θ dire is the direct-heading, which is defined as the direction of the destinationairport with reference to the waypoint where the aircraft arrives at the endof the current time-slice. The ground ATC systems are supposed to periodicallybroadcast environmental information, particularly data of unavailable-regions, toeach individual aircraft. Each individual aircraft uses the latest information tooptimize the remained flight path starting from the next time-slice. An optionalflight path is composed of a series of sub-trajectories associated with time-slices.The sub-trajectory for the current time-slice is determined by the previous runof optimization.Fig. 1. OptimizedpathinanFFenvironment2.2 Performance Index for Flight Path OptimizationIn this paper, for the sake of simplification, only flight time cost is chosen as theindex for flight path optimization. Flight time cost can be easily transformed into
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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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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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Conditions for MPC Based Stabilizat
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A Computationally Efficient Schedul
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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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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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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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A Nonlinear Model Predictive Contro
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y i (k) =∑n um=1MPC for Stochasti
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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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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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304 L. Xie, P. Li, and G. Wozny[3]
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306 H. Arellano-Garcia et al.applic
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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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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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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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Non-linear Model Predictive Control
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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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Application of the NEPSAC Nonlinear
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Page 521 and 522: 526 M. AlamirDefinition 4. The syst
Page 523 and 524: 528 M. Alamir♭V is radially unbou
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Page 565 and 566: 572 X.-B. Hu and W.-H. ChenTable 4.
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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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