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An Experimental Study of Stabilizing Receding Horizon Control 577this paper, as a first step, we propose unconstrained stabilizing receding horizoncontrol schemes. In the near future, we will consider constraints which representone of the advantages of receding horizon control, and develop it using level set,see [7].Moreover, focused on the inverse optimality approach [12], the following corollaryis derived.Corollary 1. Consider the following weights of the cost function (10)-(12).Q(t) =qN T (t)KN(t), q≥0 (13)R(t) =rK −1 , r > 0 (14)ρ =2 √ qr. (15)Then, the receding horizon control for the visual feedback system is asymptoticallystabilizing, the receding horizon control law isand the cost-to-go is given byqu ∗ = −√KNx (16)rJ ∗ = ρV (x). (17)If the weights of the terminal cost function are set to (13)-(15), then the controllerthat satisfies inf u [Ṁ(x)+l(x, u)] = 0 is analytically derived.In the next section, the stabilizing receding horizon control is applied to aplanar visual feedback system. It is expected that the control performance isimproved using the receding horizon control.4 Experimental ResultsIn this section, the proposed stabilizing receding horizon control is tested onan actual planar visual feedback systemwhichisanimagebaseddirectvisualservo system. The manipulator used in the experiments (see Fig. 1), is controlledby a digital signal processor (DSP) from dSPACE Inc., which utilizes apowerPC 750 running at 480 MHz. Control programs are written in MATLABand SIMULINK, and implemented on the DSP using the Real-Time Workshopand dSPACE Software which includes ControlDesk and Real-Time Interface. AXC-HR57 camera is attached to the tip of the manipulator. The video signalsare acquired by a frame graver board PicPort-Stereo-H4D and the image processingsoftware HALCON. The sampling time of the controller and the framerate provided by the camera are 16.7 [ms] and 60 [fps], respectively. To solvethe real time optimization problem, the software C/GMRES [13] is utilized. Thetarget object is projected on the liquid crystal monitor. The control objectiveis to bring the image feature parameter vector f to the origin. The experimentis carried out with the initial condition q 1 (0) = π/6 [rad],q 2 (0) = −π/6 [rad],
578 M. Fujita et al.ξ 2[rad/s]6420−2−40 0.5 1 1.5 2 2.5 3100 [pixel]0-100-2000 0.5 1 1.5 2 2.5 31u ξ2[Nm]0−1−20 0.5 1 1.5 2 2.5 35u d2[m/s]0−50 0.5 1 1.5 2 2.5 3time [s]Fig. 3. Experimental comparison with different control schemes (solid: receding horizoncontrol (T =0.02 [s], ρ = 1), dashed: passivity based control)˙q 1 (0) = ˙q 2 (0) = 0 [rad/s], w f = 0.0001, z wo = 0.9 [m],sλ = 1230 [pixel],f(0) = [−120 − 160] T [pixel] (1 [pixel] = 0.74 [mm]).In this experiment, we compare the performance of the receding horizon controllaw proposed in Theorem 1 and the passivity based control law u k (4). Theweights of the cost function (10) were selected as Q = diag{65, 1.5, 10, 100}×10 −9 , R =diag{0.04, 1.7, 0.005, 0.00045} and ρ = 1 satisfy P ≥0. The controllerparameters for the passivity based control law u k (4) were empirically selectedas K ξ =diag{6.5, 0.15} and K d =diag{50, 550}. The control input with thereceding horizon control is updated within every 16.7 [ms]. It must be calculatedby the receding horizon controller within that period. The horizon was selectedas T =0.02 [s].The experimental results are presented in Fig. 3, showing the velocity errorξ 2 , the image feature parameter f y and the control inputs u ξ2 and u d2 , respectively.The rise time applying the receding horizon control is shorter thanthat for the passivity based control. The controller predicts the movement ofthe target object using the visual information, as a result the manipulatormoves more aggressively. This validates one of the expected advantages of the
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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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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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Page 519 and 520: 524 M. Alamirmin V (x u(·,x),T) un
Page 521 and 522: 526 M. AlamirDefinition 4. The syst
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Page 565 and 566: 572 X.-B. Hu and W.-H. ChenTable 4.
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Page 573 and 574: 580 M. Fujita et al.Acknowledgement
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Page 579 and 580: 4. c(t) ∈Cfor all t ∈ Z + ;5. T
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Page 619 and 620: 630 J.J. Arrieta-Camacho, L.T. Bieg
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632 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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