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Title: A sample-time adjusted feedback for robust bounded output stabilization (English)
Author: Ordaz, Patricio
Author: Alazki, Hussain
Author: Poznyak, Alexander
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 49
Issue: 6
Year: 2013
Pages: 911-934
Summary lang: English
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Category: math
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Summary: This paper deals with a bounded control design for a class of nonlinear systems where the mathematical model may be not explicitly given. This class of uncertain nonlinear systems governed by a system of ODE with quasi-Lipschitz right-hand side and containing external perturbations as well. The Attractive Ellipsoid Method (AEM) application permits to describe the class of nonlinear feedbacks (containing a nonlinear projection operator, a linear state estimator and a feedback matrix-gain) guaranteeing a boundedness of all possible trajectories around the origin. To fulfill this property some modification of AEM are introduced: basically, some sort of sample-time corrections of the feedback parameters are required. The optimization of feedback within this class of controllers is associated with the selection of the feedback parameters which provide the trajectory converges within an ellipsoid of a “minimal size“. The effectiveness of the suggested approach is illustrated by its application to a flexible arm system). (English)
Keyword: sample-time data
Keyword: attractive ellipsoid
Keyword: state estimation
Keyword: saturated control process
Keyword: flexible arm system
MSC: 62A10
MSC: 93B51
MSC: 93C57
MSC: 93E12
idZBL: Zbl 1284.93242
idMR: MR3182648
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Date available: 2014-01-27T12:30:44Z
Last updated: 2015-03-29
Stable URL: http://hdl.handle.net/10338.dmlcz/143579
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Reference: [1] Ahmed-Ali, T., Lamnabhi-Lagarrigue, F.: High gain observer design for some networked control systems..IEEE Trans. Automat. Control 57 (2012), 4, 995-1000. MR 2952330, 10.1109/TAC.2011.2168049
Reference: [2] Blanchini, F.: Set invariance in control, a survey..Automatica 35 (1999), 11, 1747-1767. MR 1831764, 10.1016/S0005-1098(99)00113-2
Reference: [3] Blanchini, F., Miani, F.: Set-Theoretic Methods in Control..Birkhauser, Boston 2008. Zbl 1140.93001, MR 2359816
Reference: [4] Bortoff, S. A., Lynch, A. F.: Synthesis of Optimal Nonlinear Observersr..34th IEEE Conference on Decision and Control 1 (1995), 95-100.
Reference: [5] Dahleh, M. A., Pearson, J. B.: Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization..IEEE Trans. on Automat. Control 33 (1988), 8, 722-731. Zbl 0657.93019, MR 0950793, 10.1109/9.1288
Reference: [6] Davila, J., Poznyak, A.: Sliding mode parameter adjustment for perturbed linear systems with actuators via invariant ellipsoid method..Internat. J. Robust and Nonlinear Control 21 (2011), 473-487. Zbl 1214.93026, MR 2808892, 10.1002/rnc.1599
Reference: [7] Duncan, G. J., Schweppe, F. C.: Control of linear dynamic systems with set constrained disturbances..IEEE Trans. Automat. Control 16 (1971), 5, 411-423. MR 0287947, 10.1109/TAC.1971.1099781
Reference: [8] Gonzalez, S., Polyakov, A., Poznyak, A.: Using the method of invariant ellipsoids for linear robust output stabilization of spacecraft..Automat. Remote Control 72 (2011), 3, 540-555. Zbl 1229.93138, MR 2828448, 10.1134/S0005117911030064
Reference: [9] Ioannou, P., Sun, J.: Robust Adaptive Control..Prentice Hall, Inc, 1996. Zbl 0839.93002
Reference: [10] Jong, M. L., Jay, H. L.: Approximate dynamic programming-based approaches for input-output data-driven control of nonlinear processes..Automatica 41 (2005), 1281-1288. Zbl 1092.93011, MR 2160128, 10.1016/j.automatica.2005.02.006
Reference: [11] Kabamba, P. T., Hara, S.: Worst-case analysis and design of sampled-data control systems..IEEE Trans. Automat. Control 38 (1993), 9, 1337-1358. Zbl 0787.93068, MR 1240826, 10.1109/9.237646
Reference: [12] Kurzhanski, A. B., Veliov, V. M.: Modeling Techniques and Uncertain Systems..Birkhauser, New York 1994. MR 1287643
Reference: [13] Kou, S. R., Elliott, D. L., Tarn, T. J.: Exponential observers for non-linear dynamic systems..Inform. Control 29 (1975), 393-428. MR 0384227
Reference: [14] Min, W., Zhou, Z. Lan, Jinhua, S.: Design of observer-based $H_{\infty }$ robust repetitive-control system..IEEE Trans. Automat. Control 56 (2011), 6, 1452-1457. MR 2839242, 10.1109/TAC.2011.2112473
Reference: [15] Narendra, K. S., Annaswamy, A. M.: Stable Adaptive Systems..Dover Publications Inc., 2005. Zbl 1217.93081
Reference: [16] Nazin, A., Polyak, B., Topunov, M.: Rejection of bounded exogenous disturbances by the method of invariant ellipsoids..Automat. Remote Control 68 (2007), 3, 467-486. Zbl 1125.93370, MR 2304813, 10.1134/S0005117907030083
Reference: [17] O'Reilly, J.: Observers for Linear Systems..Academic Press, 1983. Zbl 0513.93001
Reference: [18] Ordaz, P., Poznyak, A.: Stabilizaton of furuta's pendulum with out model: Attractive ellipsoid method..In: 51th IEEE Conference of Decision and Control, Hawaii 2012, pp. 7285-7290.
Reference: [19] Poliakov, A., Poznyak, A.: Invariant ellipsoid method for minimization of unmatched disturbances effects in sliding mode control..Automatica 47 (2011), 1450-1454. MR 2889242, 10.1016/j.automatica.2011.02.013
Reference: [20] Poznyak, A.: Advanced Mathematical Tools for Automatic Control Engineers: Deterministic techniques. Vol. 1..Elsevier 2008. MR 2374025
Reference: [21] Poznyak, A., Azhmyakov, V., Mera, M.: Practical output feedback stabilization for a class of continuous-time dynamic systems under sample-data outputs..Internat. J. Control 8 (2011), 4, 1408-1416. MR 2830870, 10.1080/00207179.2011.603097
Reference: [22] Proychev, T. P., Mishkov, R. L.: Transformation of nonlinear systems in observer canonical from with reduced dependency on derivatives of the input..Automatica 29 (1993), 2, 495-498. MR 1211308, 10.1016/0005-1098(93)90145-J
Reference: [23] Rudin, W.: Functional Analysis. Second edition..MacGraw-Hill, Inc. 1991. MR 1157815
Reference: [24] Sussmann, H. J., Sontag, E. D., Yang, Y.: A general result on the stabilization of linear systems using bounded controls..IEEE Trans. Automat. Control 39 (1994), 12, 2411-2425. Zbl 0811.93046, MR 1337566, 10.1109/9.362853
Reference: [25] Tingshu, H., Zongli, L.: Control Systems with Actuator Saturation: Analyze and Design..Birkhauser, Boston 2001.
Reference: [26] Teel, A. R.: A nonlinear small gain theorem for the analysis of control systems with saturation..IEEE Trans. Automat. Control 41 (1996), 9, 1256-1270. Zbl 0863.93073, MR 1409471, 10.1109/9.536496
Reference: [27] Utkin, V.: Sliding mode control design principles and applications to electric drives..IEEE Trans. on Industrial Electronics 40 (1993), 1, 23-36. 10.1109/41.184818
Reference: [28] Walcott, B., Corless, M., Zak, S.: Comparative study of non-linear state-observation techniques..Internat. J. Control 45 (1987), 6, 2109-2132. Zbl 0627.93012, MR 0891800, 10.1080/00207178708933870
Reference: [29] Zeitz, M.: The extended Luenberger observer for nonlinear systems..Systems Control Lett. 9 (1987), 149-156. Zbl 0624.93012, MR 0906234, 10.1016/0167-6911(87)90021-1
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