“Master-slave H-Infinity robust controller design for synchronization of chaotic systems”
Authors: Vojtech Vesely, Adrian Ilka, Ladislav Korosi and Martin Ernek,Affiliation: Slovak University of Technology and Chalmers University of Technology
Reference: 2019, Vol 40, No 1, pp. 41-50.
Keywords: Chaotic systems, master-slave systems, H-Infinity robust controller, Synchronization of chaotic systems, L2 gain performance
Abstract: This paper is devoted to robust master-slave controller design for generalized chaotic systems synchronization. The closed-loop system is asymptotically stable when the robust stability conditions hold and while the H-Infinity norm of the closed-loop transfer function with respect to defined output and input is strictly less than gamma>0. In this paper a modified L2 gain approach is used and an original design procedure is proposed to decrease the conservativeness of the former method. The effectiveness of the proposed method is shown in numerical examples.
PDF (473 Kb)
DOI: 10.4173/mic.2019.1.4DOI forward links to this article:
| [1] Vojtech Vesely and Ladislav Korosi (2019), doi:10.1109/ACCS-PEIT48329.2019.9062893 |
| [2] Yang Wang, Zhen Wang, Lingyun Kong and Hassan Zargarzadeh (2021), doi:10.1155/2021/8845553 |
| [3] Min Zou, Yongchun Wang, Weibing Zhu, Yu Wang, Dou Xie, Chunyan Kong and Song Tang (2025), doi:10.1016/j.ymssp.2024.111820 |
[1] Boccaletti, S., Kurths, J., Osipov, G., Valladares, D., and Zhou, C. (2002). Boccaletti, S, , Kurths, J., Osipov, G., Valladares, D., and Zhou, C. The synchronization of chaotic systems. Physics Reports. 366(1):1 -- 101. doi:10.1016/S0370-1573(02)00137-0
[2] Boyd, S., Ghaoui, L.E., Feron, E., and Balakrishnan, V. (1994). Boyd, S, , Ghaoui, L.E., Feron, E., and Balakrishnan, V. Linear Matrix Inequalities in System and Control Theory. Number15 in Studies in applied mathematics. SIAM. .
[3] Burke, J.V., Henrion, D., Lewis, A.S., , and Overton, M.L. (2006). Burke, J, V., Henrion, D., Lewis, A.S., , and Overton, M.L. HIFOO - a MATLAB Package for Fixed-order Controller Design and H-infinity Optimization. In IFAC Symposium on Robust Control Design. pages 339--344, 2006. .
[4] Chen, H.-H. (2009). Chen, H, -H. Chaos control and global synchronization of liu chaotic systems using linear balanced feedback control. Chaos, Solitons & Fractals. 40(1):466 -- 473. doi:10.1016/j.chaos.2007.07.098
[5] Czyzyk, J., Mesnier, M.P., and More, J.J. (1998). Czyzyk, J, , Mesnier, M.P., and More, J.J. The neos server. IEEE Journal on Computational Science and Engineering. 5(3):68--75. .
[6] Dinh, Q.T., Gumussoy, S., Michiels, W., and Diehl, M. (2011). Dinh, Q, T., Gumussoy, S., Michiels, W., and Diehl, M. Combining convex-concave decompositions and linearization approaches for solving bmis, with application to static output feedback. Technical report, Department of Electrical Engineering (ESAT-SCD) and Optimization in Engineering Center (OPTEC), K.U. Leuven, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium, 2011. http://arxiv.org/abs/1202.5488, .
[7] Dinh, Q.T., Michiels, W., and Diehl, M. (2011). Dinh, Q, T., Michiels, W., and Diehl, M. An inner convex approximation algorithm for bmi optimization and applications in control. Technical report, Department of Electrical Engineering (ESAT-SCD) and Optimization in Engineering Center (OPTEC), K.U. Leuven, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium, 2011. http://arxiv.org/abs/1202.5488, .
[8] Farghaly, A. A.M. (2013). Farghaly, A, A.M. Chaos synchronization of complex roessler system. Applied Mathematics & Information Sciences. 7(4):1415--1420. .
[9] Fiala, J., Kocvara, M., and Stingl, M. (2013). Fiala, J, , Kocvara, M., and Stingl, M. Penlab: A matlab solver for nonlinear semidefinite optimization, 2013. Submitted to Mathematical Programming Computation. .
[10] Henrion, D., Lofberg, J., Kocvara, M., and Stingl, M. (2005). Henrion, D, , Lofberg, J., Kocvara, M., and Stingl, M. Solving polynomial static output feedback problems with PENBMI. In 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. pages 7581--7586. .
[11] Hoi, C., Scherer, C., vander Meché, E., and Bosgra, O. (2003). Hoi, C, , Scherer, C., vander Meché, E., and Bosgra, O. A nonlinear sdp approach to fixed-order controller synthesis and comparison with two other methods applied to an active suspension system*. European Journal of Control. 9(1):13 -- 28. doi:10.3166/ejc.9.13-28
[12] Ilka, A. (2018). Ilka, A, Matlab/Octave toolbox for structurable and robust output-feedback LQR design. IFAC-PapersOnLine. 51(4):598 -- 603. 3rd IFAC Conference on Advances in Proportional-Integral-Derivative Control PID 2018. doi:10.1016/j.ifacol.2018.06.161
[13] Isidori, A. (2011). Isidori, A, Robust stability via H-Infinity methods. Technical report, European Embedded Control Institute. http://www.eeci-institute.eu/GSC2012/Photos-EECI/EECI-GSC-2012-M9/Handout_1.pdf, .
[14] Isidori, A. (2017). Isidori, A, Lectures in Feedback Design for Multivariable Systems. Springer International Publishing, 1st edition. doi:10.1007/978-3-319-42031-8
[15] Krokavec, D. and Filasova, A. (2016). Krokavec, D, and Filasova, A. On enhanced mixed H2/H-Infinity design conditions for control of linear time-invariant systems. In 2016 17th International Carpathian Control Conference (ICCC). pages 384--389. doi:10.1109/CarpathianCC.2016.7501128
[16] LFradkov, A. (2007). LFradkov, A, Cybernetical Physics - From Control of Chaos to Quantum Control. Springer. .
[17] Leibfritz, F. (2004). Leibfritz, F, COMPl_eib: COnstraint Matrix-optimization Problem library - a collection of test examples for nonlinear semidefinite programs, control system design and related problems. Technical report, University of Trier, Department of Mathematics, D-54286 Trier, Germany. http://www.friedemann-leibfritz.de/COMPlib_Data/COMPlib_Main_Paper.pdf, .
[18] Lofberg, J. (2004). Lofberg, J, YALMIP : A Toolbox for Modeling and Optimization in MATLAB. In Proceedings of the CACSD Conference. Taipei, Taiwan, pages 284--289. .
[19] Mobayen, S. and Javadi, S. (2015). Mobayen, S, and Javadi, S. Disturbance observer and finite-time tracker design of disturbed third-order nonholonomic systems using terminal sliding mode. Journal of Vibration and Control. doi:10.1177/1077546315576611
[20] Mobayen, S. and Tchier, F. (2017). Mobayen, S, and Tchier, F. Synchronization of a class of uncertain chaotic systems with lipschitz nonlinearities using state-feedback control design: A matrix inequality approach. Asian Journal of Control. 20. doi:10.1002/asjc.1512
[21] Pecora, L. and Carroll, T. (1990). Pecora, L, and Carroll, T. Synchronization in chaotic system. Physical Review Letters. 64:821. .
[22] Shahverdiev, E., Hashimova, L., and Hashimova, N. (2008). Shahverdiev, E, , Hashimova, L., and Hashimova, N. Chaos synchronization in some power systems. Chaos, Solitons & Fractals. 37(3):827 -- 834. doi:10.1016/j.chaos.2006.09.071
[23] Song, Y. and Yu, X. (2003). Song, Y, and Yu, X. Chaos synchronization from an invariant manifold approach. Dynamics of Continuous, Discrete and Impulsive Systems. Series B: Applications and Algorithms. 10(6):879--890. .
[24] Sprott, J.C. (2015). Sprott, J, C. New chaotic regimes in the lorenz and chen systems. International Journal of Bifurcation and Chaos. 25:1550033. .
[25] The Mathworks, Inc. (2018). The Mathworks, Inc, MATLAB R2018a. The Mathworks, Inc., Natick, Massachusetts. .
[26] Vesely, V. and Rosinova, D. (2013). Vesely, V, and Rosinova, D. Robust pid-psd controller design: Bmi approach. Asian Journal of Control. 15(2):469--478. doi:10.1002/asjc.559
[27] Wang, B., Shi, P., RezaKarimi, H., and Wang, J. (2012). Wang, B, , Shi, P., RezaKarimi, H., and Wang, J. H-Infinity robust controller design for the synchronization of master-slave chaotic systems with disturbance input. Modeling, Identification and Control: A Norwegian Research Bulletin. 33. doi:10.4173/mic.2012.1.3
[28] Wang, F. and Balakrishnan, V. (2002). Wang, F, and Balakrishnan, V. Improved stability analysis and gain-scheduled controller synthesis for parameter-dependent systems. IEEE Transactions on Automatic Control. 47(5):720--734. doi:10.1109/TAC.2002.1000267
[29] Zeng, H.-B., Park, J.H., Xiao, S.-P., and Liu, Y. (2015). Zeng, H, -B., Park, J.H., Xiao, S.-P., and Liu, Y. Further results on sampled-data control for master--slave synchronization of chaotic lur'e systems with time delay. Nonlinear Dynamics. 82(1):851--863. doi:10.1007/s11071-015-2199-6
BibTeX:
@article{MIC-2019-1-4,
title={{Master-slave H-Infinity robust controller design for synchronization of chaotic systems}},
author={Vesely, Vojtech and Ilka, Adrian and Korosi, Ladislav and Ernek, Martin},
journal={Modeling, Identification and Control},
volume={40},
number={1},
pages={41--50},
year={2019},
doi={10.4173/mic.2019.1.4},
publisher={Norwegian Society of Automatic Control}
};