×

Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller. (English) Zbl 1221.93131

Summary: A robust adaptive sliding mode controller (RASMC) is proposed to realize chaos synchronization between two different chaotic systems with uncertainties, external disturbances and fully unknown parameters. It is assumed that both master and slave chaotic systems are perturbed by uncertainties, external disturbances and unknown parameters. The bounds of the uncertainties and external disturbances are assumed to be unknown in advance. Suitable update laws are designed to tackle the uncertainties, external disturbances and unknown parameters. For constructing the RASMC a simple sliding surface is first designed. Then, the RASMC is derived to guarantee the occurrence of the sliding motion. The robustness and stability of the proposed RASMC is proved using Lyapunov stability theory. Finally, the introduced RASMC is applied to achieve chaos synchronization between three different pairs of the chaotic systems (Lorenz–Chen, Chen–Lorenz, and Liu–Lorenz) in the presence of the uncertainties, external disturbances and unknown parameters. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed RASMC.

MSC:

93C40 Adaptive control/observation systems
34D06 Synchronization of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
93B12 Variable structure systems
93D20 Asymptotic stability in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chen, G.; Dong, X., From chaos to order: methodologies, perspectives and applications (1998), World Scientific: World Scientific Singapore
[2] Nayfeh, A. H., Applied nonlinear dynamics (1995), Wiley: Wiley New York
[3] Kapitaniak, T., Chaotic oscillations in mechanical systems (1991), Manchester University Press: Manchester University Press New York · Zbl 0786.58027
[4] Wang, H.; Han, Z.; Xie, Q.; Zhang, W., Finite-time chaos control via nonsingular terminal sliding mode control, Commun Nonlinear Sci Numer Simulat, 14, 2728-2733 (2009) · Zbl 1221.37225
[5] Xiang, W.; Huangpu, Y., Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties, Commun Nonlinear Sci Numer Simulat, 15, 3241-3247 (2010) · Zbl 1222.93045
[6] Wang, H.; Han, Z.; Xie, Q.; Zhang, W., Sliding mode control for chaotic systems based on LMI, Commun Nonlinear Sci Numer Simulat, 14, 1410-1417 (2009) · Zbl 1221.93049
[7] Fuh, C., Optimal control of chaotic systems with input saturation using an input-state linearization scheme, Commun Nonlinear Sci Numer Simulat, 14, 3424-3431 (2009)
[8] Grzybowski, J. M.V.; Rafikov, M.; Balthazar, J. M., Synchronization of the unified chaotic system and application in secure communication, Commun Nonlinear Sci Numer Simulat, 14, 2793-2806 (2009) · Zbl 1221.94047
[9] Rafikov, M.; Balthazar, J. M., On control and synchronization in chaotic and hyperchaotic systems via linear feedback control, Commun Nonlinear Sci Numer Simulat, 13, 1246-1255 (2008) · Zbl 1221.93230
[10] Bowong, S., Adaptive synchronization between two different chaotic dynamical systems, Commun Nonlinear Sci Numer Simulat, 12, 976-985 (2007) · Zbl 1115.37030
[11] Lazzouni, S. A.; Bowong, S.; Kakmeni, F. M.M.; Cherki, B., An adaptive feedback control for chaos synchronization of nonlinear systems with different order, Commun Nonlinear Sci Numer Simulat, 12, 568-583 (2007) · Zbl 1234.70006
[12] Chen, H.; Sheu, G.; Lin, Y.; Chen, C., Chaos synchronization between two different chaotic systems via nonlinear feedback control, Nonlinear Anal, 70, 4393-4401 (2009) · Zbl 1171.34324
[13] Wang, B.; Wen, G., On the synchronization of a class of chaotic systems based on backstepping method, Phys Lett A, 370, 35-39 (2007) · Zbl 1209.93108
[14] Yassen, M. T., Controlling, synchronization and tracking chaotic Liu system using active backstepping design, Phys Lett A, 360, 582-587 (2007) · Zbl 1236.93086
[15] Wang, F.; Liu, C., Synchronization of unified chaotic system based on passive control, Physica D, 225, 55-60 (2007) · Zbl 1119.34332
[16] Lee, S. M.; Ji, D. H.; Park, J. H.; Won, S. C., \(H\)∞ synchronization of chaotic systems via dynamic feedback approach, Phys Lett A, 372, 4905-4912 (2008) · Zbl 1221.93087
[17] Yau, H.; Shieh, C., Chaos synchronization using fuzzy logic controller, Nonlinear Anal: RWA, 9, 1800-1810 (2008) · Zbl 1154.34334
[18] Chang, W., PID control for chaotic synchronization using particle swarm optimization, Chaos Soliton Fract, 39, 910-917 (2009) · Zbl 1197.93118
[19] Sun, Y., Chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity, Phys Lett A, 373, 3273-3276 (2009) · Zbl 1233.34016
[20] Yan, J.; Yang, Y.; Chiang, T.; Chen, C., Robust synchronization of unified chaotic systems via sliding mode control, Chaos Soliton Fract, 34, 947-954 (2007) · Zbl 1129.93489
[21] Jianwen, F.; Ling, H.; Chen, X.; Austin, F.; Geng, W., Synchronizing the noise-perturbed Genesio chaotic system by sliding mode control, Commun Nonlinear Sci Numer Simulat, 15, 2546-2551 (2010) · Zbl 1222.93121
[22] Yau, H., Design of adaptive sliding mode controller for chaos synchronization with uncertainties, Chaos Soliton Fract, 22, 341-347 (2004) · Zbl 1060.93536
[23] Zhang, H.; Ma, X.; Liu, W., Synchronization of chaotic systems with parametric uncertainty using active sliding mode control, Chaos Soliton Fract, 21, 1249-1257 (2004) · Zbl 1061.93514
[24] Feki, M., Sliding mode control and synchronization of chaotic systems with parametric uncertainties, Chaos Soliton Fract, 41, 1390-1400 (2009) · Zbl 1198.93056
[25] Lin, C.; Peng, Y.; Lin, M., CMAC-based adaptive backstepping synchronization of uncertain chaotic systems, Chaos Soliton Fract, 42, 981-988 (2009) · Zbl 1198.93110
[26] Ahmadi, A. A.; Majd, V. J., Robust synchronization of a class of uncertain chaotic systems, Chaos Soliton Fract, 42, 1092-1096 (2009) · Zbl 1198.93005
[27] Asheghan, M. M.; Beheshti, M. T.H., An LMI approach to robust synchronization of a class of chaotic systems with gain variations, Chaos Soliton Fract, 42, 1106-1111 (2009) · Zbl 1198.93195
[28] Zhang, H.; Ma, X., Synchronization of uncertain chaotic systems with parameters perturbation via active control, Chaos Soliton Fract, 21, 39-47 (2004) · Zbl 1048.37031
[29] Cai, N.; Jing, Y.; Zhang, S., Modified projective synchronization of chaotic systems with disturbances via active sliding mode control, Commun Nonlinear Sci Numer Simulat, 15, 1613-1620 (2010) · Zbl 1221.37211
[30] Haeri, M.; Tavazoei, M. S.; Naseh, M. R., Synchronization of uncertain chaotic systems using active sliding mode control, Chaos Soliton Fract, 33, 1230-1239 (2007) · Zbl 1138.93045
[31] Kebriaei, H.; Yazdanpanah, M. J., Robust adaptive synchronization of different uncertain chaotic systems subject to input nonlinearity, Commun Nonlinear Sci Numer Simulat, 15, 430-441 (2010) · Zbl 1221.34139
[32] Chen, C., Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems, Expert Syst Appl, 36, 11827-11835 (2009)
[33] Yan, J.; Hung, M.; Liao, T., Adaptive sliding mode control for synchronization of chaotic gyros with fully unknown parameters, J Sound Vibr, 298, 298-306 (2006) · Zbl 1243.93097
[34] Li, W.; Chang, K., Robust synchronization of drive-response chaotic systems via adaptive sliding mode control, Chaos Soliton Fract, 39, 2086-2092 (2009) · Zbl 1197.93146
[35] Wang, H.; Han, Z.; Xie, Q.; Zhang, W., Finite-time chaos synchronization of unified chaotic system with uncertain parameters, Commun Nonlinear Sci Numer Simulat, 14, 2239-2247 (2009)
[36] Salarieh, H.; Alasty, A., Adaptive chaos synchronization in Chua’s systems with noisy parameters, Math Comput Simulat, 79, 233-241 (2008) · Zbl 1166.34029
[37] Zhang, G.; Liu, Z.; Zhang, J., Adaptive synchronization of a class of continuous chaotic systems with uncertain parameters, Phys Lett A, 372, 447-450 (2008) · Zbl 1217.37036
[38] Shen, L.; Wang, M., Robust synchronization and parameter identification on a class of uncertain chaotic systems, Chaos Soliton Fract, 38, 106-111 (2008)
[39] Ma, J.; Zhang, A.; Xia, Y.; Zhang, L., Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems, Appl Math Comput, 215, 3318-3326 (2010) · Zbl 1181.93032
[40] El-Gohary, A., Optimal synchronization of Rossler system with complete uncertain parameters, Chaos Soliton Fract, 27, 345-355 (2006) · Zbl 1091.93025
[41] El-Gohary, A.; Sarhan, A., Optimal control and synchronization of Lorenz system with complete unknown parameters, Chaos Soliton Fract, 30, 1122-1132 (2006) · Zbl 1142.93408
[42] Zhang, L.; Huang, L.; Zhang, Z.; Wang, Z., Fuzzy adaptive synchronization of uncertain chaotic systems via delayed feedback control, Phys Lett A, 372, 6082-6086 (2008) · Zbl 1223.93050
[43] Kim, J.; Park, C.; Kim, E.; Park, M., Fuzzy adaptive synchronization of uncertain chaotic systems, Phys Lett A, 334, 295-305 (2005) · Zbl 1123.37307
[44] Hwang, E.; Hyun, C.; Kim, E.; Park, M., Fuzzy model based adaptive synchronization of uncertain chaotic systems: robust tracking control approach, Phys Lett A, 373, 1935-1939 (2009) · Zbl 1229.34080
[45] Huang, J., Chaos synchronization between two novel different hyperchaotic systems with unknown parameters, Nonlinear Anal, 69, 4174-4181 (2008) · Zbl 1161.34338
[46] Yassen, M. T., Adaptive synchronization of two different uncertain chaotic systems, Phys Lett A, 337, 335-341 (2005) · Zbl 1136.34314
[47] Chen, X.; Lu, J., Adaptive synchronization of different chaotic systems with fully unknown parameters, Phys Lett A, 364, 123-128 (2007) · Zbl 1203.93161
[48] Zhang, H.; Huang, W.; Wang, Z.; Chai, T., Adaptive synchronization between two different chaotic systems with unknown parameters, Phys Lett A, 350, 363-366 (2006) · Zbl 1195.93121
[49] Salarieh, H.; Shahrokhi, M., Adaptive synchronization of two different chaotic systems with time varying unknown parameters, Chaos Soliton Fract, 37, 125-136 (2008) · Zbl 1147.93397
[50] Yan, J.; Hung, M.; Chiang, T.; Yang, Y., Robust synchronization of chaotic systems via adaptive sliding mode control, Phys Lett A, 356, 220-225 (2006) · Zbl 1160.37352
[51] Wang, C.; Ge, S. S., Adaptive synchronization of uncertain chaotic systems via backstepping design, Chaos Soliton Fract, 12, 1199-1206 (2001) · Zbl 1015.37052
[52] Utkin, V., Sliding modes in control and optimization (1992), Springer Verlag: Springer Verlag Berlin · Zbl 0748.93044
[53] Khalil, H-K., Nonlinear system (2002), Prentice Hall: Prentice Hall New Jersey
[54] Lorenz, E., Deterministic nonperiodic flow, J Atmos Sci, 20, 130-141 (1963) · Zbl 1417.37129
[55] Chen, G.; Ueta, T., Yet another chaotic attractor, Int J Bifur Chaos, 9, 1465-1466 (1999) · Zbl 0962.37013
[56] Liu, C.; Liu, T.; Liu, L.; Liu, K., A new chaotic attractor, Chaos Soliton Fract, 22, 1031-1038 (2004) · Zbl 1060.37027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.