zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities. (English) Zbl 1243.93071
Summary: The problem of chaos synchronization between two different uncertain chaotic systems with input nonlinearities is investigated. Both master and slave systems are perturbed by model uncertainties, external disturbances and unknown parameters. The bounds of the model uncertainties and external disturbances are assumed to be unknown in advance. First, a simple linear sliding surface is selected. Then, appropriate adaptive laws are derived to tackle the model uncertainties, external disturbances and unknown parameters. Subsequently, based on the adaptive laws and Lyapunov stability theory, a robust adaptive sliding mode control law is designed to guarantee the existence of the sliding motion. Two illustrative examples are presented to verify the usefulness and applicability of the proposed technique.
MSC:
93C95Applications of control theory
34H10Chaos control (ODE)
34C28Complex behavior, chaotic systems (ODE)
34D06Synchronization
References:
[1]Kuo, C. -L.: Design of a fuzzy sliding-mode synchronization controller for two different chaos systems, Comput. math. Appl. 61, 2090-2095 (2011) · Zbl 1219.93042 · doi:10.1016/j.camwa.2010.08.080
[2]Pai, N. -S.; Yau, H. -T.; Kuo, C. -L.: Fuzzy logic combining controller design for chaos control of a rod-type plasma torch system, Expert syst. Appl. 37, 8278-8283 (2010)
[3]Guo, W.; Chen, S.; Zhou, H.: A simple adaptive-feedback controller for chaos synchronization, Chaos soliton fract. 39, 316-321 (2009) · Zbl 1197.93099 · doi:10.1016/j.chaos.2007.01.096
[4]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 · doi:10.1016/j.cnsns.2008.09.028
[5]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 · doi:10.1016/j.na.2008.10.069
[6]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 · doi:10.1016/j.physleta.2008.05.047
[7]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 · doi:10.1016/j.cnsns.2009.09.021
[8]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 · doi:10.1016/j.cnsns.2009.06.012
[9]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 · doi:10.1016/j.chaos.2006.04.003
[10]Yau, H.: Design of adaptive sliding mode controller for chaos synchronization with uncertainties, Chaos soliton fract. 22, 341-347 (2004) · Zbl 1060.93536 · doi:10.1016/j.chaos.2004.02.004
[11]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)
[12]Yau, H.; Shieh, C.: Chaos synchronization using fuzzy logic controller, Nonlinear anal. RWA 9, 1800-1810 (2008) · Zbl 1154.34334 · doi:10.1016/j.nonrwa.2007.05.009
[13]Chen, C.: Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems, Expert syst. Appl. 36, 11827-11835 (2009)
[14]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 · doi:10.1016/j.chaos.2009.02.028
[15]Lin, J.; Yan, J.: Adaptive synchronization for two identical generalized Lorenz chaotic systems via a single controller, Nonlinear anal. RWA 10, 1151-1159 (2009) · Zbl 1167.37329 · doi:10.1016/j.nonrwa.2007.12.005
[16]Yan, J.; Hung, M.; Liao, T.: Adaptive sliding mode control for synchronization of chaotic gyros with fully unknown parameters, J. sound vib. 298, 298-306 (2006)
[17]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 · doi:10.1016/j.physleta.2006.03.047
[18]Pourmahmood, M.; Khanmohammadi, S.; Alizadeh, G.: Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller, Commun. nonlinear sci. Numer. simulat. 16, 2853-2868 (2011) · Zbl 1221.93131 · doi:10.1016/j.cnsns.2010.09.038
[19]Aghababa, M. P.; Khanmohammadi, S.; Alizadeh, G.: Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique, Appl. math. Model. 35, 3080-3091 (2011) · Zbl 1219.93023 · doi:10.1016/j.apm.2010.12.020
[20]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 · doi:10.1016/j.physleta.2007.07.080
[21]Chen, X.; Lu, J.: Adaptive synchronization of different chaotic systems with fully unknown parameters, Phys. lett. A 364, 123-128 (2007) · Zbl 1203.93161 · doi:10.1016/j.physleta.2006.11.092
[22]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 · doi:10.1016/j.physleta.2005.10.033
[23]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 · doi:10.1016/j.chaos.2006.08.038
[24]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 · doi:10.1016/j.amc.2009.10.020
[25]El-Gohary, A.: Optimal synchronization of Rössler system with complete uncertain parameters, Chaos soliton fract. 27, 345-355 (2006) · Zbl 1091.93025 · doi:10.1016/j.chaos.2005.03.043
[26]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 · doi:10.1016/j.chaos.2005.09.025
[27]Yu, Y.; Zhang, S.: Adaptive backstepping synchronization of uncertain chaotic system, Chaos soliton fract. 21, 643-649 (2004) · Zbl 1062.34053 · doi:10.1016/j.chaos.2003.12.067
[28]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 · doi:10.1016/j.physleta.2008.08.022
[29]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 · doi:10.1016/j.chaos.2007.06.067
[30]Lin, J.; Yan, J.; Liao, T.: Chaotic synchronization via adaptive sliding mode observers subject to input nonlinearity, Chaos soliton fract. 24, 371-381 (2005) · Zbl 1094.93512 · doi:10.1016/j.chaos.2004.09.042
[31]Yau, H.; Yan, J.: Chaos synchronization of different chaotic systems subjected to input nonlinearity, Appl. math. Comput. 197, 775-788 (2008) · Zbl 1135.65409 · doi:10.1016/j.amc.2007.08.014
[32]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 · doi:10.1016/j.cnsns.2009.04.005
[33]Utkin, V. I.: Sliding modes in control and optimization, (1992) · Zbl 0748.93044
[34]Khalil, H. -K.: Nonlinear system, (2002) · Zbl 1003.34002