메뉴 건너뛰기




Volumn 73, Issue 1-2, 2013, Pages 907-919

A modified adaptive control method for synchronization of some fractional chaotic systems with unknown parameters

Author keywords

Chaotic systems; Fractional derivative; Modified adaptive control method; Synchronization; Unknown parameters

Indexed keywords

FRACTIONAL CHAOTIC SYSTEMS; FRACTIONAL DERIVATIVES; FRACTIONAL-ORDER CHAOTIC SYSTEMS; FRACTIONAL-ORDER SYSTEMS; LYAPUNOV STABILITY THEORY; MODIFIED ADAPTIVE CONTROLS; PARAMETERS IDENTIFICATION; UNKNOWN PARAMETERS;

EID: 84879783840     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-0842-7     Document Type: Article
Times cited : (53)

References (34)
  • 2
    • 0000241853 scopus 로고
    • Deterministic non-periodic flows
    • 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
    • Lorenz, E.N.: Deterministic non-periodic flows. J. Atmos. Sci. 20, 130-141 (1963)
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 5
    • 33749563875 scopus 로고    scopus 로고
    • On chaos synchronization of fractional differential equations
    • 2280115 10.1016/j.chaos.2005.11.062 1132.37308
    • Yan, J.P., Li, C.P.: On chaos synchronization of fractional differential equations. Chaos Solitons Fractals 32, 725-735 (2007)
    • (2007) Chaos Solitons Fractals , vol.32 , pp. 725-735
    • Yan, J.P.1    Li, C.P.2
  • 6
    • 0343689904 scopus 로고
    • Synchronization in chaotic systems
    • 1038263 10.1103/PhysRevLett.64.821
    • Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821-824 (1990)
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 821-824
    • Pecora, L.M.1    Carroll, T.L.2
  • 7
    • 63449125876 scopus 로고    scopus 로고
    • Chaos synchronization between two different chaotic systems via nonlinear feedback control
    • 2514770 1171.34324
    • Chen, H.H., Sheu, G.J., Lin, Y.L., Chen, C.S.: Chaos synchronization between two different chaotic systems via nonlinear feedback control. Nonlinear Anal., Real World Appl. 70, 4393-4401 (2009)
    • (2009) Nonlinear Anal., Real World Appl. , vol.70 , pp. 4393-4401
    • Chen, H.H.1    Sheu, G.J.2    Lin, Y.L.3    Chen, C.S.4
  • 8
    • 38049079764 scopus 로고    scopus 로고
    • On control and synchronization in chaotic and hyperchaotic systems via linear feedback control
    • 2369454 10.1016/j.cnsns.2006.12.011 1221.93230
    • Rafikov, M., Balthazar, J.M.: On control and synchronization in chaotic and hyperchaotic systems via linear feedback control. Commun. Nonlinear Sci. Numer. Simul. 13, 1246-1255 (2008)
    • (2008) Commun. Nonlinear Sci. Numer. Simul. , vol.13 , pp. 1246-1255
    • Rafikov, M.1    Balthazar, J.M.2
  • 9
    • 77956057555 scopus 로고    scopus 로고
    • Chaos feedback control and synchronization of a fractional-order modified autonomous Van der Pol-Duffing circuit
    • 2725819 10.1016/j.cnsns.2010.04.027 1221.93227
    • Matouk, A.E.: Chaos feedback control and synchronization of a fractional-order modified autonomous Van der Pol-Duffing circuit. Commun. Nonlinear Sci. Numer. Simul. 16, 975-986 (2011)
    • (2011) Commun. Nonlinear Sci. Numer. Simul. , vol.16 , pp. 975-986
    • Matouk, A.E.1
  • 10
    • 4243135936 scopus 로고    scopus 로고
    • A novel criterion for delayed feedback control of time-delay chaotic systems
    • 2089574 10.1016/j.chaos.2004.05.023 1061.93507
    • Park, J.H., Kwon, O.M.: A novel criterion for delayed feedback control of time-delay chaotic systems. Chaos Solitons Fractals 23, 495-501 (2005)
    • (2005) Chaos Solitons Fractals , vol.23 , pp. 495-501
    • Park, J.H.1    Kwon, O.M.2
  • 11
    • 79961046349 scopus 로고    scopus 로고
    • Feedback control and hybrid projective synchronization of a fractional-order Newton-Leipnik system
    • 2826010 10.1016/j.cnsns.2011.04.003 1248.93074
    • Zhang, K., Wang, H., Fang, H.: Feedback control and hybrid projective synchronization of a fractional-order Newton-Leipnik system. Commun. Nonlinear Sci. Numer. Simul. 17, 317-328 (2012)
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 317-328
    • Zhang, K.1    Wang, H.2    Fang, H.3
  • 12
    • 47949103726 scopus 로고    scopus 로고
    • Simple adaptive controller for chaos and hyperchaos synchronization
    • 10.1016/j.physleta.2008.07.016 1223.34078
    • Guo, R.A.: Simple adaptive controller for chaos and hyperchaos synchronization. Phys. Lett. A 372, 5593-5597 (2008)
    • (2008) Phys. Lett. A , vol.372 , pp. 5593-5597
    • Guo, R.A.1
  • 13
    • 51749111833 scopus 로고    scopus 로고
    • Adaptive synchronization between different hyperchaotic systems with fully uncertain parameters
    • 10.1016/j.physleta.2008.05.025 1221.93127
    • Huang, J.: Adaptive synchronization between different hyperchaotic systems with fully uncertain parameters. Phys. Lett. A 372, 4799-4804 (2008)
    • (2008) Phys. Lett. A , vol.372 , pp. 4799-4804
    • Huang, J.1
  • 14
    • 0036722179 scopus 로고    scopus 로고
    • Synchronization of an uncertain unified chaotic system via adaptive control
    • 10.1016/S0960-0779(02)00006-1 1005.93020
    • Chen, S.H., Lu, J.: Synchronization of an uncertain unified chaotic system via adaptive control. Chaos Solitons Fractals 14, 643-647 (2002)
    • (2002) Chaos Solitons Fractals , vol.14 , pp. 643-647
    • Chen, S.H.1    Lu, J.2
  • 15
    • 31144433846 scopus 로고    scopus 로고
    • Adaptive synchronization between two different chaotic systems with unknown parameters
    • 10.1016/j.physleta.2005.10.033 1195.93121
    • 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)
    • (2006) Phys. Lett. A , vol.350 , pp. 363-366
    • Zhang, H.1    Huang, W.2    Wang, Z.3    Chai, T.4
  • 16
    • 0037043301 scopus 로고    scopus 로고
    • Parameters identification and synchronization of chaotic systems based upon adaptive control
    • 1916475 10.1016/S0375-9601(02)00522-4 0996.93016
    • Chen, S.H., Lu, J.: Parameters identification and synchronization of chaotic systems based upon adaptive control. Phys. Lett. A 299, 353-358 (2002)
    • (2002) Phys. Lett. A , vol.299 , pp. 353-358
    • Chen, S.H.1    Lu, J.2
  • 17
    • 1842842989 scopus 로고    scopus 로고
    • Design of adaptive sliding mode controller for chaos synchronization with uncertainties
    • 2060871 10.1016/j.chaos.2004.02.004 1060.93536
    • Yau, H.T.: Design of adaptive sliding mode controller for chaos synchronization with uncertainties. Chaos Solitons Fractals 22, 341-347 (2004)
    • (2004) Chaos Solitons Fractals , vol.22 , pp. 341-347
    • Yau, H.T.1
  • 18
    • 33846878521 scopus 로고    scopus 로고
    • Adaptive synchronization between two different chaotic dynamical systems
    • 2309769 10.1016/j.cnsns.2005.10.003 1115.37030
    • Bowong, S.: Adaptive synchronization between two different chaotic dynamical systems. Commun. Nonlinear Sci. Numer. Simul. 12, 976-985 (2007)
    • (2007) Commun. Nonlinear Sci. Numer. Simul. , vol.12 , pp. 976-985
    • Bowong, S.1
  • 19
    • 1042290520 scopus 로고    scopus 로고
    • Adaptive synchronization of uncertain Rössler hyperchaotic system based on parameter identification
    • 10.1016/j.physleta.2003.12.011 1118.81326
    • Chen, S., Hu, J., Wang, C., Lü, J.: Adaptive synchronization of uncertain Rössler hyperchaotic system based on parameter identification. Phys. Lett. A 321, 50-55 (2004)
    • (2004) Phys. Lett. A , vol.321 , pp. 50-55
    • Chen, S.1    Hu, J.2    Wang, C.3    Lü, J.4
  • 20
    • 3142716961 scopus 로고    scopus 로고
    • Chaos synchronization between two different chaotic systems using active control
    • 2101570 10.1016/j.chaos.2004.03.038 1091.93520
    • Yassen, M.T.: Chaos synchronization between two different chaotic systems using active control. Chaos Solitons Fractals 23, 131-140 (2005)
    • (2005) Chaos Solitons Fractals , vol.23 , pp. 131-140
    • Yassen, M.T.1
  • 21
    • 84860168517 scopus 로고    scopus 로고
    • Synchronization of fractional order chaotic systems using active control
    • 10.1016/j.chaos.2012.02.004
    • Agrawal, S.K., Srivastava, M., Das, S.: Synchronization of fractional order chaotic systems using active control. Chaos Solitons Fractals 45, 737-752 (2012)
    • (2012) Chaos Solitons Fractals , vol.45 , pp. 737-752
    • Agrawal, S.K.1    Srivastava, M.2    Das, S.3
  • 22
    • 84866101967 scopus 로고    scopus 로고
    • Synchronization between fractional-order Ravinovich-Fabrikant and Lotka-Volterra systems
    • 2945558 10.1007/s11071-012-0426-y
    • Agrawal, S.K., Srivastava, M., Das, S.: Synchronization between fractional-order Ravinovich-Fabrikant and Lotka-Volterra systems. Nonlinear Dyn. 69, 2277-2288 (2012)
    • (2012) Nonlinear Dyn. , vol.69 , pp. 2277-2288
    • Agrawal, S.K.1    Srivastava, M.2    Das, S.3
  • 23
    • 0038239769 scopus 로고    scopus 로고
    • Parameter identification and backstepping control of uncertain Lü system
    • 1984055 10.1016/S0960-0779(02)00659-8 1068.93019
    • Wu, X., Lü, J.: Parameter identification and backstepping control of uncertain Lü system. Chaos Solitons Fractals 18, 721-729 (2003)
    • (2003) Chaos Solitons Fractals , vol.18 , pp. 721-729
    • Wu, X.1    Lü, J.2
  • 24
    • 84861713425 scopus 로고    scopus 로고
    • Active sliding observer scheme based fractional chaos synchronization
    • 2930340 10.1016/j.cnsns.2012.03.004 1253.34056
    • Senejohnny, D.M., Delavari, H.: Active sliding observer scheme based fractional chaos synchronization. Commun. Nonlinear Sci. Numer. Simul. 17, 4373-4383 (2012)
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 4373-4383
    • Senejohnny, D.M.1    Delavari, H.2
  • 25
    • 84862792637 scopus 로고    scopus 로고
    • Projective lag synchronization of spatiotemporal chaos via active sliding mode control
    • 2904230 10.1016/j.cnsns.2011.12.011 1245.93031
    • Chai, Y., Chen, L.Q.: Projective lag synchronization of spatiotemporal chaos via active sliding mode control. Commun. Nonlinear Sci. Numer. Simul. 17, 3390-3398 (2012)
    • (2012) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 3390-3398
    • Chai, Y.1    Chen, L.Q.2
  • 26
    • 40249087307 scopus 로고    scopus 로고
    • Phase synchronization in fractional differential chaotic systems
    • 10.1016/j.physleta.2007.11.065 1220.34004
    • Erjaee, G.H., Momani, S.: Phase synchronization in fractional differential chaotic systems. Phys. Lett. A 372, 2350-2354 (2008)
    • (2008) Phys. Lett. A , vol.372 , pp. 2350-2354
    • Erjaee, G.H.1    Momani, S.2
  • 27
    • 4043121080 scopus 로고    scopus 로고
    • Detailed error analysis for a fractional Adams method
    • 2063572 10.1023/B:NUMA.0000027736.85078.be 1055.65098
    • Diethelm, K., Ford, J., Freed, A.: Detailed error analysis for a fractional Adams method. Numer. Algorithms 36, 31-52 (2004)
    • (2004) Numer. Algorithms , vol.36 , pp. 31-52
    • Diethelm, K.1    Ford, J.2    Freed, A.3
  • 28
    • 3042709180 scopus 로고    scopus 로고
    • Multi-order fractional differential equations and their numerical solution
    • 2072809 10.1016/S0096-3003(03)00739-2 1060.65070
    • Diethelm, K., Ford, J.: Multi-order fractional differential equations and their numerical solution. Appl. Math. Comput. 154, 621-640 (2004)
    • (2004) Appl. Math. Comput. , vol.154 , pp. 621-640
    • Diethelm, K.1    Ford, J.2
  • 30
    • 0004058249 scopus 로고
    • Elsevier/Academic Press New York/London
    • Liapunov, A.M.: Stability of Motion. Elsevier/Academic Press, New York/London (1966)
    • (1966) Stability of Motion
    • Liapunov, A.M.1
  • 32
    • 80052380812 scopus 로고    scopus 로고
    • Chaos in fractional-order Genesio-Tesi system and its synchronization
    • 2834432 10.1016/j.cnsns.2011.05.038
    • Faieghi, M.R., Delavari, H.: Chaos in fractional-order Genesio-Tesi system and its synchronization. Commun. Nonlinear Sci. Numer. Simul. 17, 731-741 (2011)
    • (2011) Commun. Nonlinear Sci. Numer. Simul. , vol.17 , pp. 731-741
    • Faieghi, M.R.1    Delavari, H.2
  • 34
    • 23144435914 scopus 로고    scopus 로고
    • A note on the fractional-order Chen system
    • 10.1016/j.chaos.2005.04.037 1101.37307
    • Lu, J.G., Chen, G.: A note on the fractional-order Chen system. Chaos Solitons Fractals 27, 685-688 (2006)
    • (2006) Chaos Solitons Fractals , vol.27 , pp. 685-688
    • Lu, J.G.1    Chen, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.