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Erschienen in: Soft Computing 14/2019

28.08.2018 | Foundations

Intelligent fractional-order control-based projective synchronization for chaotic optical systems

verfasst von: A. Boubellouta, A. Boulkroune

Erschienen in: Soft Computing | Ausgabe 14/2019

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Abstract

This paper investigates the problem of chaos synchronization based on fractional-order intelligent sliding-mode control approach for a class of fractional-order chaotic optical systems with unknown dynamics and disturbances. Two simple but effective fractional dynamic sliding surfaces with some desired stability features are adequately used to derive two fuzzy sliding-mode controllers. Fuzzy systems are used to online estimate the nonlinear functions. The stability analysis of the closed-loop system is rigorously performed by means of a fractional Lyapunov theory. Finally, some illustrative simulation examples are given to demonstrate the applicability and effectiveness of the proposed controllers. The obtained simulation results clearly confirm that the proposed chaos synchronization controllers are not only strongly robust with respect to the system’s uncertainties and external disturbances, but also one of these controllers can significantly reduce the chattering effect.

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Literatur
Zurück zum Zitat Abdelouahab MS, Hamri N (2014) Fractional-order hybrid optical system and its chaos control synchronization. Electron J Theor Phys 11:49–62 Abdelouahab MS, Hamri N (2014) Fractional-order hybrid optical system and its chaos control synchronization. Electron J Theor Phys 11:49–62
Zurück zum Zitat Aghaba MP (2012) Comments on “H∞ synchronization of uncertain fractional order chaotic systems: adaptive fuzzy approach”. ISA Trans 5:11–12CrossRef Aghaba MP (2012) Comments on “H synchronization of uncertain fractional order chaotic systems: adaptive fuzzy approach”. ISA Trans 5:11–12CrossRef
Zurück zum Zitat Aghababa MP (2014) A Lyapunov-based control scheme for robust stabilization of fractional chaotic systems. Nonlinear Dyn 78:2129–2140MathSciNetCrossRefMATH Aghababa MP (2014) A Lyapunov-based control scheme for robust stabilization of fractional chaotic systems. Nonlinear Dyn 78:2129–2140MathSciNetCrossRefMATH
Zurück zum Zitat Aziz-Alaoui MA (2005) A survey on chaos synchronization. In: Proceedings of the 12th IEEE-ICECS, December 11–15, pp 523–527 Aziz-Alaoui MA (2005) A survey on chaos synchronization. In: Proceedings of the 12th IEEE-ICECS, December 11–15, pp 523–527
Zurück zum Zitat Behinfaraz R, Badamchizadeh MA (2015) Synchronization of different fractional-ordered chaotic systems using optimized active control. In Proceedings of the 6th international conference on modeling, simulation, and applied optimization (ICMSAO) Behinfaraz R, Badamchizadeh MA (2015) Synchronization of different fractional-ordered chaotic systems using optimized active control. In Proceedings of the 6th international conference on modeling, simulation, and applied optimization (ICMSAO)
Zurück zum Zitat Benzaoui M, Chekireb H, Tadjine M, Boulkroune A (2016) Trajectory tracking with obstacle avoidance of redundant manipulator based on fuzzy inference systems. Neurocomputing 196:23–30CrossRef Benzaoui M, Chekireb H, Tadjine M, Boulkroune A (2016) Trajectory tracking with obstacle avoidance of redundant manipulator based on fuzzy inference systems. Neurocomputing 196:23–30CrossRef
Zurück zum Zitat Bhalekar S, Daftardar-Gejji V (2010) Synchronization of different fractional order chaotic systems using active control. Commun Nonlinear Sci Numer Simul 15:3536–3546CrossRefMATH Bhalekar S, Daftardar-Gejji V (2010) Synchronization of different fractional order chaotic systems using active control. Commun Nonlinear Sci Numer Simul 15:3536–3546CrossRefMATH
Zurück zum Zitat Boulkroune A (2016) A fuzzy adaptive control approach for nonlinear systems with unknown control gain sign. Neurocomputing 179:318–325CrossRef Boulkroune A (2016) A fuzzy adaptive control approach for nonlinear systems with unknown control gain sign. Neurocomputing 179:318–325CrossRef
Zurück zum Zitat Boulkroune A, Bouzeriba A, Hamel S, Bouden T (2015) Adaptive fuzzy control-based projective synchronization of uncertain nonaffine chaotic systems. Complexity 21:180–192MathSciNetCrossRefMATH Boulkroune A, Bouzeriba A, Hamel S, Bouden T (2015) Adaptive fuzzy control-based projective synchronization of uncertain nonaffine chaotic systems. Complexity 21:180–192MathSciNetCrossRefMATH
Zurück zum Zitat Bouzeriba A, Boulkroune A, Bouden T (2015) Fuzzy adaptive synchronization of a class of fractional-order chaotic systems. In: Proceedings of the international conference on control, engineering and information technology (CEIT) Bouzeriba A, Boulkroune A, Bouden T (2015) Fuzzy adaptive synchronization of a class of fractional-order chaotic systems. In: Proceedings of the international conference on control, engineering and information technology (CEIT)
Zurück zum Zitat Bouzeriba A, Boulkroune A, Bouden T (2016a) Fuzzy generalized projective synchronization of incommensurate fractional-order chaotic systems. Neurocomputing 173:606–614CrossRefMATH Bouzeriba A, Boulkroune A, Bouden T (2016a) Fuzzy generalized projective synchronization of incommensurate fractional-order chaotic systems. Neurocomputing 173:606–614CrossRefMATH
Zurück zum Zitat Bouzeriba A, Boulkroune A, Bouden T (2016b) Fuzzy adaptive synchronization of uncertain fractional-order chaotic systems. Int J Mach Learn Cybern 7:893–908CrossRefMATH Bouzeriba A, Boulkroune A, Bouden T (2016b) Fuzzy adaptive synchronization of uncertain fractional-order chaotic systems. Int J Mach Learn Cybern 7:893–908CrossRefMATH
Zurück zum Zitat Bouzeriba A, Boulkroune A, Bouden T (2016c) Projective synchronization of two different fractional-order chaotic systems via adaptive fuzzy control. Neural Comput Appl 27:1349–1360CrossRefMATH Bouzeriba A, Boulkroune A, Bouden T (2016c) Projective synchronization of two different fractional-order chaotic systems via adaptive fuzzy control. Neural Comput Appl 27:1349–1360CrossRefMATH
Zurück zum Zitat Chen G, Dong X (1998) From chaos to order perspectives methodologies and applications. World Scientific Pub, SingaporeCrossRefMATH Chen G, Dong X (1998) From chaos to order perspectives methodologies and applications. World Scientific Pub, SingaporeCrossRefMATH
Zurück zum Zitat Efe MO (2008) Fractional fuzzy adaptive sliding mode control of a 2-DOF direct-drive robot arm. IEEE Trans Syst Man Cybernet 38:1561–1570CrossRef Efe MO (2008) Fractional fuzzy adaptive sliding mode control of a 2-DOF direct-drive robot arm. IEEE Trans Syst Man Cybernet 38:1561–1570CrossRef
Zurück zum Zitat Efe MÖ, Kasnakog̃lu C (2008) A fractional adaptation law for sliding mode control. Int J Adapt Control Signal Process 22:968–986MathSciNetCrossRefMATH Efe MÖ, Kasnakog̃lu C (2008) A fractional adaptation law for sliding mode control. Int J Adapt Control Signal Process 22:968–986MathSciNetCrossRefMATH
Zurück zum Zitat Faieghi MR, Kuntanapreeda S, Delavari H, Baleanu D (2014) Robust stabilization of fractional-order chaotic systems with linear controllers: LMIC based sufficient conditions. J Vib Control 20:1042–1051MathSciNetCrossRef Faieghi MR, Kuntanapreeda S, Delavari H, Baleanu D (2014) Robust stabilization of fractional-order chaotic systems with linear controllers: LMIC based sufficient conditions. J Vib Control 20:1042–1051MathSciNetCrossRef
Zurück zum Zitat Hamel S, Boulkroune A (2016) A generalized function projective synchronization scheme for uncertain chaotic systems subject to input nonlinearities. Int J Gen Syst 45:689–710MathSciNetCrossRefMATH Hamel S, Boulkroune A (2016) A generalized function projective synchronization scheme for uncertain chaotic systems subject to input nonlinearities. Int J Gen Syst 45:689–710MathSciNetCrossRefMATH
Zurück zum Zitat Li Y, Chen YQI (2009) Podlubny. Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica 45:1965–1969 Li Y, Chen YQI (2009) Podlubny. Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica 45:1965–1969
Zurück zum Zitat Li Z, Zhang Z (2011) Chaotic communication based on single mode laser Lorenz system. In: International conference on electronics, communications and control (ICECC). IEEE, pp 1928–1931 Li Z, Zhang Z (2011) Chaotic communication based on single mode laser Lorenz system. In: International conference on electronics, communications and control (ICECC). IEEE, pp 1928–1931
Zurück zum Zitat Li Y, Chen YQ, Podlubny I (2010) Stability of fractional-order nonlinear dynamic systems: lyapunov direct method and generalized Mittag–Leffler stability. Comput Math Appl 59:1810–1821MathSciNetCrossRefMATH Li Y, Chen YQ, Podlubny I (2010) Stability of fractional-order nonlinear dynamic systems: lyapunov direct method and generalized Mittag–Leffler stability. Comput Math Appl 59:1810–1821MathSciNetCrossRefMATH
Zurück zum Zitat Li-Ming W, Yong-Guang T, Yong-Quan C, Feng W (2014) Generalized projective synchronization of the fractional-order chaotic system using adaptive fuzzy sliding mode control. Chin Phys B 23(10):100501CrossRef Li-Ming W, Yong-Guang T, Yong-Quan C, Feng W (2014) Generalized projective synchronization of the fractional-order chaotic system using adaptive fuzzy sliding mode control. Chin Phys B 23(10):100501CrossRef
Zurück zum Zitat Lin TC, Kuo CH (2011) H ∞ synchronization of uncertain fractional order chaotic systems: adaptive fuzzy approach. ISA Trans 50:548–556CrossRef Lin TC, Kuo CH (2011) H synchronization of uncertain fractional order chaotic systems: adaptive fuzzy approach. ISA Trans 50:548–556CrossRef
Zurück zum Zitat Lin TC, Lee TY (2011) Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control. IEEE Trans Fuzzy Syst 19:623–635CrossRef Lin TC, Lee TY (2011) Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control. IEEE Trans Fuzzy Syst 19:623–635CrossRef
Zurück zum Zitat Mahmoudian M, Ghaderi R, Ranjbar A, Sadati J, Hosseinnia SH, Momani S (2010) Synchronization of fractional-order chaotic system via adaptive PID controller. In: Baleanu D, Güvenç ZB, Machado JAT (eds) New trends in nanotechnology and fractional calculus applications. Springer, Berlin, pp 445–452CrossRef Mahmoudian M, Ghaderi R, Ranjbar A, Sadati J, Hosseinnia SH, Momani S (2010) Synchronization of fractional-order chaotic system via adaptive PID controller. In: Baleanu D, Güvenç ZB, Machado JAT (eds) New trends in nanotechnology and fractional calculus applications. Springer, Berlin, pp 445–452CrossRef
Zurück zum Zitat Matignon D (1996) Stability results of fractional differential equations with applications to control processing. In: IEEE-SMC proceedings of the computational engineering in systems and application multi-conference, IMACS. Lille, vol 2, pp 963–968 Matignon D (1996) Stability results of fractional differential equations with applications to control processing. In: IEEE-SMC proceedings of the computational engineering in systems and application multi-conference, IMACS. Lille, vol 2, pp 963–968
Zurück zum Zitat Maybhate A, Amritkar RE (1999) Use of synchronization and adaptive control in parameter estimation from a time series. Phys Rev E 59:284–293CrossRef Maybhate A, Amritkar RE (1999) Use of synchronization and adaptive control in parameter estimation from a time series. Phys Rev E 59:284–293CrossRef
Zurück zum Zitat Mitschke F, Fluggen N (1984) Chaotic behavior of a hybrid optical bistable system without time delay. Appl Phys B 35:59–64CrossRef Mitschke F, Fluggen N (1984) Chaotic behavior of a hybrid optical bistable system without time delay. Appl Phys B 35:59–64CrossRef
Zurück zum Zitat Pan L, Zhou W, Zhou L, Sun K (2011) Chaos synchronization between two different fractional-order hyperchaotic systems. Commun Nonlinear Sci Numer Simul 16:2628–2640MathSciNetCrossRefMATH Pan L, Zhou W, Zhou L, Sun K (2011) Chaos synchronization between two different fractional-order hyperchaotic systems. Commun Nonlinear Sci Numer Simul 16:2628–2640MathSciNetCrossRefMATH
Zurück zum Zitat Pisano A, Jelicic Z, Usai E (2010) Sliding mode control approaches to the robust regulation of linear multivariable fractional-order dynamics. Int J Robust Nonlinear Control 20:2021–2044MathSciNetCrossRefMATH Pisano A, Jelicic Z, Usai E (2010) Sliding mode control approaches to the robust regulation of linear multivariable fractional-order dynamics. Int J Robust Nonlinear Control 20:2021–2044MathSciNetCrossRefMATH
Zurück zum Zitat Podlubny I (1999) Fractional differential equations. Academic Press, San DiegoMATH Podlubny I (1999) Fractional differential equations. Academic Press, San DiegoMATH
Zurück zum Zitat Pyragas K (1992) Continuous control of chaos by self-controlling feedback. Phys Lett A 170:421–428CrossRef Pyragas K (1992) Continuous control of chaos by self-controlling feedback. Phys Lett A 170:421–428CrossRef
Zurück zum Zitat Rigatos G, Zhu G, Yousef H, Boulkroune A (2016) Flatness-based adaptive fuzzy control of electrostatically actuated MEMS using output feedback. Fuzzy Sets Syst 290:138–157MathSciNetCrossRefMATH Rigatos G, Zhu G, Yousef H, Boulkroune A (2016) Flatness-based adaptive fuzzy control of electrostatically actuated MEMS using output feedback. Fuzzy Sets Syst 290:138–157MathSciNetCrossRefMATH
Zurück zum Zitat Si-Ammour A, Djennoune S, Bettayeb M (2009) A sliding mode control for linear fractional systems with input and state delays. Commun Nonlinear Sci Numer Simul 14:2310–2318MathSciNetCrossRefMATH Si-Ammour A, Djennoune S, Bettayeb M (2009) A sliding mode control for linear fractional systems with input and state delays. Commun Nonlinear Sci Numer Simul 14:2310–2318MathSciNetCrossRefMATH
Zurück zum Zitat Tavazoei MS (2012) Comments on “Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control”. IEEE Trans Fuzzy Syst 20:993–995CrossRef Tavazoei MS (2012) Comments on “Chaos synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive fuzzy sliding mode control”. IEEE Trans Fuzzy Syst 20:993–995CrossRef
Zurück zum Zitat Wang LX (1994) Adaptive fuzzy systems and control: design and stability analysis. Prentice-Hall, Englewood Cliffs Wang LX (1994) Adaptive fuzzy systems and control: design and stability analysis. Prentice-Hall, Englewood Cliffs
Zurück zum Zitat Wang J, Zhang Y (2006) Designing synchronization schemes for chaotic fractional order unified systems. Chaos Solitons Fractals 30:1265–1272MathSciNetCrossRefMATH Wang J, Zhang Y (2006) Designing synchronization schemes for chaotic fractional order unified systems. Chaos Solitons Fractals 30:1265–1272MathSciNetCrossRefMATH
Zurück zum Zitat Wang X, Zhang X, Ma C (2012) Modified projective synchronization of fractional order chaotic systems via active sliding mode control. Nonlinear Dyn 69:511–517MathSciNetCrossRefMATH Wang X, Zhang X, Ma C (2012) Modified projective synchronization of fractional order chaotic systems via active sliding mode control. Nonlinear Dyn 69:511–517MathSciNetCrossRefMATH
Zurück zum Zitat Xi H, Yu S, Zhang R, Xu L (2014) Adaptive impulsive synchronization for a class of fractional-order chaotic and hyper-chaotic systems. Optik Int J Light Electron Opt 125:2036–2040CrossRef Xi H, Yu S, Zhang R, Xu L (2014) Adaptive impulsive synchronization for a class of fractional-order chaotic and hyper-chaotic systems. Optik Int J Light Electron Opt 125:2036–2040CrossRef
Zurück zum Zitat Yan JJ, Hung ML, Chiang TY, Yang YS (2006) Robust synchronization of chaotic systems via adaptive sliding mode control. Phys Lett A 356:220–225CrossRefMATH Yan JJ, Hung ML, Chiang TY, Yang YS (2006) Robust synchronization of chaotic systems via adaptive sliding mode control. Phys Lett A 356:220–225CrossRefMATH
Zurück zum Zitat Zhang W, Li J, Ding C (2016) Anti-synchronization control for delayed memristor-based distributed parameter NNs with mixed boundary conditions. Adv Differ Equ 2016:320MathSciNetCrossRefMATH Zhang W, Li J, Ding C (2016) Anti-synchronization control for delayed memristor-based distributed parameter NNs with mixed boundary conditions. Adv Differ Equ 2016:320MathSciNetCrossRefMATH
Zurück zum Zitat Zouari F, Boulkroune A, Ibeas A, Arefi MM (2017) Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation. Neural Comput Appl 28:993–1010CrossRef Zouari F, Boulkroune A, Ibeas A, Arefi MM (2017) Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation. Neural Comput Appl 28:993–1010CrossRef
Metadaten
Titel
Intelligent fractional-order control-based projective synchronization for chaotic optical systems
verfasst von
A. Boubellouta
A. Boulkroune
Publikationsdatum
28.08.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 14/2019
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-018-3490-5

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