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Projective synchronization of chaotic fractional-order energy resources demand-supply systems via linear control. (English) Zbl 1222.93108
Summary: A fractional-order energy resources demand-supply system is proposed. A projective synchronization scheme is proposed as an extension on the synchronization scheme of {\it Z. M. Odibat, N. Corson, M. A. Aziz-Alaoui} and {\it C. Bertelle} [Int. J. Bifurcation Chaos Appl. Sci. Eng. 20, No. 1, 81--97 (2010; Zbl 1183.34095)]. The scheme is applied to achieve projective synchronization of the chaotic fractional-order energy resource demand-supply systems. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.

93C15Control systems governed by ODE
34A08Fractional differential equations
93B52Feedback control
Full Text: DOI
[1] Odibat, Z.; Corson, N.; Aziz-Alaoui, M.; Bertelle, C.: Synchronization of chaotic fractional-order systems via linear control, Int J bifurcation chaos 20, 81-97 (2010) · Zbl 1183.34095 · doi:10.1142/S0218127410025429
[2] Oldham, K.; Spanier, J.: The fractional calculus, (1974) · Zbl 0292.26011
[3] Samko, S.; Kilbas, A.; Marichev, O.: Fractional integrals and derivatives: theory and applications, (1993) · Zbl 0818.26003
[4] Wang, S.; Xu, M.: Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus, Nonlinear anal-real 10, 1087-1096 (2009) · Zbl 1167.76311 · doi:10.1016/j.nonrwa.2007.11.027
[5] Jiang, X.; Xu, M.; Qi, H.: The fractional diffusion model with an absorption term and modified fick’s law for non-local transport processes, Nonlinear anal-real 10, 262-269 (2009) · Zbl 1196.37120 · doi:10.1016/j.nonrwa.2008.10.057
[6] Liu, Y.; Ma, J.: Exact solutions of a generalized multi-fractional nonlinear diffusion equation in radical symmetry, Commun theor phys 52, 857-861 (2009) · Zbl 1182.35067 · doi:10.1088/0253-6102/52/5/20
[7] Asheghan, M.; Beheshti, M.; Tavazoei, M.: Robust synchronization of perturbed Chen’s fractional-order chaotic systems, Commun nonlinear sci numer simul 16, 1044-1051 (2011) · Zbl 1221.34007 · doi:10.1016/j.cnsns.2010.05.024
[8] Shahiri, M.; Ghaderi, R.; Ranjbar, N.; Hosseinnia, S.; Momani, S.: Chaotic fractional-order coullet system: synchronization and control approach, Commun nonlinear sci numer simul 15, 665-674 (2010) · Zbl 1221.37222 · doi:10.1016/j.cnsns.2009.05.054
[9] Meral, F.; Royston, T.; Magin, R.: Fractional calculus in viscoelasticity: an experimental study, Commun nonlinear sci numer simul 15, 939-945 (2010) · Zbl 1221.74012 · doi:10.1016/j.cnsns.2009.05.004
[10] Sabatier, J.; Cugnet, M.; Laruelle, S.; Grugeon, S.; Sahut, B.; Oustaloup, A.: A fractional order model for lead-acid battery crankability estimation, Commun nonlinear sci numer simul 15, 1308-1317 (2010)
[11] Hamamci, S.; Koksal, M.: Calculation of all stabilizing fractional-order PD controllers for integrating time delay systems, Comput math appl 59, 1621-1629 (2010) · Zbl 1189.93125 · doi:10.1016/j.camwa.2009.08.049
[12] Bouafoura, M.; Braiek, N.: PI$\lambda d\mu $ controller design for integer and fractional plants using piecewise orthogonal functions, Commun nonlinear sci numer simul 15, 1267-1278 (2010) · Zbl 1221.93073 · doi:10.1016/j.cnsns.2009.05.047
[13] Ahmed, E.; Elgazzar, A. S.: On fractional order differential equations model for nonlocal epidemics, Physica A 379, 607-614 (2007)
[14] Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A.: Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models, J math anal appl 325, 542-553 (2007) · Zbl 1105.65122 · doi:10.1016/j.jmaa.2006.01.087
[15] Matouk, A.: 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) · Zbl 1221.93227 · doi:10.1016/j.cnsns.2010.04.027
[16] Ahmad, W.; El-Khazali, R.: Fractional-order dynamical models of love, Chaos soliton fract 33, 1367-1375 (2007) · Zbl 1133.91539 · doi:10.1016/j.chaos.2006.01.098
[17] Song, L.; Xu, S.; Yang, J.: Dynamical models of happiness with fractional order, Commun nonlinear sci numer simul 15, 616-628 (2010) · Zbl 1221.93234 · doi:10.1016/j.cnsns.2009.04.029
[18] Chen, W.: Nonlinear dynamics and chaos in a fractional-order financial system, Chaos soliton fract 36, 1305-1314 (2008)
[19] Deng, W.; Li, C.: Chaos synchronization of the fractional Lü system, Physica A 353, 61-72 (2005)
[20] Wang, X.; Song, J.: Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control, Commun nonlinear sci numer simul 14, 3351-3357 (2009) · Zbl 1221.93091 · doi:10.1016/j.cnsns.2009.01.010
[21] Wang, X.; He, Y.: Projective synchronization of fractional order chaotic system based on linear separation, Phys lett A 372, 435-441 (2008) · Zbl 1217.37035 · doi:10.1016/j.physleta.2007.07.053
[22] Wang, X.; Wang, M.: Dynamic analysis of the fractional-order Liu system and its synchronization, Chaos 17, 033106 (2007) · Zbl 1163.37382 · doi:10.1063/1.2755420
[23] Bhalekar, S.; Daftardar-Gejji, V.: Synchronization of different fractional order chaotic systems using active control, Commun nonlinear sci numer simul 15, 3536-3546 (2010) · Zbl 1222.94031 · doi:10.1016/j.cnsns.2009.12.016
[24] Wu, X.; Lu, H.; Shen, S.: Synchronization of a new fractional-order hyperchaotic system, Phys lett A 373, 2329-2337 (2009) · Zbl 1231.34091 · doi:10.1016/j.physleta.2009.04.063
[25] Wu, X.; Chen, G.; Cai, J.: Chaos synchronization of the master -- slave generalized Lorenz systems via linear state error feedback control, Physica D 229, 52-80 (2007) · Zbl 1131.34040 · doi:10.1016/j.physd.2007.03.014
[26] Sun, M.; Tian, L.; Fu, Y.: An energy resources demand -- supply system and its dynamical analysis, Chaos soliton fract 32, No. 1, 168-180 (2007) · Zbl 1133.91524 · doi:10.1016/j.chaos.2005.10.085
[27] Sun, M.; Tian, L.; Fu, Y.; Qian, W.: Dynamics and adaptive synchronization of the energy resource system, Chaos soliton fract 31, 879-888 (2007) · Zbl 1149.34032 · doi:10.1016/j.chaos.2005.10.035
[28] Sun, M.; Tian, L.; Jia, Q.: Adaptive control and synchronization of a four-dimensional energy resources system with unknown parameters, Chaos soliton fract 39, 1943-1949 (2009) · Zbl 1197.93100 · doi:10.1016/j.chaos.2007.06.117
[29] Li, X.; Xu, W.; Li, R.: Chaos synchronization of the energy resource system, Chaos soliton fract 40, 642-652 (2009) · Zbl 1197.93127 · doi:10.1016/j.chaos.2007.08.008
[30] Huang, C.; Cheng, K.; Yan, J.: Robust chaos synchronization of four-dimensional energy resource systems subject to unmatched uncertainties, Commun nonlinear sci numer simul 14, 2784-2792 (2009)
[31] Wang, Z.: Chaos synchronization of an energy resource system based on linear control, Nonlinear anal-real 11, 3336-3343 (2010) · Zbl 1216.34061 · doi:10.1016/j.nonrwa.2009.11.026
[32] Wang, Z.; Shi, X.: Synchronization of a four-dimensional energy resource system via linear control, Commun nonlinear sci numer simul 16, 463-474 (2011) · Zbl 1221.93238 · doi:10.1016/j.cnsns.2010.03.008
[33] Deng, W.: Smoothness and stability of the solutions for nonlinear fractional differential equations, Nonlinear anal-theor 72, 1768-1777 (2010) · Zbl 1182.26009 · doi:10.1016/j.na.2009.09.018
[34] Podlubny, I.: Fractional differential equations, (1999) · Zbl 0924.34008
[35] Matignon D. Stability results for fractional differential equations with applications to control processing. In Proc IMACS. IEEE-SMC; Lille, France, 1996, p. 963 -- 968.
[36] Wang, X.; He, Y.: Projective synchronization of fractional order chaotic system based on linear separation, Phys lett A 372, 435-441 (2008) · Zbl 1217.37035 · doi:10.1016/j.physleta.2007.07.053
[37] Diethelm, K.; Ford, N.; Freed, A.: A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear dyn 29, 3-22 (2002) · Zbl 1009.65049 · doi:10.1023/A:1016592219341
[38] Diethelm, K.; Ford, N.; Freed, A.: Detailed error analysis for a fractional Adams method, Numer alg 36, 31-52 (2004) · Zbl 1055.65098 · doi:10.1023/B:NUMA.0000027736.85078.be