Unexpected results of Extended Fractional Kalman Filter for parameter identification in fractional order chaotic systems

International Journal of Innovative Computing, Information and Control

Volumn 7, Issue 9, 2011, Pages 5341-5352

  Sun, Guanghui ^a   Wang, Mao ^a   Wu, Ligang ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Extended fractional Kalman filter; Fractional order system; Parameter identification; Synchronization

Indexed keywords

CHEN SYSTEM; EXTENDED FRACTIONAL KALMAN FILTER; FRACTIONAL-ORDER CHAOTIC SYSTEMS; FRACTIONAL-ORDER SYSTEMS; NUMERICAL EXAMPLE; REAL VALUES; UNKNOWN PARAMETERS;

ALGEBRA; IDENTIFICATION (CONTROL SYSTEMS); KALMAN FILTERS; NUMERICAL METHODS; PARAMETER ESTIMATION;

CHAOTIC SYSTEMS;

EID: 80052465626     PISSN: 13494198     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. T. L. Carroll and L. M. Pocora, Synchronizing chaotic circuits. IEEE Trans. on Circuits and Systems, vol.38, pp.453-456. 1991.
2. L. M. Pocora and T. L. Carroll. Driving systems with chaotic signals. Phys. Rev. A, vol.44, pp.2374-2383. 1991.
3. H. Y. Du, Q. S. Zeng and C. H. Wang. A general method for function projective synchronization. International Journal of Innovative Computing, Information and Control, vol.5, no.8. pp.2239-2248. 2009.
4. Z. Q. Yang. Q. Zhang. Z. Q. Chen and Z. L. Jiang. Synchronization of delayed complex dynamical networks using active control. ICIC Express Letters, vol.3, no.3(B). pp.567-572. 2009.
5. X. Y. Chen and J. F. Lu, Adaptive synchronization of different chaotic systems with fully unknown parameters. Phys. Lett. A, vol.364, pp.123-128. 2007.
6. H. G. Zhang. W. Huang. Z. L. Wang and T. Y. Chai, Adaptive synchronization between two different chaotic systems with unknown parameters, Phys. Lett. A, vol.350, pp.363-366. 2006.
7. H. C. Cho. K. S. Lee and M. S. Fadali, Adaptive control of PMSM systems with chaotic nature using Lyapunov stability based feedback linearization. International Journal of Innovative Computing, Information and Control, vol.5, no.2. pp.479-488. 2009.
8. H. Zhang. X. K. Ma and W. Z. Liu. Synchronization of chaotic systems with parametric uncertainty using active sliding mode control. Chaos, Solitons and Fractals, vol.21, pp.1249-1257. 2004.
9. X. R. Li. L. Y. Zhao and G. Z. Zhao. Sliding mode control for synchronization of chaotic systems with structure or parameters mismatching. J. Zhejiang University SCI, vol.6, no.A. pp.571-576. 2005.
10. F. Q. Wang and C. X. Liu. A new criterion for chaos and hyperchaos synchronization using linear feedback control. Phys. Lett. A, vol.360, pp.274-278. 2007.
11. H. H. Chen. Global synchronization of chaotic systems via linear balanced feedback control. Applied Mathematics and Computation, vol.186, pp.923-931. 2007.
12. A. Ohsuriii, T. Kimura and M. Kono, Kalnian filter-based identification of unknown exogenous input of stochastic linear systems via pseudomeasurement approach. International Journal of Innovative Computing, Information and Control, vol.5, no.1, pp.1-16, 2009.
13. W. Xue, Y. Q. Guo and X. D. Zhang, Application of a bank of Kalman filters and a robust Kalman filter for aircraft engine sensor/actuator fault diagnosis, International Journal of Innovative Computing, Information and Control, vol.4, no. 12, pp.3161-3168, 2008.
14. J. Shen, M. H. Yang, X. H. Yao and R. H. Zhong, A new two-stage Kalman filter method for chaos system, ICIC Express Letters, vol.4, no.2, pp.539-546, 2010.
15. H. Nijmeijer, A dynamical control view on synchronization, Physical D, vol.154, pp.219-228, 2001.
16. C. Cruz and H. Nijmeijer, Synchronization through filtering, Int. J. Bifurcation Chaos Appl. Sci. Eng., vol.10, pp.763-775, 2000.
17. M. Behzad, H. Salarieh and A. Alasty, Chaos synchronization in noisy environment using nonlinear filtering and sliding mode control, Chaos, Solitons and Fractals, vol.36, pp. 1295-1304, 2008.
18. D. Sierociuk and D. Rzej, Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation, Int. J. Appl. Math. Comput. Sci., vol.16, no.1, pp.129-140, 2006.
19. A. Kiani-B, K. Fallahi, N. Pariz and H. Leung, A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter, Communications in Nonlinear Science and Numerical Simulation, vol.14, pp.863-879, 2009.
20. K. Fallahi, R. Raoufi and H. Khoshbin, An application of Chen system for secure chaotic communication based on extended Kalman filter and multi-shift cipher algorithm, Communications in Nonlinear Science and Numerical Simulation, vol.13, pp.763-781, 2008.
21. I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
22. S. C. Jun, A note on fractional differences based on a linear combination between forward and backward differences, Comput. Math. Applic., vol.41, no.3, pp.373-378, 2001.
23. A. Chareff, H. H. Sun, Y. Y. Tsao and B. Onaral, Fractal system as represented by singularity-function, IEEE Transactions on Automatic Control, vol.37, pp.1465-1470, 1992.
24. M. S. Tavazoei and M. Haeri, Limitations of frequency domain approximation for detecting chaos in fractional order systems, Nonlinear Analysis: Theory, Methods and Applications, vol.69, pp. 1299-1320, 2008.
25. K. Diethelm, N. J. Ford and A. D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dynamics, vol.29, pp.3-22, 2002.
26. K. Diethelm and N. J. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl, vol.265, pp.220-248, 2002.
27. I. Grigorenko and E. Grigorenko, Chaotic dynamics of the fractional Lorenz system, Phys. Rev. Lett., vol.91, 2003.