Design of asymptotically convergent frequency estimator using contraction theory

IEEE Transactions on Automatic Control

Volumn 53, Issue 8, 2008, Pages 1932-1937

  Sharma, B B ^a   Kar, I N ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

Author keywords

Contraction theory; Exponential convergence; Frequency estimator; Semi contracting; Sinusoidal signal

Indexed keywords

ASYMPTOTIC ANALYSIS; COMPUTER SIMULATION; ESTIMATION; SHRINKAGE;

CONTRACTION THEORY; EXPONENTIAL CONVERGENCE; FREQUENCY ESTIMATOR; SEMI-CONTRACTING; SINUSOIDAL SIGNAL;

FREQUENCY ESTIMATION;

EID: 54049093127     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.927682     Document Type: Article

References (29)

1. M. Bodson and S. C. Douglas, "Adaptive algorithms for the rejection of periodic disturbances with unknown frequency," Automatica, vol. 33, pp. 2213-2221, 1997.
2. C. Fuller and A. Von Flotow, "Active control of sound and vibration," IEEE Control Syst. Mag., vol. 15, no. 6, pp. 9-19, 1996.
3. S. Hall and N. Wereley, "Performance of higher harmonic control algorithms for helicopter vibration reduction," J. Guidance Contr. Dynam., vol. 116, no. 4, pp. 793-797, 1993.
4. R. Herzog, P. Buhler, C. Gahler, and R. Larsonneur, "Unbalance compensation using generalized notch filters in the multivariable feedback of magnetic bearings," IEEE Trans. Control Syst. Technol. vol. 4, pp. 580-586, Sep. 1996.
5. D. W. Clarke, "On the design of adaptive notch filters," Int. J. Adapt. Control, vol. 15, pp. 715-744, 2001.
6. P. Stoica, H. B. Li, and J. Li, "Amplitude estimation of sinusoidal signals: Survey, new results, and an application," IEEE Trans. Signal Process., vol. 48, no. 2, pp. 338-352, Feb. 2000.
7. L. Hsu, R. Ortega, and G. Damm, "A globally convergent frequency estimator," IEEE Trans. Automat. Control, vol. 44, no. 4, pp. 698-713, Apr. 1999.
8. P. A. Regalia, "An improved lattice-based IIR notch filter," IEEE Trans. Signal Process., vol. 39, no. 9, pp. 2124-28, Sep. 1991.
9. R. Marino and P. Tomei, "Global estimation of n unknown frequencies," IEEE Trans. Automat. Control, vol. 47, no. 8, pp. 1324-1328, Aug. 2002.
10. R. Marino and P. Tomei, "Global adaptive observers for nonlinear systems via filtered transformations," IEEE Trans. Automat. Control vol. 37, no. 8, pp. 1239-1245, Aug. 1992.
11. G. O. Pulido, B. C. Toledo, and A. Loukianov, "Globally convergent estimator for n frequencies," IEEE Trans. Automat. Contr., vol. 47, no. 5, pp. 857-863, May 2002.
12. M. Hou, "Amplitude and frequency estimator of a sinusoid," IEEE Trans. Automat. Contr., vol. 50, no. 6, pp. 855-58, 2005.
13. M. Hou, "Estimation of sinusoidal frequencies and amplitudes using adaptive identifier and observer," IEEE Trans. Automat. Contr., vol. 52, no. 3, pp. 493-499, Mar. 2007.
14. W. Lohmiller and J. J. E. Slotine, "On contraction analysis for nonlinear systems," Automatica, vol. 34, no. 6, pp. 683-96, 1998.
15. W. Lohmiller, "Contraction Analysis of Nonlinear Systems," Ph.D. Thesis, Dept. Mech. Eng., MIT, Cambridge, MA, 1999.
16. W. Lohmiller and J. J. E. Slotine, "Nonlinear process control using contraction theory," AIChE J., vol. 46, no. 3, pp. 588-96, 2000.
17. W. Lohmiller and J. J. E. Slotine, "Control system design for mechanical systems using contraction theory," IEEE Trans. Automat. Control, vol. 45, no. 5, pp. 884-889, May 2000.
18. J. J. E. Slotine and W. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice Hall, 1991.
19. D. Angeli, "A Lyapunov approach to incremental stability properties," IEEE Trans. Automat. Control, vol. 47, no. 3, pp. 410-21, Mar. 2002.
20. A. Pavlov, A. Y. Pogromsky, N. van de Wouw, and H. Nijmeijer, "Convergent dynamics, a tribute to Boris Pavlovich Demidovich," Syst. Control Lett., vol. 52, pp. 257-261, 2004.
21. A. Pavlov, N. van de Wouw, and H. Nijmeijer, "The global output regulation problem: An incremental stability approach," in Proc. 6th IFAC Symp. Nonlinear Control Systems (NOLCOS), Stuttgart, Germany, 2004, pp. 119-124.
22. V. Fromian, G. Scorletti, and G. Ferreres, "Nonlinear performance of a PI controlled missile: An explanation," Int. J. Robust Nonlinear Control, vol. 9, no. 8, pp. 485-518, 1999.
23. W. Lohmiller and J. J. E. Slotine, "On metric observers for nonlinear observers," in Proc. IEEE Int. Conf. Control Applications, Dearborn, MI, Sep. 1996, pp. 320-326.
24. W. Lohmiller and J. J. E. Slotine, "Applications of metric observers for nonlinear observers," in Proc. IEEE Int. Conf. Control Applications, Dearborn, MI, Sep. 1996.
25. J. Jouffroy and J. Lottin, "On the use of contraction theory for the design of nonlinear observers for ocean vehicles," in Proc. American Control Conf., Anchorage, AK, May 8-10, 2002, vol. 4, pp. 2647-2652.
26. J. Jouffroy and J. Lottin, "Integrator backstepping using contraction theory: A brief technological note," in Proc. IFAC World Cong., Barcelona, Spain, 2002.
27. J. Jouffroy, "A simple extension of contraction theory to study incremental stability properties," in Proc. European Control Conf. Cambridge, U.K., 2003.
28. J. Jouffroy, "Some ancestors of contraction analysis," in Proc. Conf. Decision and Contr., Seville, Spain, 2005, pp. 5450-55.
29. J. Jouffroy and J. J. E. Slotine, "Methodological remarks on contraction theory," in Proc. IEEE Conf. Decision and Contr., Atlantis, Paradise Island, Bahamas, 2004, pp. 2537-2543.