Newton-like extremum-seeking for the control of thermoacoustic instability

IEEE Transactions on Automatic Control

Volumn 55, Issue 9, 2010, Pages 2094-2105

  Moase, William H ^a   Manzie, Chris ^a   Brear, Michael J ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Extremum seeking; Newton step; Thermoacoustic instability

Indexed keywords

ADAPTATION ALGORITHMS; CONVERGENCE RATES; EXTREMUM-SEEKING; GAS TURBINE COMBUSTOR; GRADIENT DESCENT; LOCAL ANALYSIS; LYAPUNOV ANALYSIS; NEWTON STEP; NONLOCAL; OPERATING CONDITION; PLANT DYNAMICS; PREMIXED; RATE OF CONVERGENCE; THERMOACOUSTIC INSTABILITY; THERMOACOUSTIC OSCILLATIONS;

APPROXIMATION THEORY; COMBUSTION; COMBUSTORS; OPTIMIZATION; PLASMA OSCILLATIONS; STABILITY;

CONTROL THEORY;

EID: 77956496351     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2042981     Document Type: Article

References (29)

1. K. B. Ariyur and M. Krstic, Real-Time Optimization by Extremum-Seeking Control. New York: Wiley, 2003.
2. M. Krstic and H. Wang, "Stability of externum seeking feedback for general nonlinear dynamic systems," Automatica, vol. 36, pp. 595-601, 2000.
3. R. N. Banavar, D. F. Chichka, and J. L. Speyer, "Convergence and synthesis issues in extremum-seeking control," in Proc. Amer. Control Conf., 2000, pp. 438-443.
4. E. Elong, M. Krstic, and K. B. Ariyur, "A case study of performance improvement in extremum seeking control," in Proc. Amer. Control Conf., 2000, pp. 428-432.
5. M. A. Rotea, "Analysis of multivariable extremum seeking algorithms," in Proc. Amer. Control Conf., 2000, pp. 433-437.
6. G. C. Walsh, "On the application of multi-parameter extremum seeking control," in Proc. Amer. Control Conf., 2000, pp. 411-415.
7. J.-Y. Choi, M. Krstic, K. Ariyur, and J. S. Lee, "Extremum seeking control for discrete time systems," IEEE Trans. Autom. Control, vol. 47, no. 2, pp. 318-323, Feb. 2002.
8. Y. Tan, D. Nešic, and I. Mareels, "On non-local stability properties of extremum seeking control," Automatica, vol. 42, pp. 889-903, 2006.
9. D. Nešic, Y. Tan, and I. Mareels, "On the choice of dither in extremum seeking systems: A case study," in Proc. IEEE Conf. Decision Control, 2006, pp. 2789-2794.
10. Y. Tan, D. Nešic, I. Mareels, and A. Astolfi, "On global extremum seeking in the presence of local extrema," Automatica, vol. 45, no. 1, pp. 245-251, 2009.
11. C. Manzie and M. Krstic, "Extremum seeking with stochastic perturbations," IEEE T. Autom. Control, vol. 54, no. 3, pp. 580-585, Mar. 2009.
12. M. Krstic, "Performance improvement and limitations in extremum seeking control," Syst. Control Lett., vol. 39, pp. 313-326, 2000.
13. A. Banaszuk, K. B. Ariyur, M. Krstic, and C. A. Jacobsen, "An adaptive algorithm for control of thermoacoustic instability," Automatica, vol. 40, pp. 1965-1972, 2004.
14. Y. Zhang, "Stability and performance tradeoff with discrete time triangular search minimum seeking," in Proc. Amer. Control Conf., 2000, pp. 423-427.
15. A. Banaszuk, Y. Zhang, and C. A. Jacobson, "Adaptive control of combustion instability using extremum-seeking," in Proc. Amer. Control Conf., 2000, pp. 416-422.
16. J. Kiefer and J. Wolfowitz, "Stochastic estimation of a regression function," Annu. Math. Stat, vol. 23, pp. 462-466, 1952.
17. J. R. Blum, "Multidimensional stochastic approximation methods," Annu. Math. Stat, vol. 25, pp. 737-744, 1954.
18. H. J. Kushner and D. S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems. New York: Springer-Verlag, 1978.
19. J. C. Spall, "Multivariate stochastic approximation using a simultaneous perturbation gradient," IEEE T. Autom. Control, vol. 37, no. 3, pp. 332-341, Mar. 1992.
20. H. J. Kushner, "Stochastic approximation algorithms for constrained optmization problems," Annu. Stat., vol. 2, no. 4, pp. 713-723, 1974.
21. A. R. Teel, "Lyapunov methods in nonsmooth optimization, part II: Persistently exciting finite differences," in Proc. IEEE Conf. Decision Control, 2000, pp. 118-123.
22. S. Yakowitz, P. L'Ecuyer, and F. Vazquez-Abad, "Global stochastic optmization with low-dispersion point sets," Oper. Res., vol. 48, no. 6, pp. 939-950, 2000.
23. V. Fabian, "Stochastic approximation," in Optimizing Methods in Statistics. New York: Academic Press, 1971, pp. 439-470.
24. J. C. Spall, "Adaptive stochastic approximation by the simultaneous perturbation method," IEEE T. Autom. Control, vol. 45, no. 10, pp. 1839-1853, Oct. 2000.
25. P. A. Hield and M. J. Brear, "Comparison ofopen and choked premixed combustor exits during thermoacoustic limit cycle," AIAA J., vol. 46, no. 2, pp. 517-526, 2008.
26. W. H. Moase, "Dynamics and Control of Thermoacoustic Instability," Ph.D. dissertation, Dept. Mech. Eng., Univ. of Melbourne, Melbourne, Australia, 2009.
27. L. Henning, R. Becker, G. Feuerbach, R. Muminovic, R. King, A. Brunn, and W. Nitsche, "Extensions of adaptive slope-seeking for active flow control," P. I. Mech. Eng. I-J. Syst., vol. 222, pp. 309-322, 2008.
28. D. F. Chichka, J. L. Speyer, C. Fanti, and C. G. Park, "Peak-seeking control for drag reduction in formation flight," J. Guid. Control Dynam., vol. 29, no. 5, pp. 1221-1230, 2006.
29. H. Khalil, Nonlinear Systems, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 2002.