Newton-like extremum-seeking part I: Theory

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2009, Pages 3839-3844

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

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

GRADIENT METHODS;

ADAPTATION ALGORITHMS; ADAPTATION LAW; CONVERGENCE RATES; EXTREMUM SEEKING; GRADIENT DESCENT; OPERATING CONDITION; OPTIMISATIONS; STABILITY AND CONVERGENCE;

CONTROL THEORY;

EID: 77950809177     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2009.5400198     Document Type: Conference Paper

References (25)

1. K. B. Ariyur and M. Krstic, Real-Time Optimization by Extremum- Seeking Control. John Wiley & Sons, 2003.
2. M. Krstic and H. Wang, "Stability of extremum 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 Proceedings of the American Control Conference, 2000, pp. 438-443.
4. M. A. Rotea, "Analysis of multivariable extremum seeking algorithms," in Proceedings of the American Control Conference, 2000, pp. 433-437.
5. G. C.Walsh, "On the application of multi-parameter extremum seeking control," in Proceedings of the American Control Conference, 2000, pp. 411-415.
6. J.-Y. Choi, M. Krstic, K. Ariyur, and J. S. Lee, "Extremum seeking control for discrete time systems," IEEE T. Automat. Contr., vol.47, pp. 318-323, 2002.
7. Y. Tan, D. Nesic, and I. Mareels, "On non-local stability properties of extremum seeking control," Automatica, vol.42, pp. 889-903, 2006.
8. D. Nesic, Y. Tan, and I. Mareels, "On the choice of dither in extremum seeking systems: a case study," in Proceedings of the IEEE Conference on Decision and Control, 2006, pp. 2789-2794.
9. Y. Tan, D. Nesic, I. Mareels, and A. Astolfi, "On global extremum seeking in the presence of local extrema," in Proceedings of the IEEE Conference on Decision and Control, 2006, pp. 5663-5668.
10. C. Manzie and M. Krstic, "Extremum seeking with stochastic perturbations," IEEE T. Automat. Contr., vol.54, pp. 580-585, 2009.
11. M. Krstic, "Performance improvement and limitations in extremum seeking control," Syst. Control Lett., vol.39, pp. 313-326, 2000.
12. 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.
13. Y. Zhang, "Stability and performance tradeoff with discrete time triangular search minimum seeking," in Proceedings of the American Control Conference, 2000, pp. 423-427.
14. A. Banaszuk, Y. Zhang, and C. A. Jacobson, "Adaptive control of combustion instability using extremum-seeking," in Proceedings of the American Control Conference, 2000, pp. 416-422.
15. J. Kiefer and J. Wolfowitz, "Stochastic estimation of a regression function," Ann. Math. Stat, vol.23, pp. 462-466, 1952.
16. J. R. Blum, "Multidimensional stochastic approximation methods," Ann. Math. Stat, vol.25, pp. 737-744, 1954.
17. H. J. Kushner and D. S. Clark, Stochastic approximation methods for constrained and unconstrained systems. Springer-Verlag, 1978.
18. J. C. Spall, "Multivariate stochastic approximation using a simultaneous perturbation gradient," IEEE T. Automat. Contr., vol.37, no.3, pp. 332-341, 1992.
19. H. J. Kushner, "Stochastic approximation algorithms for constrained optmization problems," Ann. Stat, vol.2, no.4, pp. 713-723, 1974.
20. A. R. Teel, "Lyapunov methods in nonsmooth optimization, part II: persistently exciting finite differences," in Proceedings of the IEEE Conference on Decision and Control, 2000, pp. 118-123.
21. 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.
22. V. Fabian, "Stochastic approximation," in Optimizing Methods in Statistics. Academic Press, 1971, pp. 439-470.
23. J. C. Spall, "Adaptive stochastic approximation by the simultaneous perturbation method," IEEE T. Automat. Contr., vol.45, no.10, pp. 1839-1853, 2000.
24. W. H. Moase, C. Manzie, and M. J. Brear, "Newton-like extremum-seeking for the control of thermoacoustic instability," IEEE T. Automat. Contr., (In press).
25. H. Khalil, Nonlinear systems, 3rd ed. Prentice Hall, 2002.