Analysis of Adaptive Step-Size Sa Algorithms for Parameter Tracking

IEEE Transactions on Automatic Control

Volumn 40, Issue 8, 1995, Pages 1403-1410

  Kushner, Harold J ^a   Yang, J ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; ERRORS; FINITE DIFFERENCE METHOD; OPTIMIZATION; RANDOM PROCESSES; TIME VARYING CONTROL SYSTEMS; WHITE NOISE;

ADAPTIVE STEP SIZE STOCHASTIC APPROXIMATION ALGORITHMS; PARAMETER TRACKING; STATIONARY ERROR;

ADAPTIVE ALGORITHMS;

EID: 0029359844     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/9.402231     Document Type: Article

References (13)

1. A. Benveniste, M. Metivier, and P. Priouret, Adaptive Algorithms and Stochastic Approximation. New York, Berlin: Springer-Verlag, 1990.
2. J.-M. Brossier, Egalization Adaptive et Estimation de Phase: Application aux Communications Sous-Marines, Ph.D. thesis, Institut National Polytechnique de Grenoble, 1992.
3. S. Gunnarsson and L. Ljung, “Frequency domain tracking characteristics of adaptive algorithms, “IEEE Trans. Acoustics, Speech, Sig. Proces., vol. 37, pp. 1072-1089, 1989.
4. L. Guo, L. Ljung, and P. Priouret, “Tracking performance analyses of the forgetting factor RLS algorithm.” in Proc. 31st Conf. Decis. Contr., Tucson, AZ, 1992, pp. 688-693.
5. H. J. Kushner and F. J. Vázquez-Abad, “Stochastic approximation algorithms for problems of interest over an infinite horizon, “Brown University, Division of Applied Math., Tech. Rep., 1994. to appear SIAM J. Contr.
6. H. J. Kushner, Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic System Theory. Cambridge, MA: MIT Press, 1984.
7. H. J. Kushner and A. Shwartz, “Weak convergence and asymptotic properties of adaptive filters with constant gains, “IEEE Trans. Inform. Theory, vol. IT-30, pp. 177-182, 1984.
8. H. J. Kushner and J. Yang, “Stochastic approximation with averaging and feedback: Rapidly convergent “on line" algorithms, and applications to adaptive systems, “IEEE Trans. Automat. Contr., vol. 40, pp. 24-34, 1995.
9. ——, “Stochastic approximation with averaging: Optimal asymptotic rates of convergence for general processes, “SIAM J. Contr. Optim., 1993.
10. B. T. Polyak and A. B. Juditsky, “Acceleration of stochastic approximation by averaging, “SIAM J. Contr. Optim., vol. 30, pp. 838-855, 1992.
11. V. Solo, “The limit behavior of LMS.” IEEE Trans. Acoustics, Speech, Sig. Proces., vol. 37, pp. 1909-1922, 1989.
12. B. Widrow and S. D. Steams, Adaptive Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1985.
13. G. Yin, “Stochastic approximation via averaging: Polyak's approach revisited, “in Lecture Notes in Economics and Mathematical Systems 374.G. Pflug and U. Dieter, Eds. Berlin: Springer, 1992, pp. 119-134.