Abstract
We give a brief review of some ideas in averaging methods for analysing adaptive algorithms. The 3 types of first order averaging result are described and a mention is given as to how averaging can be used to get second order results in particular perturbation expansions for invariant measures.
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References
M. Balachandra, P.R. Sethna, A Generalization of the Method of Averaging for Systems with Two Time Scales, Archiv. Rat. Mech. Anal., Vol. 58 (1975).
A. Benveniste, M. Metivier AND P. Priouret, Adaptive Algorithms and Stochastic Approximations, Springer-Verlag (1990).
G. Glankenship AND G.C. Papanicoloau, Stability and Control of Stochastic Systems with Wide-band Noise Disturbances, SIAM J. Appl. Math., 34 (1978), pp. 437–476.
N.N. Bogoliubov, Y. Mitropolsky, Asymptotic Methods in Nonlinear Mechanics, Gordon and Breach, New York (1961).
B.P. Deveritskii AND A. Fradkov, TWO models for analysing the dynamics of adaptive algorithms, Automatikha i Telemekhanica, 1 (1974), pp. 66–75.
M.I. Freidlin, A.D. Wentzell, Random Perturbations of Dynamical Systems, Springer-Verlag (1984).
I.I. Gikhman, Poporodu Odnoi Teoremy N.I. Bogolybova, Ukrain. Mat. Zh., 4 (1952), pp. 215–218.
L. Guo AND H.F. Chen, Identification and Stochastic Adaptive Control, Birkhauser, Boston (1991).
H. Kushner, Approximation and Weak Convergence Methods for Random Process, MIT Press (1984).
L. Ljung AND T. Soderstrom, Theory and Practice of Recursive Identification, MIT Press (1983).
B.D. Riedle, P.V. Kokotovic, Integral Manifolds of Slow Adaptation, IEEE Trans. Autom. Contr., Vol. AC-31 (1986), pp. 316–324.
J.A. Sanders AND F. Verhulst, Averaging Methods in nonlinear dynamical systems, Springer-Verlag, Berlin (1985).
V. Solo, The error variance of LMS with time-varying weights, IEEE Trans. Sig. Proc, 40 (1992), pp. 803–813.
V. Solo, Adaptive Control Performance with time varying parameters, Proc. 12th World Congress of IFAC, 18-23 July, Sydney, Australia, Vol. 10 (1993), pp. 173–175.
V. Solo, Averaging Analysis of the LMS algorithm, in Advances in Control and Dynamic Systems, Academic Press, Vol. 65, C.T. Leondes, editor (1994).
V. Solo, Deterministic Adaptive Control with slowly time varying parameters: an averaging analysis, submitted to Int. J. Control (1993).
V. Solo AND X. Kong, Adaptive Signal Processing: Stability and Performance, Prentice-Hall, to appear (1994).
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© 1995 Springer Science+Business Media New York
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Solo, V. (1995). Averaging Methods for the Analysis of Adaptive Algorithms. In: Åström, K.J., Goodwin, G.C., Kumar, P.R. (eds) Adaptive Control, Filtering, and Signal Processing. The IMA Volumes in Mathematics and its Applications, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8568-2_16
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DOI: https://doi.org/10.1007/978-1-4419-8568-2_16
Publisher Name: Springer, New York, NY
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