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ABSTRACT: We present proofs and data for adaptive step-size algorithms for
tracking time-varying parameters when recursive stochastic approximation
type algorithms are used. A classical problem in adaptive control and
communication theory concerns the tracking of the best fit of a given
form when the statistics or the parameters change slowly. A major, and
yet unresolved, problem has been the choice of the step sizes in the
tracking algorithm. An algorithm for adapting the step size using the
same system measurements which are used for the tracking was suggested
by Benveniste and various examples worked out by Brossier. The numerical
results were very encouraging. But proofs were lacking. These proofs are
supplied here together with supporting numerical data. The proofs are
based on recent results in stochastic approximation. The adaptive
step-size technique works very well indeed. Much supporting analysis is
presented, particularly concerning the interpretation of certain
stationary processes as “stationary” pathwise derivatives.
Finite difference forms are also treated. These are mathematically
simpler and can be applied to a wide variety of systems, even when the
system is not well modeled. The data shows that they work well
IEEE Transactions on Automatic Control 09/1995; · 2.11 Impact Factor
