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Convergence and rate of convergence of a recursive identification and adaptive control method which uses truncated estimators

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2 Author(s)
H. Kushner ; Brown University, Providence, RI, USA ; R. Kumar

A stochastic approximation-like method is used for the recursive identification of the coefficients in y_{n}=\sum \min{1}\max {l_{1}}a_{i}y_{n-i}+\sum \min{0}\max {l_{2}}b_{i}u_{n-i}+ \sum \min{1}\max {l_{3}}c_{i}w_{n-i}+w_{n} , where {w_{n}} is a sequence of mutually independent and bounded random variables, and is independent of the bounded {u_{n}} . Such methods normally require the recursive estimation of the "residuals" or the {w_{n}} , and the algorithms for doing this can be unstable if the parameter estimates are not close enough to their true values. The problem is solved here by use of a simple truncated estimator, which is probably what would be used in implementation in any, case. Then, under a stability, and strict positive real type condition, with probability 1 (w.p.1) convergence is proved and the rate of convergence is obtained. An associated adaptive control problem is also treated.

Published in:

IEEE Transactions on Automatic Control  (Volume:27 ,  Issue: 4 )