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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)
Kushner, H.J. ; Brown University, Providence, RI, USA ; Kumar, R.

A stochastic approximation-like method is used for the recursive identification of the coefficients iny_{n}=summin{1}max{l_{1}}a_{i}y_{n-i}+summin{0}max{l_{2}}b_{i}u_{n-i}+ summin{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.

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