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

Author

Kushner, Harold J. ; Kumar, Rajendra

Author_Institution

Brown University, Providence, RI, USA

Volume

27

Issue

4

fYear

1982

fDate

8/1/1982 12:00:00 AM

Firstpage

775

Lastpage

782

Abstract

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.

Keywords

Adaptive control, linear systems; Parameter identification, linear systems; Recursive estimation; Adaptive control; Convergence; Helium; Iterative methods; Parameter estimation; Programmable control; Random variables; Recursive estimation; Stability; Stochastic processes;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1982.1103039

Filename

1103039