Application of averaging method for integro-differential equations to model reference adaptive control of parabolic systems
✍ Scribed by Keum-Shik Hong; Joseph Bentsman
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 490 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0005-1098
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✦ Synopsis
Al~traet--An averaging theorem for integro-differential equations is applied to the convergence analysis of controller parameters of a model reference adaptive control (MRAC) algorithm for a class of parabolic partial differential equations (PDEs) with constant coefficients. The stability of an adaptive control algorithm is proven as well.
1. Introduction
THIS PAPER PRESENTS an application of an averaging theorem for nonlinear integro-differential equations to a model reference adaptive control (MRAC) algorithm for linear one-dimensional, parabolic partial differential equations (PDEs). The method of averaging is an asymptotic method which permits the analysis of the dynamic behavior of a nonautonomous system via an autonomous (averaged) system obtained by time-averaging of the original nonautonomous system. Since the first systematic averaging analysis for systems of ordinary differential equations (ODEs) in the standard form was introduced by Bogoliubov and Mitropolsky (1961), this method has been extended to various equations including functional, integro-differential, difference and PDEs. Recently, this method has emerged as a creditable tool for stability analysis in vibrational control and adaptive control (