Abstract
This paper gives a proof of the stability of discrete-time model reference adaptive control systems (MRACS) including filters with arbitrarily assigned poles by using Schauder's fixed point theorem. The MRACS uses an adjusting law derived from least square method with forgetting factor, which is less sensitive to measurement noise than other adjusting laws. Also, in order to reduce the influence of the noise, the scheme in this paper is extended to include filters with arbitrarily assigned poles, whereas schemes by other authors have filters with poles at zero. The stability of the MRACS with filters having assigned poles has not yet been proved and the proving method given by Goodwin and others which succeeded to prove stability of other schemes of MRACS cannot be applied to MRACS of this paper. This paper gives a new method of proving of the stability by using Schauder's fixed point theorem. The results of an experiment using a thermal system with 2nd order show the effect of assigned poles in filters.
