QUALITATIVE CLASSIFICATION OF THE DYNAMICS OF A CLASS OF ADAPTIVE FEEDBACK-SYSTEMS

In this paper we consider a class adaptive feedback systems of arbitra ry order with unmodeled dynamics and constant disturbances. We demonst rate that the dynamical behavior of any system in this class must conf orm to a limited number of options varying according to the selection of system parameters such as the leakage constant and the adaptation s tep-size. Our main tool is bifurcation analysis, which describes in a qualitative fashion how the stability properties of a dynamical system may alter as a parameter is varied. The importance of the results pre sented in this paper is that they permit the generation of adaptation leakage tuning rules akin to those for setting controller gains in pro cess control.