Qualitative classification of the dynamics of a class of adaptive feedback systems

In this paper we consider a class adaptive feedback systems of arbitrary order with unmodeled dynamics and constant disturbances. We demonstrate that the dynamical behavior of any system in this class must conform to a limited number of options varying according to the selection of system parameters such as the leakage constant and the adaptation step-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 presented in this paper is that they permit the generation of adaptation leakage tuning rules akin to those for setting controller gains in process control.