There are many practical engineering applications which can be described as an adaptive feedback system. The distinguishing feature of an adaptive feedback system is that one component in the feedback loop has its parameters adapted according to a prescribed algorithm. Adaptive control in manufacturing systems and adaptive echo cancellers in telephone lines are two such examples. Adaptive feedback systems are nonlinear because the recursive parameter adaption laws are driven by signals that are functions of the past adapted parameters. Due to this nonlinear nature, different selections of design parameters, as well as different selections of adaptive algorithms, bring about qualitatively different types of behavior. We propose to initiate an effort to discern and classify the types of behavior from a system dynamic point of view. The tools to be employed are primarily standard dynamics analysis techniques that we, and others, have utilized before for adaptive systems analysis. The expected significance of a carefully composed classification is in its provision of the fundamental knowledge for the development of needed qualitative design guidelines, e.g. leakage factor selection for avoidance of bounded instabilities such as bursting. Good design is always preceded by good understanding of the problem and its "solution" candidates. A well-structured taxonomy is critical to well-informed design choices. Such a behavior/design-oriented knowledge base will be vital for the future success of emerging intelligent controllers. To contribute to such an expansion of adaptive feedback systems theory, we propose to clarify and propound our notion of a qualitative classification of the behavior of poorly excited adaptive feedback systems, and to develop some prototypes for elements of this nascent taxonomy.
