Averaging Analysis For Adaptive Systems

Abstract

It can be gleaned from the previous chapters that successful adaptive algorithms share the common feature that the identification or adaptive part of the overall system is in some sense slowly time varying when compared to the linear plant part. In case of the identification based algorithms, Chapters 4 and 5, this property is a consequence of the result that the time difference of the estimated parameter converges to zero. In the case of the universal controllers, Chapter 6, this is embodied in the assumptions about the search speed through the controller space. This time scale separation is a crucial ingredient in linking the equilibrium analysis with the actual adaptive system behavior (examples exist of sheer craziness with common time scales). It is our opinion that this two time scale nature is also at the heart of all successful practical applications of adaptive systems in control or signal processing.