The Class of Unmodeled Dynamics in Robust Adaptive Control

The global stability properties of robust adaptive controllers, which are recently established, are based on the assumption that the modeling error signal is "small" relative to the normalizing signal used in the adaptive law. The class of unmodeled dynamics however, for which such an assumption is satisfied, has not been fully explored. In this paper we use time-domain and frequency-domain bounds to characterize the class of allowable unmodeled dynamics in robust adaptive control. This class is a general one and includes time-delays, distributed system etc. It is also shown that the class of allowable uncertainty can be further expanded to be qualitatively similar to that allowed in non-adaptive robust control by incorporating a slow filter in the plant. The time and frequency domain bounds can be improved by properly choosing the filter parameters.