Multiple model adaptive control. Part 1: Finite controller coverings

We consider the problem of determining an appropriate model set on which to design a set of controllers for a multiple model switching adaptive control scheme. We show that, given mild assumptions on the uncertainty set of linear time-invariant plant models, it is possible to determine a finite set of controllers such that for each plant in the uncertainty set, satisfactory performance will be obtained for some controller in the finite set. We also demonstrate how such a controller set may be found. The analysis exploits the Vinnicombe metric and the fact that the set of approximately bandand time-limited transfer functions is approximately finite-dimensional. Key PhrasesBand-Limited, epsilon-Entropy ( -Entropy), Finite Covering, Multiple Model Control, Time-limited, Vinnicombe Metric ∗This research was supported by the Office of Naval Research, grant numbers N00014-97-1-0946 and N00014-98-10535. The authors would also like to acknowledge the support of the NSF, AFOSR and DARPA.