Input frequency requirements for identification through Liapunov methods

Abstract

The theorem derived in this paper provides sufficient conditions regarding the frequency content of the inputs to a Liapunov-adaptive identification process, so as to guarantee nullification of the parameter error vector. As such it complements the several other similar theorems which have appeared in the literature. In contrast to previous work, however, this theorem utilizes knowledge of specific locations of unknown parameters in the A, B matrices, thereby in some instances significantly reducing the frequency requirements.

Because this theorem, as well as others, provide sufficient conditions only, several simulations have been made to test whether these conditions may in fact not be necessary. It is found, notably, that the controllability condition is not necessary, while the number of frequencies required appears to be a necessary condition.