On Parameter Convergence in Adaptive Control

S. Boyd and S. Sastry

Systems and Control Letters, 3(6):311-319, December 1983.

It is well known that the parameter error as well as the model-plant mismatch error in a model reference adaptive scheme tends exponentially to zero iff a certain sufficient richness condition holds for signals inside the time-varying plant control loop. In this paper we give conditions on the reference signal (the exogenous input to the adaptive loop) - namely, that it have as many spectral lines as there are unknown parameters, in order to guarantee parameter convergence.