Necessary and Sufficient Conditions for Parameter Convergence in Adaptive Control

S. Boyd and S. Sastry

Automatica, 22(6):629-639, 1986.
Shorter version appeared in Proceedings of the American Control Conference, pp.1584-1587, June 1984.

Using Generalized Harmonic Analysis, a complete description of parameter convergence in Model Reference Adaptive Control (MRAC) is given in terms of the spectrum of the exogenous reference input signal. Roughly speaking, if the reference signal “contains enough frequencies” then the parameter vector converges to its correct value. If not, it converges to an easily characterizable subspace in parameter space.