Robust Adaptive Control

The paper addresses an open problem concerned with the boundedness of signals in an adaptive loop when external perturbations are present. A complete solution is provided for the case of a first order plant with an unknown parameter by analyzing a nonlinear differential equation in R². It is shown that if the persistent excitation of the reference input is larger than the perturbation in some sense, the solutions will be globally bounded. The same methodology appears to be applicable to the general adaptive control problem.