Parameter convergence and minimal internal model with an adaptive output regulation problem

The parameter convergence of nonlinear adaptive control systems is an important yet not well addressed issue. In this paper, using the global robust output regulation problem of output feedback systems with unknown exosystems as a platform, we will show that the well known persistency of excitation (PE) condition still guarantees the convergence of the estimated parameter vector to the true parameter vector. Moreover, the PE condition will be satisfied if the internal model is minimal in certain sense.