An Averaging Gradient Algorithm for the Identification of Perturbed Plant

The problem of identification of plant perturbed by unmodeled dynamics (UD) and bounded output disturbance (BOD), motivated by the study of robust adaptive control, is analyzed in this paper. We propose an Averaging Gradient Algorithm (AGA), which updates parameter estimates using the averaging gradient taken over a time horizon determined by the richness of the driving signal. By assuming the sufficient richness of the driving signal (in the sense that it has sufficient distinct spectral lines) and imposing the magnitude on UD and bound on BOD, it is shown that the parameter estimates converge exponentially to a neighborhood of the parameters of the nominal model, which reduces to a single point (the true one) with UD and BOD removed. In the latter case, the exponential convergence may be achieved provided the driving signal satisfies a Sufficient Excitation condition, which is strictly weaker than the Persistent Excitation one.