Nonlinear averaging theorems, and the determination of parameter convergence rates in adaptive control

Abstract

The paper presents nonlinear averaging theorems for two-time scale systems, where the dynamics of the fast system are allowed to vary with the slow system. The results are applied to the Narendra-Valavani adaptive control algorithm, and estimates of the parameter convergence rates are obtained which do not rely on a linearization of the system around the equilibrium, and therefore are valid in a larger region in the parameter space. Show more