An Averaging Analysis of Discrete-Time Indirect Adaptive Control

An averaging analysis of indirect, discrete-time, adaptive control systems is presented. The analysis results in a signal dependent stablity condition and accounts for unmodeled plant dynamics as well as exogenous disturbances. This analysis is applied to two discrete-time adaptive algorithms: An unnormalized gradient algorithm and a recursive least squares algorithm with resetting. Since linearization and averaging are used for the gradient analysis, a local stability result valid for small adaptation gains is found. For RLS with resetting, the assumption is that there is a long time between resets. The results for the two algorithms are virtually identical emphasizing their similarities in adaptive control.