H^∞ bounds for the recursive-least-squares algorithm
We obtain upper and lower bounds for the H^∞ norm of the RLS (recursive-least-squares) algorithm. The H^∞ norm may be regarded as the worst-case energy gain from the disturbances to the prediction errors, and is therefore a measure of the robustness of an algorithm to perturbations and model uncertainty. Our results allow one to compare the robustness of RLS compared to the LMS (least-mean-squares) algorithm, which is known to minimize the H^∞ norm. Simulations are presented to show the behaviour of RLS relative to these bounds.
© 1994 IEEE. This research was supported by the Advanced Research Projects Agency of the Department of Defense monitored by the Air Force Office of Scientific Research under Contract F4962G93-1-008.
Published - 00411555.pdf