Convex-Optimization-Based Enforcement of Robust BIBO Stability on the AIC Scheme Using a Modified RLS Algorithm

This paper addresses the issues relating to the enforcement of robust BIBO (l_infin) stability when implementing the adaptive inverse control (AIC) scheme for noise cancellation. In this scheme, an adaptive FIR-form filter is added to a closed-loop system in order to reduce the output error caused by external disturbances. A small-gain-theorem-based sufficient stability condition, which accounts for the feedback interaction between the time-varying adaptive filter and the unmodeled dynamics existing in the closed-loop plant, is derived. This condition leads to the formulation of a constrained convex optimization problem solvable recursively using a modified RLS algorithm that preserves the converge properties of the original RLS algorithm