RECURSIVE LEAST-SQUARES IDENTIFICATION ALGORITHMS WITH INCOMPLETE EXCITATION - CONVERGENCE ANALYSIS AND APPLICATION TO ADAPTIVE-CONTROL

In this note, the convergence properties of a fairly general class of adaptive recursive least-squares algorithms are studied under the assumption that the data generation mechanism is deterministic and time invariant. First, the (open-loop) identification case is considered. By a suitable notion of excitation subspace, the convergence analysis of the identification algorithm is carried out with no persistent excitation hypothesis. Precisely, it is proven that the projection of the parameter error on the excitation subspace tends to zero, while the orthogonal component of the error remains bounded. Then, the convergence of an adaptive control scheme based on the minimum variance control law is dealt with. By suitably exploiting the previously-mentioned convergence result relative to the identification case, it can be shown that, under the standard minimum-phase assumption, the tracking error tends to zero and the control variable is bounded. © 1990 IEEE