Adaptive pole placement by means of a simple, singularity free, identification algorithm

Reportedly, guaranteeing the controllability of the estimated system is a crucial problem in adaptive control. We introduce a recursive least squares-based identification algorithm for stochastic SISO systems, which secures the uniform controllability of the estimated system and presents closed-loop identification properties similar to those of the least squares algorithm. The proposed algorithm is recursive and, therefore, easily implementable. Its use, however, is confined to cases in which the parameter uncertainty is highly structured. This new identification algorithm can be safely used in adaptive control applications. As a matter of fact, we introduce a pole placement adaptive control scheme equipped with such an algorithm and prove a pathwise stability result for the so-obtained closed-loop system