Robustness of the Astrom-Wittenmark´s self-tuning controller

In robust adaptive control, the problem concerning robustness of the original self-tuning controller proposed by K. J. Astrom and B. Wittenmark in 1973 is still open. A solution of this problem is presented, and it is proved that a least-squares based self-tuning controller is robust with respect to unmodeled dynamics and unstructured external disturbances. Global stability of the considered self-tuning controller is established by incorporating projection of the parameter estimates in the estimation algorithm and assuming that the reference signal is persistently exciting. It is shown that behind the robustnsss of the least-squares based self-tuning controller is the self-excitation mechanism, which provides a condition number of the ponderation matrix in the estimation algorithm to be always bounded