Robustness of extended least squares based adaptive control

The authors show that the popular extended least-squares-based one-step ahead adaptive tracking algorithm is robust to both the presence of small unmodeled dynamics and violation of the stochasticity assumption on the noise. Specifically, the noise is allowed to be any bounded sequence. The only modification used is a projection of the parameter estimates. The adaptive control algorithm is a weighted extended least-squares type noninterlaced adaptation law with projection. Assuming the nominal plant to be minimum-phase, without the small unmodeled dynamics, it is proved that all the signals in the closed-loop system are uniformly bounded