The method of Pseudo-Linear Identification (PLID) is developed for application in an adaptive control loop. The effects of noise are investigated for the case of full-order system identification, and the results are applied to the use of PLID as a reduced-order system estimator. A self-tuning regulator (STR) is constructed using PLID and the effects of reducing the expected order of the system are demonstrated. A second adaptive control algorithm is presented wherein the STR controller is varied to achieve some degree of closeness to a given model (model-reference adaptive control).