This paper provides a way to optimize the overall disturbances rejection performance of the adaptive control system in the presence of unknown external disturbances.Especially,the updatable non-empty admissible model set,which is consistent to the a priori knowledge of the plant parameter and the online measurements,is computed.With the overall system performance as the criteria,the nominal model is optimally chosen within the admissible model set.The optimal nominal model is subsequently used to synthesize the optimal closed-loop controller based on the 1 design methodology.Combining the above two aspects,an optimal adaptive control scheme is proposed.Because of the consistency of the identification criteria and control object,the adaptive control scheme proposed in this paper can achieve the overall optimal disturbances rejection performance,and the effect of the interplay between the identification and control of the adaptive system can be handled effectively.In addition,the computable optimal performance is also provided. This paper provides a way to optimize the overall disturbances rejection performance of the adaptive control system in the presence of unknown external disturbances. Especially, the updatable non-empty admissible model set, which is consistent to the a priori knowledge of the plant parameter and the online measurements, is computed.With the overall system performance as the criteria, the nominal model is optimally chosen within the admissible model set. The optimal nominal model is subsequently used to synthesize the optimal closed-loop controller based on the 1 design methodology. Combining the above two aspects, an optimal adaptive control scheme is proposed.Because of the consistency of the identification criteria and control object, the adaptive control scheme proposed in this paper can achieve the overall optimal disturbances rejection performance, and the effect of the interplay between the identification and control of the adaptive system can be handled effectively.In addition, the computa ble optimal performance is also provided.