The Closed-loop Identification Problem in Indirect Adaptive Control

It is well known that in indirect adaptive control algorithms, the system to be controlled is not necessarily identified due to lack of excitation caused by the fact that identification takes place in closed-loop. Whether or not this leads to undesirable behaviour depends on the underlying control criterion. A classification is made of all control criteria for which the closed-loop identification problem does not obstruct the desired controlled behaviour of the system. Under mild assumptions it is proved that these criteria are all of the pole assignment type.