Studying identifiability in adaptive control systems by the averaging method

In identifying a linear process with an arbitrary closed-loop controller, in particular using the recurrent estimates, the estimates converge to a manifold which is defined by the shape of the control function. In the framework of the averaging method a general form of the control function is found which is proved to be locally optimal for the quadratic state function or the process outputs with which non-identifiability of the control law does not follow from that of the process because in the entire manifold the controller parameter take on the same values which are equal to actual ones.