A behavioral approach to H₂ optimal control

In this paper we consider a formulation of the $H_2$ optimal control problem in which the controller is not viewed as an operator that transforms measurements to controls. Instead, the controller is assumed to be a device that constrains a set of a-priori specified interconnection variables so as to achieve a controlled system whose manifest variables have a free component and satisfy an upperbound on the $L_2$ norm of its impulse response. We formalize and solve this problem in a behavioral setting, that is, without reference to system representations and input-output structures. The equivalance between the $H_2$ control problem, the generalized $H_2$ control problem and the LQ optimal control problem are established.