CANONICAL CORRELATION ANALYSIS APPROACH TO: (I) REDUCED-ORDER LQR DESIGN, AND (II) CHARACTERIZATION OF STRONG AND WEAK INTERACTIONS IN LARGE SCALE INTERCONNECTED SYSTEMS.

In the approach taken here, the reduced-order controller is obtained by reducing the optimal LQR, or, equivalently, by approximating the dimension of the subspace to which the optimal control belongs. Using CCA theory, an explicit characterization of the optimal control subspace is obtained, which immediately leads to the reduced-order controller. The most significant aspect of the reduction scheme is closed-loop stability; i. e. , the original plant closed by the reduced controller is asymptotically stable.