Reduced-complexity LQR design using canonical correlation analysis (Q1085127)

Canonical correlation analysis is developed for the discrete infinite time LQR problem having an asymptotically stable plant. It is shown that the optimal control sequence belongs to the range space of the canonical vectors weighted by the canonical correlation coefficients. Using this analysis a reduced-complexity controller for the LQR problem is obtained. Furthermore, it is established that when this reduced-complexity controller is applied to the original plant, the corresponding closed loop system is asymptotically stable.