Output Feedback Control for Irregular LQ Problem

In this letter, we study the irregular output feedback linear quadratic (LQ) control problem where state is measured through a system with noise. It interesting to show that standard average LQ cost unsolvable even if solvable, which completely different from classical regular control. order guarantee solvability of control, modified at terminal time expectation in letter. framework function, it shown separation principle holds and explicitly optimal controller given form Kalman filtering. particular, gain calculated by two Riccati equations, independently The key technique analytical solution forward backward differential equations (FBDEs). We also emphasize required be deterministic.