A separation theorem for stochastic singular linear quadratic control problem with partial information

Abstract

In this paper, we provide a separation theorem for the singular linear quadratic (LQ) control problem of Ito-type linear systems in the case of the state being partially observable. Above all, the Kalman-Bucy filtering of the dynamics is given by means of Girsanov transformation, by which the suboptimal feedback control of the LQ problem is determined. Furthermore, it is shown that the well-posedness of the LQ problem is equivalent to the solvability of a generalized differential Riccati equation (GDRE).