Optimal control of partially observed systems with arbitrary dependent noises: linear quadratic case

This paper deals with linear quadratic optimal control problem when signal and observation noises can be dependent. It is proved the separation principle for such case and it is shown how this separation principle enlarges the well-known duality between control and estimation problems. There are given existence results for three cases of the relations between signal and observation noises. One of them is a well-known independent noises case. Others concern the dependent noises.