SEPARATION PRINCIPLE IN STOCHASTIC CONTROL VIA GIRSANOV SOLUTIONS

The separation of estimation and control for linear systems with additive Gaussian white noise and nonquadratic cost function is considered. All measurable functions of the observations are admissible as controls, the corresponding solutions being defined by the Girsanov measure transformation. The separation principle is established, under certain conditions, if the dimension of the observation process is equal to that of the state; if there are fewer observations, then additional ones of arbitrarily low signal-to-noise ratio can be adjoined such that there is a separated policy based on the augmented observations which is superior to any policy using the original observations.