Optimal control of the linear regulator using the partial state observer

This paper considers the problem of designing an optimal partial state observer which minimizes the increase in the cost functional for the usual regulator. It is assumed that the initial system state is an unknown random vector with known mean and covariance. The necessary and sufficient conditions for this optimality are derived when the subspace, for which a partial state observer could be constructed, is given. And a design algorithm is obtained which can be directly solved for the parameters of the optimal observer, and requires the solution of a Riccati equation of observer order. It is also shown that the separation property in the restricted sense does apply in this problem.