Abstract
In this paper, we consider an optimization problem for observations of stationary LQG stochastic control systems which employ the stationary Kalman filter. The performance of the Kalman filter and that of the LQG stochastic optimal control are both dependent on the gain matrix in the linear observation. One of the authors has already developed methods of optimizing this gain matrix based on the estimation or control individual performance under a quadratic performance criterion. This paper discusses a hybrid problem by taking into account of both estimator and regulator performances. By introducing the eigenvalues-eigenvectors representation of a nonnegative definite symmetric matrix, the condition of optimality is derived. Also, numerical calculations are easily carried out by introducing multi-dimensional polar coordinates systems.
