OPTIMIZATION OF OBSERVATIONS FOR LQG CONTROL SYSTEMS BY AN INFORMATION THEORETIC APPROACH

In this paper, we are concerned with an optimal selection of the gain matrix of the noisy observation, for stationary LQG stochastic control systems. By introducing an information theoretic criterion based on a generalized Water Filling Theorem, we obtain a set of the observation gains which maximize the mutual information between the system state and the observations. Then, in order to find the optimal gain matrix from this set of gains which produces the best performance of the optimal LQG regulator, we solve an optimization problem with respect to the variables which are components of an orthogonal matrix. For easy numerical calculations of the solution, the constrained problem is converted to unconstrained one by introducing an n-dimensional polar coordinates system.