Performance-measure densities for a class of LQG control systems

When linear-quadratic-Gaussian (LQG) control problems are solved, the performance measure takes on a probability density function Of a type which has received very little attention in the literature because of the nonzero-mean multidimensional character of the state process. This paper combines techniques of the fast Fourier transform, recent results of Baggeroer and Schwartz, and the classic methods of Karhunen-Loeve to present what seem to be the first published curves of such densities. As a vehicle for discussion, a one-parameter family of LQG control systems of the minimal variance type serves both to provide examples of the new density curves and to display certain controlled behaviors of the moments of the densities.