Numerical Fixed Point Solution of Linear Quadratic Gaussian Control Problem for Singularly Perturbed Systems

The fixed point method is developed for obtaining efficient numerical solution of linear-quadratic Gaussian problem for singularly perturbed systems. It is shown that each iteration step improves the accuracy by an order of magnitude, i.e., the accuracy of O(¿^k) can be obtained by doing only k-1 iterations. On the other hand, only low-order systems are involved in algebraic manipulations, and no analicity requirements are imposed on the system coefficients.