非標準特異摂動システムにおけるLinear-Quadratic-Gaussian (LQG)問題のための再帰的アルゴリズム

抄録

This paper considers the Linear-Quadratic-Gaussian (LQG) problem for nonstandard singularly perturbed systems making use of the recursive technique. In order to obtain the optimal control law, we must solve the generalized algebraic Riccati equation. Using the recursive technique, we show that the solution of the generalized algebraic Riccati equation converges with the rate of convergence of O(ε). The existence of a bounded solution of error term can be proved by the implicit function theorem. As a result, the solution of LQG problem for nonstandard singularly perturbed systems can be obtained with an accuracy of O(ε^k).