Asymptotic Solution of the Singularly Perturbed Infinite Dimensional Riccati Equation

A singularly perturbed linear-quadratic optimal control problem in an infinite dimensional Hilbert space is considered. An asymptotic solution of the corresponding operator Riccati equation is constructed. This result is illustrated by its application to the asymptotic solution of a set of integral-differential equations of the Riccati type associated with the control problem of a linear singularly perturbed integral-differential equation of the second order.