SOLUTIONS AND APPROXIMATIONS TO THE RICCATI INTEGRAL EQUATION WITH VALUES IN A SPACE OF COMPACT OPERATORS

摘要

In this paper, we present conditions that ensure the existence of Bochner integrable solutions of infinite dimensional Riccati integral equations. In particular, we focus on I-p-valued continuous solutions. We formulate an optimal sensor location problem that is based on optimal filtering and show that when the underlying system is of convection-diffusion type the Riccati integral equation has Bochner integrable solutions. We use these results to approximate the sensor placement problem by using a simple quadrature rule. A numerical example is given to illustrate the results.