International Journal of Differential Equations
Volume 2011 (2011), Article ID 319375, 13 pages
http://dx.doi.org/10.1155/2011/319375
Research Article

Existence of Solutions of a Riccati Differential System from a General Cumulant Control Problem

Stanley R. Liberty1 and Libin Mou2

1Department of Electrical & Computer Engineering, Kettering University, Flint, MI 48504, USA
2Department of Mathematics, Bradley University, Peoria, IL 61625, USA

Received 31 May 2011; Accepted 15 November 2011

Academic Editor: A. M. El-Sayed

Copyright © 2011 Stanley R. Liberty and Libin Mou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a system of infinitely many Riccati equations that arise from a cumulant control problem, which is a generalization of regulator problems, risk-sensitive controls, minimal cost variance controls, and 𝑘 -cumulant controls. We obtain estimates for the existence intervals of solutions of the system. In particular, new existence conditions are derived for solutions on the horizon of the cumulant control problem.