Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 41926, 22 pages

Existence and uniqueness of constrained globally optimal feedback controls in a linear-quadratic framework

Yashan Xu

Institute of Mathematics, Fudan University, Shanghai 200433, China

Received 14 January 2006; Revised 5 March 2006; Accepted 15 March 2006

Copyright © 2006 Yashan Xu. 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.


A constrained closed-loop optimal control problem is considered in a linear-quadratic framework. To solve the problem, a special type open-loop optimal control problem and a standard open-loop optimal control problem are introduced and carefully studied, via which the existence and uniqueness of the globally optimal closed-loop control is established by a synthesis method.