Mathematical Problems in Engineering
Volume 5 (1999), Issue 4, Pages 275-289

Linear-quadratic optimization and some general hypotheses on optimal control

L. I. Rozonoer1,2

1Institute of Control Sciences, Moscow, Russia
261 Moraine Street, #4, Belmont 02478, MA, USA

Received 18 July 1997; Revised 18 June 1999

Copyright © 1999 L. I. Rozonoer. 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.


Necessary and sufficient conditions for existence of optimal control for all initial data are proved for LQ-optimization problem. If these conditions are fulfilled, necessary and sufficient conditions of optimality are formulated. Basing on the results, some general hypotheses on optimal control in terms of Pontryagin's maximum condition and Bellman's equation are proposed.