Mathematical Problems in Engineering 
Volume 5 (1999), Issue 4, Pages 275-289
doi:10.1155/S1024123X9900109X

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

Abstract

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.