Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 2, Pages 137-151

On distributed parameter control systems in the abnormal case and in the case of nonoperator equality constraints

Urszula Ledzewicz

Southern Illinois University at Edwardsville, Department of Mathematics and Statistics, Edwardsville 62026, IL, USA

Received 1 January 1993; Revised 1 May 1993

Copyright © 1993 Urszula Ledzewicz. 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.


In this paper, a general distributed parameter control problem in Banach spaces with integral cost functional and with given initial and terminal data is considered. An extension of the Dubovitskii-Milyutin method to the case of nonregular operator equality constraints, based on Avakov's generalization of the Lusternik theorem, is presented. This result is applied to obtain an extension of the Extremum Principle for the case of abnormal optimal control problems. Then a version of this problem with nonoperator equality constraints is discussed and the Extremum Principle for this problem is presented.