Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 2, Pages 137-151
doi:10.1155/S1048953393000139
Abstract
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.