Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 3, Pages 227-236

Admissible relaxation in optimal control problems for infinite dimensional uncertain systems

N. U. Ahmed1 and X. Xiang2

1University of Ottawa, Department of Electrical Engineering, Department of Mathematics and Department of Systems Science, Ontario, Ottawa, Canada
2Guizhou University, Department of Mathematics, Guizhou, Guiyang, China

Received 1 March 1992; Revised 1 August 1992

Copyright © 1992 N. U. Ahmed and X. Xiang. 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 we present a result on admissible relaxation for a class of systems governed by an uncertain evolution equation on Banach space. We show that the set of original trajectories is dense in the set of relaxed trajectories and that under certain assumptions the relaxed system is equivalent to the original system.