Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 96505, 12 pages

Minimum principle and controllability for multiparameter discrete inclusions via derived cones

Aurelian Cernea

Faculty of Mathematics and Informatics, University of Bucharest, Street Academiei 14, Bucharest 010014, Romania

Received 13 December 2005; Accepted 13 February 2006

Copyright © 2006 Aurelian Cernea. 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.


We consider a multiparameter discrete inclusion and we prove that the reachable set of a certain variational multiparameter discrete inclusion is a derived cone in the sense of Hestenes to the reachable set of the discrete inclusion. This result allows to obtain sufficient conditions for local controllability along a reference trajectory and a new proof of the minimum principle for an optimization problem given by a multiparameter discrete inclusion with endpoint constraints.