Discrete Dynamics in Nature and Society
Volume 2006 (2006), Issue 4, Article ID 96505, 12 pages
doi:10.1155/DDNS/2006/96505

Minimum principle and controllability for multiparameter discrete inclusions via derived cones

Abstract

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.