Advances in Difference Equations
Volume 2008 (2008), Article ID 654267, 14 pages
Research Article

Infinite Horizon Discrete Time Control Problems for Bounded Processes

Joël Blot1 and Naïla Hayek1,2

1Laboratoire Marin Mersenne, Université Paris I, Panthéon Sorbonne, Centre Pierre-Mendès-France, 90 rue de Tolbiac, 75013 Paris, France
2Université de Franche-Comté, 45 Avenue de l'Observatoire, 25030 Besançon, France

Received 15 October 2008; Accepted 27 December 2008

Academic Editor: Leonid Shaikhet

Copyright © 2008 Joël Blot and Naïla Hayek. 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 establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.