tailieunhanh - Báo cáo hóa học: " Research Article Infinite Horizon Discrete Time Control Problems for Bounded Processes"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Infinite Horizon Discrete Time Control Problems for Bounded Processes | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 654267 14 pages doi 2008 654267 Research Article Infinite Horizon Discrete Time Control Problems for Bounded Processes Joel Blot1 and Na ila Hayek1 2 1 Laboratoire Marin Mersenne Universite Paris I Pantheon Sorbonne Centre Pierre-Mendes-France 90 rue de Tolbiac 75013 Paris France 2 Universite de Franche-Comte 45 Avenue de 1 Observatoire 25030 Besancon France Correspondence should be addressed to Na ila Hayek hayek@ Received 15 October 2008 Accepted 27 December 2008 Recommended by Leonid Shaikhet 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. Copyright 2008 J. Blot and N. 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. 1. Introduction The first works on infinite horizon optimal control problems are due to Pontryagin and his school 1 . They were followed by few others 2-6 . We consider in this paper an infinite horizon Optimal Control problem in the discrete time framework. Such problems are fundamental in the macroeconomics growth theory 7-10 and see references of 11 . Even in the finite horizon case the discrete time framework presents significant differences from the continuous time one. Boltianski 12 shows that in the discrete time case a convexity condition is needed to guarantee a strong Pontryagin Principle while this last one