Infinite horizon discrete time problems for bounded processes.
Résumé
We establish Pontryagin maximum principles in the strong form for infinite horizon optimal control problems in spaces of bounded sequances, 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.