Infinite-horizon Pontryagin principles without invertibility
Résumé
We give new statements of Pontryagin principles in the setting of infinite-horizon discre-time optimal control problems with various criteria, when the system is governed by a difference equation or by a difference inequation. In a previous work an invertibility condition of the vector field with respect to the state variable was used. In the present work, after a section devoted to the comparison between the problems goverened by difference equations and problems governed by difference inequations, we give new conditions to obtain Pontryagin principles without the using of the above-mentioned invertibility condition: a positivity condition and a partial surjectivity condition.