The Pontryagin Maximum Principle for Nonlinear Infinite Horizon Optimal Control Problems with State Constraints

Abstract: The famous proof of the Pontryagin maximum principle for control problems on a finite horizon bases on the needle variation technique, as well as the separability concept of cones created by disturbances of the trajectories. In this preprint, we develop this method for infinite horizon optimal control problems. The results are necessary conditions for a strong local minimizer in form of the Pontryagin maximum principle, Arrow type sufficiency conditions and the validity of diverse transversality conditions.