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

TL;DR

This paper extends the Pontryagin maximum principle to nonlinear infinite horizon optimal control problems with state constraints, providing necessary and sufficient conditions for optimality.

Contribution

It develops the needle variation technique for infinite horizon problems, establishing necessary conditions, sufficiency, and transversality conditions for such control problems.

Findings

Derived necessary conditions for local optimality.

Established Arrow type sufficiency conditions.

Validated transversality conditions for infinite horizon control.

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.