Pontryagin Principles in Infinite Horizon in Presence of Asymptotical Constraints

TL;DR

This paper develops Pontryagin principles for infinite-horizon optimal control problems with asymptotic constraints, using functional analysis and providing both necessary and sufficient optimality conditions.

Contribution

It introduces new Pontryagin principles for infinite-horizon control with asymptotic constraints using a Banach space framework.

Findings

Established weak and strong Pontryagin principles for the problem.

Provided new properties of Nemytskii operators in sequence spaces.

Derived sufficient conditions for optimality.

Abstract

We establish necessary conditions of optimality for discrete-time infinite-horizon optimal control in presence of constraints at infinity. These necessary conditions are in form of weak and strong Pontryagin principles. We use a functional analytic framework and multipliers rules in Banach (sequence) spaces. We establish new properties on Nemytskii operators in sequence spaces. We also provide sufficient conditions of optimality. MSC 2010: 49J21, 65K05, 39A99.