Discrete time pontryagin principles in banach spaces

TL;DR

This paper extends Pontryagin's maximum principle to discrete-time infinite-horizon control problems in infinite-dimensional Banach spaces, removing previous finiteness constraints using advanced functional analysis tools.

Contribution

It introduces new recursive assumptions and leverages the Baire category and Banach isomorphism theorems to generalize Pontryagin's principles in Banach spaces.

Findings

Established Pontryagin's principles without finiteness of codimension constraints

Developed recursive assumptions for infinite-dimensional spaces

Utilized Baire category and Banach isomorphism theorems effectively

Abstract

The aim of this paper is to establish Pontryagin's principles in a dicrete-time infinite-horizon setting when the state variables and the control variables belong to infinite dimensional Banach spaces. In comparison with previous results on this question, we delete conditions of finiteness of codi-mension of subspaces. To realize this aim, the main idea is the introduction of new recursive assumptions and useful consequences of the Baire category theorem and of the Banach isomorphism theorem.