On the existence of a limit value in some non expansive optimal control problems

TL;DR

This paper explores the existence of a limit value in certain infinite-horizon optimal control problems under nonexpansive-like conditions, without assuming the limit's independence from initial states.

Contribution

It introduces nonexpansive-like assumptions that do not require the limit to be independent of initial conditions, extending previous results in infinite-horizon control theory.

Findings

Establishes conditions for the existence of a limit value

Shows the limit may depend on initial state under new assumptions

Provides theoretical insights into nonexpansive optimal control problems

Abstract

We investigate a limit value of an optimal control problem when the horizon converges to infinity. For this aim, we suppose suitable nonexpansive-like assumptions which does not imply that the limit is independent of the initial state as it is usually done in the literature.