The maximum principle for discrete-time control systems and applications to dynamic games
Optimization and Control
2026-01-19 v1
Abstract
We study deterministic nonstationary discrete-time optimal control problems in both finite and infinite horizon. With the aid of Gateaux differentials, we prove a discrete-time maximum principle in analogy with the well-known continuous-time maximum principle. We show that this maximum principle, together with a transversality condition, is a necessary condition for optimality; we also show that it is sufficient under additional hypotheses. We use Gateaux differentials as a natural setting to derive first-order conditions. Additionally, we use the discrete-time maximum principle to derive the discrete-time Euler equation and to characterize Nash equilibria for discrete-time dynamic games.
Keywords
Cite
@article{arxiv.2601.11395,
title = {The maximum principle for discrete-time control systems and applications to dynamic games},
author = {Alberto Domínguez Corella and Onésimo Hernández-Lerma},
journal= {arXiv preprint arXiv:2601.11395},
year = {2026}
}