Subgradient evolution of value functions in discrete-time optimal control
Abstract
In this paper we investigate how the subgradients of the value function of a discrete-time convex Bolza problem evolve over time. In particular, we develop a discrete-time version of the characteristic method introduced by Rockafellar and Wolenski in the 2000s, by showing that the time-evolution of the subgradients of the value functions can be associated with trajectories of a discrete-time Hamiltonian system. To do so, we first prove that the value function has a dual counterpart, which corresponds to the conjugate of the value function of a suitable dual problem. We finally make a discussion about the qualification conditions we require for our results, showing in particular that classical problems, such as the Liner-Quadratic regulator, satisfy these hypotheses.
Cite
@article{arxiv.2402.00289,
title = {Subgradient evolution of value functions in discrete-time optimal control},
author = {Julio Deride and Cristopher Hermosilla and Mattia Solla},
journal= {arXiv preprint arXiv:2402.00289},
year = {2024}
}