Stochastic homogenization of deterministic control problems

TL;DR

This paper extends the homogenization theory of control problems in random environments, covering more general dynamics and weaker growth conditions, thus broadening the understanding of stochastic homogenization in control and calculus of variations.

Contribution

It introduces a generalized homogenization framework for control problems with inhomogeneous Lagrangians and weaker growth assumptions, expanding previous results in the field.

Findings

Homogenization achieved for control problems with general dynamics.

Results extend to inhomogeneous Lagrangians.

Weaker growth conditions on Lagrangians still ensure homogenization.

Abstract

In this paper we study homogenization of a class of control problems in a stationary and ergodic random environment. This problem has been mostly studied in the calculus of variations setting in connection to the homogenization of the Hamilton-Jacobi equations. We extend the result to the control problems with fairly general state dynamics and macroscopically inhomogeneous Lagrangians. Moreover, our approach proves homogenization under weaker growth assumptions on the Lagrangian even in the well-studied calculus of variations setting.