An algorithm to construct subsolutions of convex optimal control problems

TL;DR

This paper introduces an algorithm for constructing subsolutions in convex optimal control problems, ensuring convergence and demonstrating practical feasibility through numerical experiments.

Contribution

It presents a novel algorithm that generates a sequence of subsolutions for convex optimal control problems, with proven convergence and demonstrated effectiveness.

Findings

Algorithm produces a non-decreasing sequence of subsolutions.

Theoretical proofs confirm convergence of the method.

Numerical experiments validate the practical applicability.

Abstract

We propose an algorithm that produces a non-decreasing sequence of subsolutions for a class of optimal control problems distinguished by the property that the associated Bellman operators preserve convexity. In addition to a theoretical discussion and proofs of convergence, numerical experiments are presented to illustrate the feasibility of the method.