A trust-region method for optimal control of ODEs with continuous-or-off controls and TV regularization

TL;DR

This paper introduces a novel trust-region algorithm combining proximal gradient methods to solve optimal control problems with continuous-or-off controls and TV regularization, ensuring convergence and demonstrated on an SIR model.

Contribution

It proposes a new solution algorithm integrating trust-region and proximal gradient methods for a specific class of optimal control problems with proven convergence.

Findings

Convergence with respect to a criticality measure is established.

The method successfully solves an SIR model optimal control problem.

The approach effectively handles controls with TV regularization.

Abstract

A solution algorithm for a special class of optimal control problems subject to an ordinary differential equation is proposed. The controls possess a continuous-or-off structure and are priced by a convex function. Additionally, a total variation regularization is applied to penalize switches. Our solution method combines a trust-region method and a proximal gradient method. The subproblems are solved via Bellman's optimality principle. Convergence with respect to a criticality measure is proven. As a numerical example, we solve a simple optimal control problem involving an SIR model.