A semi-Lagrangian algorithm in policy space for hybrid optimal control problems

TL;DR

This paper introduces a semi-Lagrangian numerical scheme with an acceleration technique for solving infinite horizon hybrid optimal control problems, validated through numerical tests in low-dimensional systems.

Contribution

It develops a novel semi-Lagrangian algorithm in policy space specifically for hybrid systems and incorporates an acceleration method to improve convergence.

Findings

Effective in low-dimensional systems

Accelerates convergence with policy iteration

Validated through numerical experiments

Abstract

The mathematical framework of hybrid system is a recent and general tool to treat control systems involving control action of heterogeneous nature. In this paper, we construct and test a semi-Lagrangian numerical scheme for solving the Dynamic Programming equation of an infinite horizon optimal control problem for hybrid systems. In order to speed up convergence, we also propose an acceleration technique based on policy iteration. Finally, we validate the approach via some numerical tests in low dimension.