Symmetry reduction and recovery of trajectories of optimal control problems via measure relaxations

TL;DR

This paper introduces a measure relaxation approach using the moment-SOS hierarchy to reduce symmetry in optimal control problems, enabling faster computation and easier trajectory recovery.

Contribution

It presents a novel method for symmetry reduction in optimal control problems via measure relaxations and polynomial system solutions, improving efficiency.

Findings

Significant reduction in computation time and memory usage.

Effective recovery of optimal trajectories from symmetric polynomial systems.

Validated on symmetric integrator and qubit inversion problems.

Abstract

We address the problem of symmetry reduction of optimal control problems under the action of a finite group from a measure relaxation viewpoint. We propose a method based on the moment-SOS aka Lasserre hierarchy which allows one to significantly reduce the computation time and memory requirements compared to the case without symmetry reduction. We show that the recovery of optimal trajectories boils down to solving a symmetric parametric polynomial system. Then we illustrate our method on the symmetric integrator and the time-optimal inversion of qubits.