Linear conic optimization for inverse optimal control

TL;DR

This paper introduces a novel linear conic optimization approach for inverse optimal control using occupation measures, providing theoretical guarantees and demonstrating effectiveness on academic examples.

Contribution

It presents a new formulation of inverse Lagrangian identification leveraging occupation measures and linear programming, with proven approximation guarantees.

Findings

Method successfully identifies Lagrangians in academic examples

Offers theoretical guarantees for the approximation procedure

Enhances inverse optimal control with a convex, measure-based framework

Abstract

We address the inverse problem of Lagrangian identification based on trajecto-ries in the context of nonlinear optimal control. We propose a general formulation of the inverse problem based on occupation measures and complementarity in linear programming. The use of occupation measures in this context offers several advan-tages from the theoretical, numerical and statistical points of view. We propose an approximation procedure for which strong theoretical guarantees are available. Finally, the relevance of the method is illustrated on academic examples.