Inverse optimal control with polynomial optimization

Edouard Pauwels (1, 2) , Didier Henrion (2, 1) , Jean-Bernard Lasserre (1, 2)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 LAAS - Laboratoire d'analyse et d'architecture des systèmes

In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very broad as a reliable solution to the problem would provide a powerful modeling tool in many areas of experimental science. We propose to use the Hamilton-Jacobi-Bellman sufficient optimality conditions for the direct problem as a tool for analyzing the inverse problem and propose a general method that attempts at solving it numerically with techniques of polynomial optimization and linear matrix inequalities. The relevance of the method is illustrated based on simulations on academic examples under various settings.

Domaines: Optimisation et contrôle [math.OC]

Edouard Pauwels, Didier Henrion, Jean-Bernard Lasserre. Inverse optimal control with polynomial optimization. IEEE Conference on Decision and Control ( CDC ), Dec 2014, Los Angeles, United States. pp.5581-5586. ⟨hal-00961722⟩