Nonlinear optimal control synthesis via occupation measures

Didier Henrion (1, 2) , Jean-Bernard Lasserre (3) , Carlo Savorgnan (1)

1 LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 FEL CTU - Faculty of Electrical Engineering [Prague]
3 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

We consider nonlinear optimal control problems (OCPs) for which all problem data are polynomial. In the first part of the paper, we review how occupation measures can be used to approximate pointwise the optimal value function of a given OCP, using a hierarchy of linear matrix inequality (LMI) relaxations. In the second part, we extend the methodology to approximate the optimal value function on a given set and we use such a function to constructively and computationally derive an almost optimal control law. Numerical examples show the effectiveness of the approach.

Domaines: Optimisation et contrôle [math.OC]

Didier Henrion, Jean-Bernard Lasserre, Carlo Savorgnan. Nonlinear optimal control synthesis via occupation measures. 47th IEEE Conference on Decision and Control, Dec 2008, Cancun, Mexico. 16p. ⟨hal-00262309⟩