Measures and LMIs for optimal control of piecewise-affine systems

M. Rasheed Abdalmoaty (1) , Didier Henrion (2) , Luis Rodrigues (3)

1 ASTRIUM
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
3 Concordia University [Montreal]

This paper considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector field, polynomial Lagrangian and semialgebraic input and state constraints. The OCP is first relaxed as an infinite-dimensional linear program (LP) over a space of occupation measures. This LP, a particular instance of the generalized moment problem, is then approached by an asymptotically converging hierarchy of linear matrix inequality (LMI) relaxations. The relaxed dual of the original LP returns a polynomial approximation of the value function that solves the Hamilton-Jacobi-Bellman (HJB) equation of the OCP. Based on this polynomial approximation, a suboptimal policy is developed to construct a state feedback in a sample-and-hold manner. The results show that the suboptimal policy succeeds in providing a stabilizing suboptimal state feedback law that drives the system relatively close to the optimal trajectories and respects the given constraints.

Mots clés: optimal control; piecewise-affine dynamics; convex optimization

Domaines: Optimisation et contrôle [math.OC]

M. Rasheed Abdalmoaty, Didier Henrion, Luis Rodrigues. Measures and LMIs for optimal control of piecewise-affine systems. European Control Conference (ECC 2013), Jul 2013, Zurich, Switzerland. 18p. ⟨hal-00751917⟩