Measures and LMI for space launcher robust control validation

Didier Henrion (1) , Martine Ganet-Schoeller (2) , Samir Bennani (3)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 AST - Astrium Space Transportation
3 ESTEC - European Space Research and Technology Centre

We describe a new temporal verification framework for safety and robustness analysis of nonlinear control laws, our target application being a space launcher vehicle. Robustness analysis, formulated as a nonconvex nonlinear optimization problem on admissible trajectories corresponding to piecewise polynomial dynamics, is relaxed into a convex linear programming problem on measures. This infinite-dimensional problem is then formulated as a generalized moment problem, which allows for a numerical solution via a hierarchy of linear matrix inequality relaxations solved by semidefinite programming. The approach is illustrated on space launcher vehicle benchmark problems, in the presence of closed-loop nonlinearities (saturations and dead-zones) and axis coupling.

Mots clés: space launcher control; safety; verification; robustness analysis; measures; moments; polynomials; LMI; convex optimization

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Didier Henrion, Martine Ganet-Schoeller, Samir Bennani. Measures and LMI for space launcher robust control validation. IFAC Symposium on Robust Control Design (ROCOND 2012), Jun 2012, Aalborg, Denmark. pp. 230-235. ⟨hal-00695588⟩