Measures and LMI for impulsive optimal control with applications to space rendezvous problems

Mathieu Claeys (1) , Denis Arzelier (1) , Didier Henrion (1, 2) , Jean-Bernard Lasserre (1)

1 LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 FEL CTU - Faculty of Electrical Engineering [Prague]

This paper shows how to find lower bounds on, and sometimes solve globally, a large class of nonlinear optimal control problems with impulsive controls using semi-definite programming (SDP). This is done by relaxing an optimal control problem into a measure differential problem. The manipulation of the measures by their moments reduces the problem to a convergent series of standard linear matrix inequality (LMI) relaxations. After providing numerous academic examples, we apply the method to the impulsive rendezvous of two orbiting spacecrafts. As the method provides lower bounds on the global infimum, global optimality of the solutions can be guaranteed numerically by a posteriori simulations, and we can recover simultaneously the optimal impulse time and amplitudes by simple linear algebra.

Mots clés: optimal control; impulsive control; linear matrix inequality; measures; moments

Domaines: Optimisation et contrôle [math.OC]

Mathieu Claeys, Denis Arzelier, Didier Henrion, Jean-Bernard Lasserre. Measures and LMI for impulsive optimal control with applications to space rendezvous problems. American Control Conference (ACC 2012), Jun 2012, Montreal, Canada. pp.161-166. ⟨hal-00633138⟩