We consider the class of nonlinear optimal control problems with all data (differential equation, state and control constraints, cost) being polynomials. We provide a simple hierarchy of LMI-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Preliminary results show that good approximations are obtained with few moments.
LAAS report 05120, March 2005, Toulouse, France. To appear in Proceedings of the IEEE CDC Conference, Sevilla, Spain, December 2005.