A new linear approach for nonlinear control problems

A not necessarily linear optimal control problem can be reformulated as an infinite dimensional linear problem where the variables are the moments of the “occupation measures” which encode optimal trajectories and controls. We propose a linear programming hierarchy of problems that allow us to compute the moments of these measures efficiently. Furthermore, we show how to recover trajectories and controls from the moments by using some new polynomial approximations to Dirac deltas. The results are illustrated through computational simulations.