A new linear approach for nonlinear control problems

Abstract

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 hierarchy that allow us to compute the moments of these measures. 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.