Solving chance constrained optimal control problems in aerospace via kernel density estimation

The goal of this paper is to show how nonparametric statistics can be used to solve some chance constrained optimization and optimal control problems. We use the kernel density estimation method to approximate the probability density function of a random variable with unknown distribution from a relatively small sample. We then show how this technique can be applied and implemented for a class of problems including the Goddard problem and the trajectory optimization of an Ariane five-like launcher.