Contents I. INTRODUCTION
Optimal control of aerospace systems is performed by modeling the considered system by dynamics depending on multiple parameters (for example the engine thrust parameter) and an initial state (initial velocity, mass,…). Pontryagin’s Maximum Principle (PMP) provides necessary optimality conditions for the resolution of optimal control problems by transforming an optimal control problem into a two point boundary value problem which can be solved accurately [1], [2]. However, some of the parameters and initial states may be subject to uncertainties, that is, their exact value is subject to perturbations and estimation errors. Since the solution of an optimal control problem can rarely be explicitly expressed in a closed loop form, the effect of those perturbations can be hard to predict. This is complicated further by the fact that optimal trajectories tend to have hybrid behaviors: they may be subject to discrete events that abruptly change dynamics and state. For instance, Goddard’s problem [1], which consists in launching a rocket to a given position while minimizing its fuel consumption, alternates between a full throttle mode and a free fall mode. The duration of these phases depends on the parameters.
