Numerical solving of an optimal control problem in large time horizon: the aerial vehicle guidance

In this paper we consider an optimal control problem in large time horizon and solve it numerically. More precisely, we are interested in an aerial vehicle guidance problem: launched from a ground platform, the vehicle aims at reaching a ground/sea target under specified terminal conditions while minimizing a cost modelling some performance and constraint criteria. Our goal is to implement the indirect method based on the Pontryagin maximum principle (PMP) in order to solve such a problem. After modeling the problem, we implement continuations in order to ''connect'' a simple problem to the original one. Particularly, we exploit the turnpike property in order to enhance the efficiency of the shooting.