Optimal control with state constraints and the space shuttle re-entry problem

In this article, we initialize the analysis under generic assumptions of the small time optimal synthesis for single input systems with state constraints. We use geometric methods to evaluate the small time reachable set and necessary optimality conditions. Our work is motivated by the optimal control of the atmospheric arc for the re-entry of a space shuttle, where the vehicle is subject to constraints on the thermal flux and on the normal acceleration. A multiple shooting technique is finally applied to the computation of the optimal longitudinal arc.