A continuation approach to state and adjoint calculation in optimal control applied to the reentry problem

A well–known problem in indirect optimal control is to find a suitable initial guess for the adjoint states which is sufficiently close to the optimal solution. This paper presents a new homotopy approach to overcome this problem by deriving an auxiliary optimal control problem (OCP) for which the adjoint states are simply zero. A continuation method is employed to smoothly reach the original OCP. The auxiliary OCP can be derived with respect to any given initial trajectory of the system, for instance obtained by forward integration. The approach is applied to the space shuttle reentry problem, which represents a benchmark problem in optimal control due to its high numerical sensitivity with respect to the initial solution.