Periodic Optimal Trajectories with Singular Control for Aircraft with High Aerodynamic Efficiency

Abstract

Fuel minimum range cruise of aircraft with high aerodynamic efficiency is considered as an optimal periodic control problem. Optimality conditions for trajectories with singular arcs and state variable constraints are derived. Computation of periodic optimal trajectories in the case addressed presents strong requirements on the numerical algorithm. Computational difficulties become larger when aerodynamic efficiency is increased and wing loading is decreased. The specific nature of the numerical problems encountered and the means used to overcome them are described.