A numerical approach for on-line guidance of aircraft

This paper presents a numerical procedure for flight path optimization in real time. The optimal control problems are solved relative to a reduced version of the state equations: It is assumed that flight path inclination and heading angle are directly controllable. This "reduced solution" provides the basis for a feedback command of the actual controls. The optimization algorithm is a nonlinear program solver which presupposes a parametrization of the control functions. Two basic ideas render the method fast and robust and therefore make it feasible for on-line implementation: [1] Expensive numerical integration is replaced by a special integrator for the reduced ODE-system. [2] State constraints are adapted in a way that they can be satisfied by analytical elimination of parameters. The proposed control algorithm is tested at two problems: [1] range maximization in fixed time. [2] minimum-time intercept. A comparison with open-loop trajectories shows a high accuracy of the proposed feedback control.