ANALYTICAL AND NUMERICAL APPROACHES FOR IDENTIFICATION OF THE GENERAL STRUCTURE OF TERMINAL COST FUNCTIONS IN FLIGHT MECHANICS PERFORMANCE SIMUALTIONS

摘要

Analytical and numerical approaches for identification of the general structure of terminal cost functions are presented. Unlike previous works which were pointed at numerical and analytical methodologies that allowed an accurate mission performance optimization, the current treatment handles the "Inverse Problem", and identifies the rationale of a given unfamiliar yet optimized controller. The current general mathematical problem was raised from a given climb schedule of fighter aircraft, hard coded in core avionics computers, that was not decipherable by any means by the operational pilots nor in the classical flight mechanics literature. The mathematical treatment addressed a feasible simple numerical way to identify the cost function defined for the specific controller. The goal was to allow the most accurate calculation in all conditions of flight regimes, timely efficient, for all fixed wing aircrafts, using a detailed aerodynamics and engine databases to acquire the unknown cost function. The analytical solution for the problem, suggested a simple integral equation on the "Rationale Function", that had been proven to be correct for known optimal controllers such as const equivalent air speed while descending without operating engine. Furthermore, the numerical approach of the methodology enables the operational pilots to understand the rationale of the controller via the usage of scalar weight factors using structure of terminal cost function of time, distance and fuel consumed. The algorithm was applied to solve the operational problem of an unknown schedule which was a linear function of Mach number versus the altitude. Using our methodology, we have found out that the linear mach schedule might be used as a replacement for the classical constant calibrated air speed descent, which is generally used by pilots. Such schedule might be programmed in the aircraft computers, and increase the classical descent performance of the aircraft. Moreover, we may use the methodology to improve already programmed linear mach schedules, when the aerodynamic properties of the airframe are changed. The result, that was found as a by product, gives us a practical usage of the terminal cost function structure procedure as a simple numerical tool, to reveal even more challenging optimal trajectories applied to any aircraft with it own unique aerodynamic properties.