Terminal Area Energy Management Trajectory Optimization Using Interval Analysis

Abstract

*† ‡ § ¶ A new trajectory optimization algorithm for the Terminal Area Energy Management phase is presented based on interval analysis. Through a branch and bound strategy, interval analysis is able to yield guaranteed and rigorous bounds on the global minimum, i.e., on the best possible trajectory. It does so by using intervals instead of crisp numbers and interval arithmetic instead of crisp arithmetic. Even the numerical roundoff errors introduced by computers are considered and do not affect the rigor of the solution. The steering commands of the vehicle are optimized in order to regulate the kinematic and potential energies of the vehicle while aligning it with the runway. Normalized total energy is used as independent variable. Additionally, an interval algorithm for determining the initial gate of the Terminal Area Energy Management phase is presented, which is mathematically guaranteed to enclose the true solution and that facilitates the execution of sensitivity analyses. Nomenclature α = angle-of-attack subsonic α = constant angle-of-attack during the subsonic regime β = sideslip angle CD = aerodynamic drag coefficient CL = aerodynamic lift coefficient χr = vehicle’s heading angle relative to the runway’s centerline J e = stopping criterion (user-defined) E = normalized total energy of the vehicle γ = flight-path angle g = gravity’s acceleration h = altitude