Minimax Optimal Control Analysis of Lateral Escape Maneuvers for Microburst Encounters

This study examines the optimization of lateral escape trajectories in a microburst wind e owe eld for an aircraft one nalapproach.Theperformanceindexbeingminimizedisthemaximumvalueofaltitudedropatanypointalong the trajectory. In contrast to earlier work, the Chebyshev minimax performance index has not been approximated by a Bolza integral performance index. Rather, true Chebyshev solutions have been established by transforming the minimax problem into an equivalent optimal control problem with state variable inequality constraints. In comparison with Bolza solutions, Chebyshev solutions demonstrate a marked improvement in reducing the peak value of altitude drop. Moreover, the general trajectory behavior turns out to be radically different. In Chebyshev solutions, altitude typically is traded for airspeed in the initial phase of the encounter, such as to position the aircraft in a region of relatively low downdraft. The overall benee ts of lateral escape vis-a -vis nonturning escape were recone rmed in this study. OW-LEVEL windshear phenomena, and most notably microbursts, have long been recognized as potential hazards to aircraft in takeoff or approach-to-landing. A microburst is a shaft of cold air that descends rapidly, striking the ground and producing winds that diverge radially from the impact point.Flight crews need to be warned in time to avoid the hazard region or to escape in the event that avoidance is not possible. Most modern jet airliners are currently e tted with areactivewindshear sensorsystemthatpermits in situ detection of such potentially hazardous situations. Now in development are forward-look windshear detection systems to look ahead of the aircraft, thus offering improved alert times. Extensive researcheffortsalsohavebeendevotedtothedevelopmentofescape techniques that can be applied to prevent a possible crash resulting from a microburst encounter. Optimal trajectory studies have contributed signie cantly to insight about how to best e y an aircraft in a