Sequential quadratic programming solutions to related aircraft trajectory optimization problems
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Aircraft performance optimization continues to play an important role in the aerospace sciences. The studies undertaken in this dissertation explore the performance of high-speed aircraft with regard to missile evasion, minimum-time-to-climb, minimum-time-to-turn, and the unorthodox approach of obtaining a robust optimality-based control law for real-time aircraft control. The dissertation includes four papers presented or accepted for presentation at major conferences and presently in various stages of review for publication in scholarly journals;The similarity in each paper, in addition to the focus on optimal aircraft trajectories, is that an existing nonlinear programming method, sequential quadratic programming (SQP), is used to treat each trajectory optimization problem. This approach is suitable since the emphasis is on applications and problem solving, and the method is accurate and computationally inexpensive. Also, the flexibility of SQP allows for performance index, mathematical model, and constraint changes with relatively little reprogramming. This enables a wide range of trajectory optimization problems to be formulated and studied;In the study of the aircraft missile-evasion problem in horizontal planar flight, unlike earlier investigations, the full original equations of motion are used. Also, no linearization about a nominal pursuit triangle is done. The velocity ratio, that is, the velocity of the aircraft to the velocity of the missile for the duration of the confrontation, becomes a major factor in deciding optimal evasive strategies. Evasion against a surface-to-air missile involves a large nonlinear optimal control problem of dynamic order of at least thirteen. "Inward", "outward", pull-up, dive, and inverted pull-down evasive maneuvers are investigated. The results show that the missile enters the "hit region" of the aircraft for constrained vertical plane flight, but not for constrained horizontal flight. The optimal throttle setting for constrained horizontal plane flight is of "bang-bang" type;For the minimum-time turn problems, having free final velocity provides the biggest impact on turn times, which can be reduced by as much as fifty percent. For a wide range of final energies studied in the three-dimensional turns, it was found that the aircraft tends to initially lose altitude in the optimal turn even though the nominal control from which the optimization process started corresponds to an initial climbing turn. This tendency of favoring kinetic energy over potential energy had not been featured in earlier papers;Finally, the investigation of optimality-based control laws for real-time aircraft control is a significant departure from the usual open-loop solutions to trajectory optimization problems. It was found that the robustness of the optimal control obtained from the "optimality-condition" is not guaranteed, but by introducing a certain "correction" term, it can be enhanced significantly. It appears that this technique of enhancing robustness has not been used until now.