Singular Perturbation Theory (SPT) is applied to determine analytically the vertical optimal glide trajectory in an open-loop form. It provides solutions to a wide parameter envelope where numerical solutions to two point boundary problems are rarely achieved. The advantage of an openloop solution over a feedback law is that it can incorporate initial and final conditions of the state variables (altitude, speed and path-angle), as opposed to a feedback law that can incorporate only initial conditions. The disadvantage of an open-loop solution is that it does not provide a control for real-time implementation. Rather, it gives an analytical optimal trajectory that can be calculated on board and be implemented by separate control loops.
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