Abstract
Aircraft endurance is maximized by optimizing the lift to drag ratio over a two-dimensional space spanned by the angle of attack and the Mach number, constrained to a one-dimensional curve on which the lift equals the weight of the aircraft. The gradient estimator used in the optimization is excited by atmospheric turbulence in the vertical and longitudinal directions. This new form of extremum seeking requires a reformulation of the standard gradient estimator used in extremum seeking to provide gradient estimates that are independent of the amplitude of the dither signal. A new gradient estimator based on an estimation error approach is presented to this end. Through stochastic averaging analysis, the estimator is shown to stabilize the aircraft to the optimal endurance speed, with a bias that is proportional to the square of the turbulence amplitude and thus is small when the turbulence is light. The controller is tested in a high-fidelity six-degree-of-freedom simulation provided by local industry. Simulation results show the maximization of aircraft endurance and even a slight improvement compared to flight at the nominal loiter speed of the aircraft being simulated.
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