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A key challenge in solving the deterministic inverse reinforcement learning problem online and in real-time is the existence of non-unique solutions. Nonuniqueness necessitates the study of the notion of equivalent solutions and convergence to such solutions. While offline algorithms that result in convergence to equivalent solutions have been developed in the literature, online, real-time techniques that address nonuniqueness are not available. In this paper, a regularized history stack observer is developed to generate solutions that are approximately equivalent. Novel data-richness conditions are developed to facilitate the analysis and simulation results are provided to demonstrate the effectiveness of the developed technique. 

With the increase in the use of small uncrewed aircraft systems (UAS) there is a growing need for real-time weather forecasting to improve the safety of low-altitude aircraft operations. This will require integration of measurements with autonomous systems since current available sampling lack sufficient resolution within the atmospheric boundary layer (ABL). Thus, the current work aims to assess the ability to measure wind speeds from a quad-copter UAS and compare the performance with that of a fixed mast. Two laboratory tests were initially performed to assess the spatial variation in the vertically induced flow from the rotors. The horizontal distribution above the rotors was examined in a water tunnel at speeds and rotation rates to simulate nominally full throttle with a relative air speed of 0 or 8 m/s. These results showed that the sensor should be placed between rotor pairs. The vertical distribution was examined from a single rotor test in a large chamber, which suggested that at full throttle the sensor should be about 400 mm above the rotor plane. Field testing was then performed with the sensor positioned in between both pairs of rotors at 406, 508, and 610 mm above the rotor plane. The mean velocity over the given period was within 5.5% of the that measured from a fixed mast over the same period. The variation between the UAS and mast sensors were better correlated with the local mean shear than separation distance, which suggests height mismatch could be the source of error. The fluctuating velocity was quantified with the comparison of higher order statistics as well as the power spectral density, which the mast and UAS spectra were in good agreement regardless of the separation distance. This implies that for the current configuration a separation distance of 5.3 rotor diameters was sufficient to minimize the influence of the rotors.