Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

Predicting the tidal wave is essential not only to better understand hydrological cycle at the boundary between land and ocean but also to improve energy production in the coastal area. As affected by various factors such as astronomical, meteorological, and hydrological effects, predicting the tidal wave at the estuary remains uncertain. In this study, we present a novel method to improve short-term tidal wave predictions using a fixed-lag smoother based on sequential data assimilation (DA). The proposed method is implemented for the tidal wave predictions at the estuary of Nakdong River. As a result, the prediction accuracy was improved by 63.9% with DA and the calibration using the regression. Although the accuracy of DA diminished for increasing forecast lead times, the 1-hr lead forecast by DA had still 44.4% improvement over the open loop without DA. Plus, the optimal conditions for the fixed-lag smoother were analyzed in terms of the order of a smoothing function and the length of assimilation window and forecast lead time. It was suggested that the optimal DA configuration could be obtained with the 8th order polynomial as a smoothing function assimilated under 6-hr or longer past and future DA windows.

: This paper presents a comparison between direct integer orders or classical model reference adaptive control (IO-DMRAC) versus its fractional orders counterpart (FO-DMRAC) applied to the F-16 aircraft longitudinal model pitch rate control. A substantial improvement is achieved when using fractional order adaptive control, since, in addition to performance indices, such as Integral Square-Error criterion (ISE) and Integral Square-Input criterion (ISU) being lower, the oscillations of the system output (pitch rate) in the transient period, are eliminated. Moreover, it is the first attempt in literature of adaptive control that a FO-DMRAC is applied to the pitch rate control of an aircraft. A F-16 short-period model, whose relative degree is equal to 1 (n^*=1) is analyzed by mean of simulations with good results. A FO-DMRAC is designed, for a specific operating flight conditions and compared with its IO-DMRAC counterpart. Furthermore, the boundedness of all signals, including the internal ones ω(t) are assured.

The intercomparison among different atmospheric monitoring systems is key for instrument calibration and validation. Common cases involve satellites, radiosonde, radio occultation (e.g. GNSS-RO) and atmospheric model outputs (e.g. ERA5 reanalysis). Since instruments and/or measures are not perfectly collocated, the miss-collocation uncertainty must be considered in the related intercomparison uncertainty budgets.