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Incremental control strategies such as Incremental Nonlinear Dynamics Inversion (INDI) and Incremental Backstepping (IBKS) provide undeniable advantages for controlling Uncrewed Aerial Vehicles (UAVs) due to their reduced model dependency and accurate tracking capacities, which is of particular relevance for tail-sitters as these perform complex, hard to model manoeuvres when transitioning to and from aerodynamic flight. In this research article, a quaternion-based form of IBKS is originally deduced and applied to the stabilization of a tail-sitter in vertical flight, which is then implemented in a flight controller and validated in a Hardware-in-the-Loop simulation, which is also made for the INDI controller. Experimental validation with indoor flight tests of both INDI and IBKS controllers follows, evaluating their performance in stabilizing the tail-sitter prototype in vertical flight. Lastly, the tracking results obtained from the experimental trials are analysed, allowing an objective comparison to be drawn between these controllers, evaluating their respective advantages and limitations. From the successfully conducted flight tests, it was found that both incremental solutions are suited to control a tail-sitter in vertical flight, providing accurate tracking capabilities with smooth actuation, and only requiring the actuation model. Furthermore, it was found that the IBKS is significantly more computationally demanding than the INDI, although having a global proof of stability that is of interest in aircraft control. [ABSTRACT FROM AUTHOR]

In the present work we propose a modified decomposition method to derive approximate solutions for non-linear problems. Depending on the type of non-linearity, the source terms of the differential equations to be solved in each recursion step may result in extensive expressions, impractical for computational implementations and applications. This shortcomings are circumvented by the present methodology, which contemplates as a solution procedure in each recursion step a combined variable separation method together with Duhamel's principle, where the non-linearity appears as inhomogeneity. The source terms of the equation in each step of recursion are interpolated by polynomials and, using the Gröbner basis of the set points, the polynomial of reduced degree is obtained so that the integration may be carried out easily. As an application we considered a simplified version of the Navier-Stokes equation, which was used to simulate the wind field making use of the micrometeorological data from the Copenhagen experiment. The derived solution was evaluated against these experimental data from the field experiments showed that the computed results are acceptable and thus the solution may be considered an acceptable one and may be used as a simulation device for these type of field experiments. For almost all experiments twenty eigenvalues and ten recursion steps were sufficient. As results the wind speed at certain positions was simulated and compared to the measured values. The results obtained allow us to affirm that the presented methodology works satisfactorily and, therefore, can be considered a promising tool for solving non-linear problems, which are not tractable with the conventional decomposition method. [ABSTRACT FROM AUTHOR]

In this work we limit ourselves to the study of a mathematical model for Yellow Fever (YF), an acute febrile disease transmitted by vectors (in this case, mosquitoes). This is a known compartmental model, proposed by Esteva et al. (2019), which divides the population into three cycles, according to the dynamics of disease transmission: forest epidemic cycle, human-tohuman cycle in the forest region and urban cycle (urban yellow fever epidemic sustained by infectious migratory humans). Despite having other vectors, only two main vectors were considered: the Aedes aegypti (urban transmitter) and the Haemagogus (main transmitter in the forest region). In addition, we propose a modification to the model: the inclusion of vaccination. Thus, through simulations in the Scilab software, it was possible to obtain graphs of the behavior of each of the populations (both hosts and vectors) in an environment with and without the presence of vaccination, allowing a more detailed analysis of the impact of vaccination on a susceptible human population. [ABSTRACT FROM AUTHOR]