A next-to-leading order calculation of the impact of primordial magnetic fields into cosmological observables

In this thesis, we perform a next-to-leading order calculation of the impact of primordial magnetic fields (PMF) into the evolution of scalar cosmological perturbations and the cosmic microwave background (CMB) anisotropy. Magnetic fields are everywhere in the Universe at all scales probed so far, but their origin is still under debate. The current standard picture is that they originate from the amplification of initial seed fields, which could have been generated as PMFs in the early Universe. The most robust way to test their presence and constrain their features is to study how they impact on key cosmological observables, in particular the CMB anisotropies. The standard way to model a PMF is to consider its contribution (quadratic in the magnetic field) at the same footing of first order perturbations, under the assumptions of ideal magneto-hydrodynamics and compensated initial conditions. In the perspectives of ever increasing precision of CMB anisotropies measurements and of possible uncounted non-linear effects, in this thesis we study effects which go beyond the standard assumptions. We study the impact of PMFs on cosmological perturbations and CMB anisotropies with adiabatic initial conditions, the effect of Alfvén waves on the speed of sound of perturbations and possible non-linear behavior of baryon overdensity for PMFs with a blue spectral index, by modifying and improving the publicly available Einstein-Boltzmann code SONG, which has been written in order to take into account all second-order contributions in cosmological perturbation theory. One of the objectives of this thesis is to set the basis to verify by an independent fully numerical analysis the possibility to affect recombination and the Hubble constant.

Neural Network Based UAV Fault Tolerant Control with Aerodynamic Disturbance Estimation and Compensation

In this thesis, the problem of controlling a quadrotor UAV is considered. It is done by presenting an original control system, designed as a combination of Neural Networks and Disturbance Observer, using a composite learning approach for a system of the second order, which is a novel methodology in literature. After a brief introduction about the quadrotors, the concepts needed to understand the controller are presented, such as the main notions of advanced control, the basic structure and design of a Neural Network, the modeling of a quadrotor and its dynamics. The full simulator, developed on the MATLAB Simulink environment, used throughout the whole thesis, is also shown. For the guidance and control purposes, a Sliding Mode Controller, used as a reference, it is firstly introduced, and its theory and implementation on the simulator are illustrated. Finally the original controller is introduced, through its novel formulation, and implementation on the model. The effectiveness and robustness of the two controllers are then proven by extensive simulations in all different conditions of external disturbance and faults.