About stabilization of non-minimum phase systems by output feedback

This thesis work has been motivated by an internal benchmark dealing with the output regulation problem of a nonlinear non-minimum phase system in the case of full-state feedback. The system under consideration structurally suffers from finite escape time, and this condition makes the output regulation problem very hard even for very simple steady-state evolution or exosystem dynamics, such as a simple integrator. This situation leads to studying the approaches developed for controlling Non-minimum phase systems and how they affect feedback performances. Despite a lot of frequency domain results, only a few works have been proposed for describing the performance limitations in a state space system representation. In particular, in our opinion, the most relevant research thread exploits the so-called Inner-Outer Decomposition. Such decomposition allows splitting the Non-minimum phase system under consideration into a cascade of two subsystems: a minimum phase system (the outer) that contains all poles of the original system and an all-pass Non-minimum phase system (the inner) that contains all the unavoidable pathologies of the unstable zero dynamics. Such a cascade decomposition was inspiring to start working on functional observers for linear and nonlinear systems. In particular, the idea of a functional observer is to exploit only the measured signals from the system to asymptotically reconstruct a certain function of the system states, without necessarily reconstructing the whole state vector. The feature of asymptotically reconstructing a certain state functional plays an important role in the design of a feedback controller able to stabilize the Non-minimum phase system.

User scheduling for low earth orbit multi-user multiple-input-multiple-output non-terrestrial network systems

In rural and isolated areas without cellular coverage, Satellite Communication (SatCom) is the best candidate to complement terrestrial coverage. However, the main challenge for future generations of wireless networks will be to meet the growing demand for new services while dealing with the scarcity of frequency spectrum. As a result, it is critical to investigate more efficient methods of utilizing the limited bandwidth; and resource sharing is likely the only choice. The research community’s focus has recently shifted towards the interference management and exploitation paradigm to meet the increasing data traffic demands. In the Downlink (DL) and Feedspace (FS), LEO satellites with an on-board antenna array can offer service to numerous User Terminals (UTs) (VSAT or Handhelds) on-ground in FFR schemes by using cutting-edge digital beamforming techniques. Considering this setup, the adoption of an effective user scheduling approach is a critical aspect given the unusually high density of User terminals on the ground as compared to the on-board available satellite antennas. In this context, one possibility is that of exploiting clustering algorithms for scheduling in LEO MU-MIMO systems in which several users within the same group are simultaneously served by the satellite via Space Division Multiplexing (SDM), and then these different user groups are served in different time slots via Time Division Multiplexing (TDM). This thesis addresses this problem by defining a user scheduling problem as an optimization problem and discusses several algorithms to solve it. In particular, focusing on the FS and user service link (i.e., DL) of a single MB-LEO satellite operating below 6 GHz, the user scheduling problem in the Frequency Division Duplex (FDD) mode is addressed. The proposed State-of-the-Art scheduling approaches are based on graph theory. The proposed solution offers high performance in terms of per-user capacity, Sum-rate capacity, SINR, and Spectral Efficiency.

Heterogeneous multicore systems for signal processing

This thesis explores the capabilities of heterogeneous multi-core systems, based on multiple Graphics Processing Units (GPUs) in a standard desktop framework. Multi-GPU accelerated desk side computers are an appealing alternative to other high performance computing (HPC) systems: being composed of commodity hardware components fabricated in large quantities, their price-performance ratio is unparalleled in the world of high performance computing. Essentially bringing “supercomputing to the masses”, this opens up new possibilities for application fields where investing in HPC resources had been considered unfeasible before. One of these is the field of bioelectrical imaging, a class of medical imaging technologies that occupy a low-cost niche next to million-dollar systems like functional Magnetic Resonance Imaging (fMRI). In the scope of this work, several computational challenges encountered in bioelectrical imaging are tackled with this new kind of computing resource, striving to help these methods approach their true potential. Specifically, the following main contributions were made: Firstly, a novel dual-GPU implementation of parallel triangular matrix inversion (TMI) is presented, addressing an crucial kernel in computation of multi-mesh head models of encephalographic (EEG) source localization. This includes not only a highly efficient implementation of the routine itself achieving excellent speedups versus an optimized CPU implementation, but also a novel GPU-friendly compressed storage scheme for triangular matrices. Secondly, a scalable multi-GPU solver for non-hermitian linear systems was implemented. It is integrated into a simulation environment for electrical impedance tomography (EIT) that requires frequent solution of complex systems with millions of unknowns, a task that this solution can perform within seconds. In terms of computational throughput, it outperforms not only an highly optimized multi-CPU reference, but related GPU-based work as well. Finally, a GPU-accelerated graphical EEG real-time source localization software was implemented. Thanks to acceleration, it can meet real-time requirements in unpreceeded anatomical detail running more complex localization algorithms. Additionally, a novel implementation to extract anatomical priors from static Magnetic Resonance (MR) scansions has been included.

Dynamic stabilization of Rayleigh-Taylor instability of ablation fronts in inertial confinement fusion

One of the most important problems in inertial confinement fusion is how to find a way to mitigate the onset of the Rayleigh-Taylor instability which arises in the ablation front during the compression. In this thesis it is studied in detail the possibility of using for such a purpose the well-known mechanism of dynamic stabilization, already applied to other dynamical systems such as the inverted pendulum. In this context, a periodic acceleration superposed to the background gravity generates a vertical vibration of the ablation front itself. The effects of different driving modulations (Dirac deltas and square waves) are analyzed from a theoretical point of view, with a focus on stabilization of ion beam driven ablation fronts, and a comparison is made, in order to look for optimization.

Nonlinear Control Strategies for Cooperative Control of Multi-Robot Systems

This thesis deals with distributed control strategies for cooperative control of multi-robot systems. Specifically, distributed coordination strategies are presented for groups of mobile robots. The formation control problem is initially solved exploiting artificial potential fields. The purpose of the presented formation control algorithm is to drive a group of mobile robots to create a completely arbitrarily shaped formation. Robots are initially controlled to create a regular polygon formation. A bijective coordinate transformation is then exploited to extend the scope of this strategy, to obtain arbitrarily shaped formations. For this purpose, artificial potential fields are specifically designed, and robots are driven to follow their negative gradient. Artificial potential fields are then subsequently exploited to solve the coordinated path tracking problem, thus making the robots autonomously spread along predefined paths, and move along them in a coordinated way. Formation control problem is then solved exploiting a consensus based approach. Specifically, weighted graphs are used both to define the desired formation, and to implement collision avoidance. As expected for consensus based algorithms, this control strategy is experimentally shown to be robust to the presence of communication delays. The global connectivity maintenance issue is then considered. Specifically, an estimation procedure is introduced to allow each agent to compute its own estimate of the algebraic connectivity of the communication graph, in a distributed manner. This estimate is then exploited to develop a gradient based control strategy that ensures that the communication graph remains connected, as the system evolves. The proposed control strategy is developed initially for single-integrator kinematic agents, and is then extended to Lagrangian dynamical systems.

Co-simulazione e co-progetto non lineare/elettromagnetico di sistemi wireless non convenzionali

L’attività di ricerca contenuta in questa tesi si è concentrata nello sviluppo e nell’implementazione di tecniche per la co-simulazione e il co-progetto non lineare/elettromagnetico di sistemi wireless non convenzionali. Questo lavoro presenta un metodo rigoroso per considerare le interazioni tra due sistemi posti sia in condizioni di campo vicino che in condizioni di campo lontano. In sostanza, gli effetti del sistema trasmittente sono rappresentati da un generatore equivalente di Norton posto in parallelo all’antenna del sistema ricevente, calcolato per mezzo del teorema di reciprocità e del teorema di equivalenza. La correttezza del metodo è stata verificata per mezzo di simulazioni e misure, concordi tra loro. La stessa teoria, ampliata con l’introduzione degli effetti di scattering, è stata usata per valutare una condizione analoga, dove l’elemento trasmittente coincide con quello ricevente (DIE) contenuto all’interno di una struttura metallica (package). I risultati sono stati confrontati con i medesimi ottenibili tramite tecniche FEM e FDTD/FIT, che richiedono tempi di simulazione maggiori di un ordine di grandezza. Grazie ai metodi di co-simulazione non lineari/EM sopra esposti, è stato progettato e verificato un sistema di localizzazione e identificazione di oggetti taggati posti in ambiente indoor. Questo è stato ottenuto dotando il sistema di lettura, denominato RID (Remotely Identify and Detect), di funzioni di scansione angolare e della tecnica di RADAR mono-pulse. Il sistema sperimentale, creato con dispositivi low cost, opera a 2.5 GHz ed ha le dimensioni paragonabili ad un normale PDA. E’ stato sperimentata la capacità del RID di localizzare, in scenari indoor, oggetti statici e in movimento.

Non-normal modal logics, quantification, and deontic dilemmas. A study in multi-relational semantics

This dissertation is devoted to the study of non-normal (modal) systems for deontic logics, both on the propositional level, and on the first order one. In particular we developed our study the Multi-relational setting that generalises standard Kripke Semantics. We present new completeness results concerning the semantic setting of several systems which are able to handle normative dilemmas and conflicts. Although primarily driven by issues related to the legal and moral field, these results are also relevant for the more theoretical field of Modal Logic itself, as we propose a syntactical, and semantic study of intermediate systems between the classical propositional calculus CPC and the minimal normal modal logic K.

Closed-loop investigation of the dynamical properties of cardiomyocyte electrophysiology by means of Dynamic clamp and Mathematical modelling

The research field of my PhD concerns mathematical modeling and numerical simulation, applied to the cardiac electrophysiology analysis at a single cell level. This is possible thanks to the development of mathematical descriptions of single cellular components, ionic channels, pumps, exchangers and subcellular compartments. Due to the difficulties of vivo experiments on human cells, most of the measurements are acquired in vitro using animal models (e.g. guinea pig, dog, rabbit). Moreover, to study the cardiac action potential and all its features, it is necessary to acquire more specific knowledge about single ionic currents that contribute to the cardiac activity. Electrophysiological models of the heart have become very accurate in recent years giving rise to extremely complicated systems of differential equations. Although describing the behavior of cardiac cells quite well, the models are computationally demanding for numerical simulations and are very difficult to analyze from a mathematical (dynamical-systems) viewpoint. Simplified mathematical models that capture the underlying dynamics to a certain extent are therefore frequently used. The results presented in this thesis have confirmed that a close integration of computational modeling and experimental recordings in real myocytes, as performed by dynamic clamp, is a useful tool in enhancing our understanding of various components of normal cardiac electrophysiology, but also arrhythmogenic mechanisms in a pathological condition, especially when fully integrated with experimental data.

Design and Computation of Warped Time-Frequency Transforms

In this work we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed mathematical model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is known to be analytically characterized and fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped non-smooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.

Distributed optimization and games over networks: a system theoretical perspective

Several decision and control tasks involve networks of cyber-physical systems that need to be coordinated and controlled according to a fully-distributed paradigm involving only local communications without any central unit. This thesis focuses on distributed optimization and games over networks from a system theoretical perspective. In the addressed frameworks, we consider agents communicating only with neighbors and running distributed algorithms with optimization-oriented goals. The distinctive feature of this thesis is to interpret these algorithms as dynamical systems and, thus, to resort to powerful system theoretical tools for both their analysis and design. We first address the so-called consensus optimization setup. In this context, we provide an original system theoretical analysis of the well-known Gradient Tracking algorithm in the general case of nonconvex objective functions. Then, inspired by this method, we provide and study a series of extensions to improve the performance and to deal with more challenging settings like, e.g., the derivative-free framework or the online one. Subsequently, we tackle the recently emerged framework named distributed aggregative optimization. For this setup, we develop and analyze novel schemes to handle (i) online instances of the problem, (ii) ``personalized'' optimization frameworks, and (iii) feedback optimization settings. Finally, we adopt a system theoretical approach to address aggregative games over networks both in the presence or absence of linear coupling constraints among the decision variables of the players. In this context, we design and inspect novel fully-distributed algorithms, based on tracking mechanisms, that outperform state-of-the-art methods in finding the Nash equilibrium of the game.

Efficient and low-computational predictive models for spectral sensors

Spectral sensors are a wide class of devices that are extremely useful for detecting essential information of the environment and materials with high degree of selectivity. Recently, they have achieved high degrees of integration and low implementation cost to be suited for fast, small, and non-invasive monitoring systems. However, the useful information is hidden in spectra and it is difficult to decode. So, mathematical algorithms are needed to infer the value of the variables of interest from the acquired data. Between the different families of predictive modeling, Principal Component Analysis and the techniques stemmed from it can provide very good performances, as well as small computational and memory requirements. For these reasons, they allow the implementation of the prediction even in embedded and autonomous devices. In this thesis, I will present 4 practical applications of these algorithms to the prediction of different variables: moisture of soil, moisture of concrete, freshness of anchovies/sardines, and concentration of gasses. In all of these cases, the workflow will be the same. Initially, an acquisition campaign was performed to acquire both spectra and the variables of interest from samples. Then these data are used as input for the creation of the prediction models, to solve both classification and regression problems. From these models, an array of calibration coefficients is derived and used for the implementation of the prediction in an embedded system. The presented results will show that this workflow was successfully applied to very different scientific fields, obtaining autonomous and non-invasive devices able to predict the value of physical parameters of choice from new spectral acquisitions.

Exploring the internal kinematics of Galactic Globular Cluster cores

Globular clusters (GCs) are traditionally described as simple quasi-relaxed non-rotating stellar systems, characterized by spherical symmetry and isotropy in velocity space. However, recent studies have shown deviations from isotropic velocity distributions and significant internal rotation in many GCs, suggesting that their internal structure and kinematics are more complex than previously thought. The aim of this thesis is to investigate the internal kinematics of Galactic Globular Clusters (GGCs) as part of the Multi-Instrument Kinematic Survey (MIKiS), which exploits the capabilities of different ESO-VLT spectrographs to obtain comprehensive velocity dispersion (VD) and rotation profiles of GGCs. Moreover, this thesis has the particular goal of unraveling the kinematics of GC cores, which are still largely unexplored, by taking advantage of the exceptional spatial resolution of the adaptive-optics assisted integral-field spectrograph MUSE/NFM. The thesis presents a thorough kinematic study of three GGCs NGC 1904, NGC 6440, and NGC 6569. By combining the data sets acquired with four different spectrographs, we obtained the radial velocity (RV) of more than 1000 individual stars in each cluster, sampling from the innermost to the outermost regions. This allowed us to obtain the entire VD profile of each cluster and exclude the presence of an intermediate-mass black hole in the core of NGC 1904, at odds with previous findings obtained from integrated-light spectra. The studies also revealed signatures of internal rotation in each of the GCs studied. These results, supported by those of N-body simulations, prove that GCs were born with a significant initial rotation that they gradually lost through internal two-body relaxation and angular momentum loss carried away by escaping stars. Furthermore, we derived the structural parameters of NGC 6440 and NGC 6569, obtaining a comprehensive overview of the internal kinematics and structure of these GCs, which is necessary to properly reconstruct the evolutionary history of these systems.

Contribution of Non-Covalent Interactions and Electronic Effects on the Conformational Landscape and Tautomeric Equilibria of Molecules and Molecular Complexes: Structural and Dynamical Data from Rotational Spectroscopy

This thesis concerns the study of complex conformational surfaces and tautomeric equilibria of molecules and molecular complexes by quantum chemical methods and rotational spectroscopy techniques. In particular, the focus of this research is on the effects of substitution and noncovalent interactions in determining the energies and geometries of different conformers, tautomers or molecular complexes. The Free-Jet Absorption Millimeter Wave spectroscopy and the Pulsed-Jet Fourier Transform Microwave spectroscopy have been applied to perform these studies and the obtained results showcase the suitability of these techniques for the study of conformational surfaces and intermolecular interactions. The series of investigations of selected medium-size molecules and complexes have shown how different instrumental setups can be used to obtain a variety of results on molecular properties. The systems studied, include molecules of biological interest such as anethole and molecules of astrophysical interest such as N-methylaminoethanol. Moreover halogenation effects have been investigated on halogen substituted tautomeric systems (5-chlorohydroxypyridine and 6-chlorohydroxypyridine), where it has shown that the position of the inserted halogen atom affects the prototropic equilibrium. As for fluorination effects, interesting results have been achieved investigating some small complexes where a molecule of water is used as a probe to reveal the changes on the electrostatic potential of different fluorinated compounds: 2-fluoropyridine, 3-fluoropyridine and penta-fluoropyridine. While in the case of the molecular complex between water and 2-fluoropyridine and 3-fluoropyridine the geometry of the complex with one water molecule is analogous to that of pyridine with the water molecule linked to the pyridine nitrogen, the case of pentafluoropyridine reveals the effect of perfluorination and the water oxygen points towards the positive center of the pyridine ring. Additional molecular adducts with a molecule of water have been analyzed (benzylamine-water and acrylic acid-water) in order to reveal the stabilizing driving forces that characterize these complexes.

Motion control and real-time systems: an approach to trajectory rebuilding in non-deterministic networks

Motion control is a sub-field of automation, in which the position and/or velocity of machines are controlled using some type of device. In motion control the position, velocity, force, pressure, etc., profiles are designed in such a way that the different mechanical parts work as an harmonious whole in which a perfect synchronization must be achieved. The real-time exchange of information in the distributed system that is nowadays an industrial plant plays an important role in order to achieve always better performance, better effectiveness and better safety. The network for connecting field devices such as sensors, actuators, field controllers such as PLCs, regulators, drive controller etc., and man-machine interfaces is commonly called fieldbus. Since the motion transmission is now task of the communication system, and not more of kinematic chains as in the past, the communication protocol must assure that the desired profiles, and their properties, are correctly transmitted to the axes then reproduced or else the synchronization among the different parts is lost with all the resulting consequences. In this thesis, the problem of trajectory reconstruction in the case of an event-triggered communication system is faced. The most important feature that a real-time communication system must have is the preservation of the following temporal and spatial properties: absolute temporal consistency, relative temporal consistency, spatial consistency. Starting from the basic system composed by one master and one slave and passing through systems made up by many slaves and one master or many masters and one slave, the problems in the profile reconstruction and temporal properties preservation, and subsequently the synchronization of different profiles in network adopting an event-triggered communication system, have been shown. These networks are characterized by the fact that a common knowledge of the global time is not available. Therefore they are non-deterministic networks. Each topology is analyzed and the proposed solution based on phase-locked loops adopted for the basic master-slave case has been improved to face with the other configurations.

Quantum Correlations in Field Theory and Integrable Systems

In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will be therefore devoted to the study of the entanglement entropy in one- dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting model. We will derive its Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap will be analysed. In the second part of the thesis we will instead study the dynamics of correlators after a quantum quench , which represent a powerful tool to measure how perturbations and signals propagate through a quantum chain. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, which will be both studied by means of a semi-classical approach. Moreover in the last chapter we will demonstrate a general result about the dynamics of correlation functions of local observables after a quantum quench in integrable systems. In particular we will show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations).