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.

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.

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.

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.

A dynamical system approach to data assimilation in chaotic models

The Assimilation in the Unstable Subspace (AUS) was introduced by Trevisan and Uboldi in 2004, and developed by Trevisan, Uboldi and Carrassi, to minimize the analysis and forecast errors by exploiting the flow-dependent instabilities of the forecast-analysis cycle system, which may be thought of as a system forced by observations. In the AUS scheme the assimilation is obtained by confining the analysis increment in the unstable subspace of the forecast-analysis cycle system so that it will have the same structure of the dominant instabilities of the system. The unstable subspace is estimated by Breeding on the Data Assimilation System (BDAS). AUS- BDAS has already been tested in realistic models and observational configurations, including a Quasi-Geostrophicmodel and a high dimensional, primitive equation ocean model; the experiments include both fixed and“adaptive”observations. In these contexts, the AUS-BDAS approach greatly reduces the analysis error, with reasonable computational costs for data assimilation with respect, for example, to a prohibitive full Extended Kalman Filter. This is a follow-up study in which we revisit the AUS-BDAS approach in the more basic, highly nonlinear Lorenz 1963 convective model. We run observation system simulation experiments in a perfect model setting, and with two types of model error as well: random and systematic. In the different configurations examined, and in a perfect model setting, AUS once again shows better efficiency than other advanced data assimilation schemes. In the present study, we develop an iterative scheme that leads to a significant improvement of the overall assimilation performance with respect also to standard AUS. In particular, it boosts the efficiency of regime’s changes tracking, with a low computational cost. Other data assimilation schemes need estimates of ad hoc parameters, which have to be tuned for the specific model at hand. In Numerical Weather Prediction models, tuning of parameters — and in particular an estimate of the model error covariance matrix — may turn out to be quite difficult. Our proposed approach, instead, may be easier to implement in operational models.

Spectrum shaping and its application: spread-spectrum clock generator and circuits for ultra wide band

Electromagnetic spectrum can be identified as a resource for the designer, as well as for the manufacturer, from two complementary points of view: first, because it is a good in great demand by many different kind of applications; second, because despite its scarce availability, it may be advantageous to use more spectrum than necessary. This is the case of Spread-Spectrum Systems, those systems in which the transmitted signal is spread over a wide frequency band, much wider, in fact, than the minimum bandwidth required to transmit the information being sent. Part I of this dissertation deals with Spread-Spectrum Clock Generators (SSCG) aiming at reducing Electro Magnetic Interference (EMI) of clock signals in integrated circuits (IC) design. In particular, the modulation of the clock and the consequent spreading of its spectrum are obtained through a random modulating signal outputted by a chaotic map, i.e. a discrete-time dynamical system showing chaotic behavior. The advantages offered by this kind of modulation are highlighted. Three different prototypes of chaos-based SSCG are presented in all their aspects: design, simulation, and post-fabrication measurements. The third one, operating at a frequency equal to 3GHz, aims at being applied to Serial ATA, standard de facto for fast data transmission to and from Hard Disk Drives. The most extreme example of spread-spectrum signalling is the emerging ultra-wideband (UWB) technology, which proposes the use of large sections of the radio spectrum at low amplitudes to transmit high-bandwidth digital data. In part II of the dissertation, two UWB applications are presented, both dealing with the advantages as well as with the challenges of a wide-band system, namely: a chaos-based sequence generation method for reducing Multiple Access Interference (MAI) in Direct Sequence UWB Wireless-Sensor-Networks (WSNs), and design and simulations of a Low-Noise Amplifier (LNA) for impulse radio UWB. This latter topic was studied during a study-abroad period in collaboration with Delft University of Technology, Delft, Netherlands.

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).

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.

New indicators of star cluster dynamical evolution

This thesis presents a study of globular clusters (GCs), based on analysis of Monte Carlo simulations of globular clusters (GCs) with the aim to define new empirical parameters measurable from observations and able to trace the different phases of their dynamical evolution history. During their long term dynamical evolution, due to mass segregation and and dynamical friction, massive stars transfer kinetic energy to lower-mass objects, causing them to sink toward the cluster center. This continuous transfer of kinetic energy from the core to the outskirts triggers the runaway contraction of the core, known as "core collapse" (CC), followed by episodes of expansion and contraction called gravothermal oscillations. Clearly, such an internal dynamical evolution corresponds to significant variations also of the structure of the system. Determining the dynamical age of a cluster can be challenging as it depends on various internal and external properties. The traditional classification of GCs as CC or post-CC systems relies on detecting a steep power-law cusp in the central density profile, which may not always be reliable due to post-CC oscillations or other processes. In this thesis, based on the normalized cumulative radial distribution (nCRD) within a fraction of the half-mass radius is analyzed, and three diagnostics (A5, P5, and S2.5) are defined. These diagnostics show sensitivity to dynamical evolution and can distinguish pre-CC clusters from post-CC clusters.The analysis performed using multiple simulations with different initial conditions, including varying binary fractions and the presence of dark remnants showed the time variations of the diagnostics follow distinct patterns depending on the binary fraction and the retention or ejection of black holes. This analysis is extended to a larger set of simulations matching the observed properties of Galactic GCs, and the parameters show a potential to distinguish the dynamical stages of the observed clusters as well.