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.

Reconstruction and analysis of the NF-kB pathway interactome: a systems biology approach

Background. One of the phenomena observed in human aging is the progressive increase of a systemic inflammatory state, a condition referred to as “inflammaging”, negatively correlated with longevity. A prominent mediator of inflammation is the transcription factor NF-kB, that acts as key transcriptional regulator of many genes coding for pro-inflammatory cytokines. Many different signaling pathways activated by very diverse stimuli converge on NF-kB, resulting in a regulatory network characterized by high complexity. NF-kB signaling has been proposed to be responsible of inflammaging. Scope of this analysis is to provide a wider, systemic picture of such intricate signaling and interaction network: the NF-kB pathway interactome. Methods. The study has been carried out following a workflow for gathering information from literature as well as from several pathway and protein interactions databases, and for integrating and analyzing existing data and the relative reconstructed representations by using the available computational tools. Strong manual intervention has been necessarily used to integrate data from multiple sources into mathematically analyzable networks. The reconstruction of the NF-kB interactome pursued with this approach provides a starting point for a general view of the architecture and for a deeper analysis and understanding of this complex regulatory system. Results. A “core” and a “wider” NF-kB pathway interactome, consisting of 140 and 3146 proteins respectively, were reconstructed and analyzed through a mathematical, graph-theoretical approach. Among other interesting features, the topological characterization of the interactomes shows that a relevant number of interacting proteins are in turn products of genes that are controlled and regulated in their expression exactly by NF-kB transcription factors. These “feedback loops”, not always well-known, deserve deeper investigation since they may have a role in tuning the response and the output consequent to NF-kB pathway initiation, in regulating the intensity of the response, or its homeostasis and balance in order to make the functioning of such critical system more robust and reliable. This integrated view allows to shed light on the functional structure and on some of the crucial nodes of thet NF-kB transcription factors interactome. Conclusion. Framing structure and dynamics of the NF-kB interactome into a wider, systemic picture would be a significant step toward a better understanding of how NF-kB globally regulates diverse gene programs and phenotypes. This study represents a step towards a more complete and integrated view of the NF-kB signaling system.

Epidemiologia delle strongilosi dell'asino: quali applicazioni per il controllo delle infezioni da elminti?

Strongylosis in equids, despite being very common, have never been studied from a strictly ecological point of view. Mathematical models are important ecological tools used to study the temporal dynamics of parasite populations, and are useful to study the effect of different biological parameters, as well as to analyse the outcome produced by perturbations such as anthelmintic treatments. This work describes the study of the temporal dynamics of strongyles infection in an organic donkey population, performed using coprological quantitative analysis and donkeys’ age as a proxy of the time of infection. Force of infection was then estimated for Strongylus vulgaris and small strongyles and the results used as the basis for the development of mathematical models. In particular, the comparison of models output and field data made it possible to estimate the transmission coefficient  and to consequently calculate the basic reproduction number R0 and the threshold host density. Small strongyles model includes hypobiosis and, more interestingly as never found in literature, a density-dependent development rate of hypobiotic larvae in adult parasites in order to simulate a negative feedback between larvae emergence from hypobiosis and adult parasite abundance. Simulations of pharmacological and environmental treatments showed that parasite eradication was possible for S. vulgaris only, while small strongyles, due to hypobiosis and density-dependent development rate of their hypobiotic larvae, are very difficult to control and impossible to eradicate. In addition, density-dependence in larval development has been demonstrated to act as a key factor in improving parasite population survival and abundance even in absence of human intervention.

Solving the cooling flow problem through mechanical AGN feedback

A fundamental gap in the current understanding of collapsed structures in the universe concerns the thermodynamical evolution of the ordinary, baryonic component. Unopposed radiative cooling of plasma would lead to the cooling catastrophe, a massive inflow of condensing gas toward the centre of galaxies, groups and clusters. The last generation of multiwavelength observations has radically changed our view on baryons, suggesting that the heating linked to the active galactic nucleus (AGN) may be the balancing counterpart of cooling. In this Thesis, I investigate the engine of the heating regulated by the central black hole. I argue that the mechanical feedback, based on massive subrelativistic outflows, is the key to solving the cooling flow problem, i.e. dramatically quenching the cooling rates for several billion years without destroying the cool-core structure. Using an upgraded version of the parallel 3D hydrodynamic code FLASH, I show that anisotropic AGN outflows can further reproduce fundamental observed features, such as buoyant bubbles, cocoon shocks, sonic ripples, metals dredge-up, and subsonic turbulence. The latter is an essential ingredient to drive nonlinear thermal instabilities, which cause cold gas condensation, a residual of the quenched cooling flow and, later, fuel for the AGN feedback engine. The self-regulated outflows are systematically tested on the scales of massive clusters, groups and isolated elliptical galaxies: in lighter less bound objects the feedback needs to be gentler and less efficient, in order to avoid drastic overheating. In this Thesis, I describe in depth the complex hydrodynamics, involving the coupling of the feedback energy to that of the surrounding hot medium. Finally, I present the merits and flaws of all the proposed models, with a critical eye toward observational concordance.

Essays in Environmental Economics

This dissertation comprises four essays on the topic of environmental economics and industrial organization. In the first essay, we develop a two-country world differential game model with a polluting firm in each country to investigate the equilibrium of the game between firms when they decide to trade or not and to see under which conditions social welfare coincides with the market equilibrium. In the second essay, we built a model where firms strategically choose whether to participate in an auction/lottery to attain pollution permits, or instead invest in green R&D, to show that, somewhat counterintuitively, a desirable side effect of the auction is in fact that of fostering environmental R&D in an admissible range of the model parameters. The third essay investigates a second-best trade agreement between two countries when pollution spillovers are asymmetric to examine the strategic behavior of governments in using pollution taxes and tariffs under trade liberalization. The fouth essay studies the profitability of exogenous output constraint in a differential game model with price dynamics under the feedback strategies.

Essays in Industrial Organization

This dissertation comprises four essays on the topic of industrial organization and environmental economics. The first essay investigates the profitability of horizontal mergers of firms with price adjustments. We take a differential game approach and both the open-loop as well as the closed-loop equlibria are considered. In the second essay, using the same approach as the first one, we study the profitability of horizontal merger of firms where the demand function is nonlinear. We take into consideration the open-loop equilibrium. The third essay studies the profitability of exogenous output constraint in a differential game model with price dynamics under the feedback strategies. The fourth essay investigates a second-best trade agreement between two countries when pollution spillovers are asymmetric to examine the strategic behavior of governments in using pollution taxes and tariffs under trade liberalization.

Riabilitazione e valutazione di pazienti con deficit neurologici mediante l'utilizzo di realtà virtuale, feedback aumentati, sensori inerziali e tecnologie video a basso costo.

La neuroriabilitazione è un processo attraverso cui individui affetti da patologie neurologiche mirano al conseguimento di un recupero completo o alla realizzazione del loro potenziale ottimale benessere fisico, mentale e sociale. Elementi essenziali per una riabilitazione efficace sono: una valutazione clinica da parte di un team multidisciplinare, un programma riabilitativo mirato e la valutazione dei risultati conseguiti mediante misure scientifiche e clinicamente appropriate. Obiettivo principale di questa tesi è stato sviluppare metodi e strumenti quantitativi per il trattamento e la valutazione motoria di pazienti neurologici. I trattamenti riabilitativi convenzionali richiedono a pazienti neurologici l’esecuzione di esercizi ripetitivi, diminuendo la loro motivazione. La realtà virtuale e i feedback sono in grado di coinvolgerli nel trattamento, permettendo ripetibilità e standardizzazione dei protocolli. È stato sviluppato e valutato uno strumento basato su feedback aumentati per il controllo del tronco. Inoltre, la realtà virtuale permette l’individualizzare il trattamento in base alle esigenze del paziente. Un’applicazione virtuale per la riabilitazione del cammino è stata sviluppata e testata durante un training su pazienti di sclerosi multipla, valutandone fattibilità e accettazione e dimostrando l'efficacia del trattamento. La valutazione quantitativa delle capacità motorie dei pazienti viene effettuata utilizzando sistemi di motion capture. Essendo il loro uso nella pratica clinica limitato, una metodologia per valutare l’oscillazione delle braccia in soggetti parkinsoniani basata su sensori inerziali è stata proposta. Questi sono piccoli, accurati e flessibili ma accumulano errori durante lunghe misurazioni. È stato affrontato questo problema e i risultati suggeriscono che, se il sensore è sul piede e le accelerazioni sono integrate iniziando dalla fase di mid stance, l’errore e le sue conseguenze nella determinazione dei parametri spaziali sono contenuti. Infine, è stata presentata una validazione del Kinect per il tracking del cammino in ambiente virtuale. Risultati preliminari consentono di definire il campo di utilizzo del sensore in riabilitazione.

An Input-Process-Output Approach to Interorganizational Teams: The Influence of Work Group Diversity, Trust and Shared Leadership on Communication Network and Team Outputs.

The market’s challenges bring firms to collaborate with other organizations in order to create Joint Ventures, Alliances and Consortia that are defined as “Interorganizational Networks” (IONs) (Provan, Fish and Sydow; 2007). Some of these IONs are managed through a shared partecipant governance (Provan and Kenis, 2008): a team composed by entrepreneurs and/or directors of each firm of an ION. The research is focused on these kind of management teams and it is based on an input-process-output model: some input variables (work group’s diversity, intra-team's friendship network density) have a direct influence on the process (team identification, shared leadership, interorganizational trust, team trust and intra-team's communication network density), which influence some team outputs, individual innovation behaviors and team effectiveness (team performance, work group satisfaction and ION affective commitment). Data was collected on a sample of 101 entrepreneurs grouped in 28 ION’s government teams and the research hypotheses are tested trough the path analysis and the multilevel models. As expected trust in team and shared leadership are positively and directly related to team effectiveness while team identification and interorganizational trust are indirectly related to the team outputs. The friendship network density among the team’s members has got positive effects on the trust in team and on the communication network density, and also, through the communication network density it improves the level of the teammates ION affective commitment. The shared leadership and its effects on the team effectiveness are fostered from higher level of team identification and weakened from higher level of work group diversity, specifically gender diversity. Finally, the communication network density and shared leadership at the individual level are related to the frequency of individual innovative behaviors. The dissertation’s results give a wider and more precise indication about the management of interfirm network through “shared” form of governance.

Peak-to-Peak Output Current Ripple Analysis in Multiphase and Multilevel Inverters

Analysis of the peak-to-peak output current ripple amplitude for multiphase and multilevel inverters is presented in this PhD thesis. The current ripple is calculated on the basis of the alternating voltage component, and peak-to-peak value is defined by the current slopes and application times of the voltage levels in a switching period. Detailed analytical expressions of peak-to-peak current ripple distribution over a fundamental period are given as function of the modulation index. For all the cases, reference is made to centered and symmetrical switching patterns, generated either by carrier-based or space vector PWM. Starting from the definition and the analysis of the output current ripple in three-phase two-level inverters, the theoretical developments have been extended to the case of multiphase inverters, with emphasis on the five- and seven-phase inverters. The instantaneous current ripple is introduced for a generic balanced multiphase loads consisting of series RL impedance and ac back emf (RLE). Simplified and effective expressions to account for the maximum of the output current ripple have been defined. The peak-to-peak current ripple diagrams are presented and discussed. The analysis of the output current ripple has been extended also to multilevel inverters, specifically three-phase three-level inverters. Also in this case, the current ripple analysis is carried out for a balanced three-phase system consisting of series RL impedance and ac back emf (RLE), representing both motor loads and grid-connected applications. The peak-to-peak current ripple diagrams are presented and discussed. In addition, simulation and experimental results are carried out to prove the validity of the analytical developments in all the cases. The cases with different phase numbers and with different number of levels are compared among them, and some useful conclusions have been pointed out. Furthermore, some application examples are given.

Robust Nonlinear Output Regulation by Identification Tools

The present thesis focuses on the problem of robust output regulation for minimum phase nonlinear systems by means of identification techniques. Given a controlled plant and an exosystem (an autonomous system that generates eventual references or disturbances), the control goal is to design a proper regulator able to process the only measure available, i.e the error/output variable, in order to make it asymptotically vanishing. In this context, such a regulator can be designed following the well known “internal model principle” that states how it is possible to achieve the regulation objective by embedding a replica of the exosystem model in the controller structure. The main problem shows up when the exosystem model is affected by parametric or structural uncertainties, in this case, it is not possible to reproduce the exact behavior of the exogenous system in the regulator and then, it is not possible to achieve the control goal. In this work, the idea is to find a solution to the problem trying to develop a general framework in which coexist both a standard regulator and an estimator able to guarantee (when possible) the best estimate of all uncertainties present in the exosystem in order to give “robustness” to the overall control loop.