Internal Model Principle: extension to the switching case and applications

This thesis deals with a novel control approach based on the extension of the well-known Internal Model Principle to the case of periodic switched linear exosystems. This extension, inspired by power electronics applications, aims to provide an effective design method to robustly achieve the asymptotic tracking of periodic references with an infinite number of harmonics. In the first part of the thesis the basic components of the novel control scheme are described and preliminary results on stabilization are provided. In the second part, advanced control methods for two applications coming from the world high energy physics are presented.

High-performance switching architectures for optical networks

The need for high bandwidth, due to the explosion of new multi\-media-oriented IP-based services, as well as increasing broadband access requirements is leading to the need of flexible and highly reconfigurable optical networks. While transmission bandwidth does not represent a limit due to the huge bandwidth provided by optical fibers and Dense Wavelength Division Multiplexing (DWDM) technology, the electronic switching nodes in the core of the network represent the bottleneck in terms of speed and capacity for the overall network. For this reason DWDM technology must be exploited not only for data transport but also for switching operations. In this Ph.D. thesis solutions for photonic packet switches, a flexible alternative with respect to circuit-switched optical networks are proposed. In particular solutions based on devices and components that are expected to mature in the near future are proposed, with the aim to limit the employment of complex components. The work presented here is the result of part of the research activities performed by the Networks Research Group at the Department of Electronics, Computer Science and Systems (DEIS) of the University of Bologna, Italy. In particular, the work on optical packet switching has been carried on within three relevant research projects: the e-Photon/ONe and e-Photon/ONe+ projects, funded by the European Union in the Sixth Framework Programme, and the national project OSATE funded by the Italian Ministry of Education, University and Scientific Research. The rest of the work is organized as follows. Chapter 1 gives a brief introduction to network context and contention resolution in photonic packet switches. Chapter 2 presents different strategies for contention resolution in wavelength domain. Chapter 3 illustrates a possible implementation of one of the schemes proposed in chapter 2. Then, chapter 4 presents multi-fiber switches, which employ jointly wavelength and space domains to solve contention. Chapter 5 shows buffered switches, to solve contention in time domain besides wavelength domain. Finally chapter 6 presents a cost model to compare different switch architectures in terms of cost.

A bayesian model for mixed responses and skew laten variable to measure HRQoL in children

The aim of the thesi is to formulate a suitable Item Response Theory (IRT) based model to measure HRQoL (as latent variable) using a mixed responses questionnaire and relaxing the hypothesis of normal distributed latent variable. The new model is a combination of two models already presented in literature, that is, a latent trait model for mixed responses and an IRT model for Skew Normal latent variable. It is developed in a Bayesian framework, a Markov chain Monte Carlo procedure is used to generate samples of the posterior distribution of the parameters of interest. The proposed model is test on a questionnaire composed by 5 discrete items and one continuous to measure HRQoL in children, the EQ-5D-Y questionnaire. A large sample of children collected in the schools was used. In comparison with a model for only discrete responses and a model for mixed responses and normal latent variable, the new model has better performances, in term of deviance information criterion (DIC), chain convergences times and precision of the estimates.

Discharge characteristics and discharge simulation model of long air gaps containing a floating conductor

Long air gaps containing a floating conductor are common insulation types in power grids. During the transmission line live-line work, the process of lineman entering the transmission line air gap constitutes a live-line work combined air gap, which is a typical long air gap containing a floating conductor. This thesis investigates the discharge characteristics, the discharge mechanism and a discharge simulation model of long air gaps containing a floating conductor in order to address the engineering issues in live-line work. The innovative achievements of the thesis are as follows: (1) The effect of the gap distance, the floating electrode structure, the switching impulse wavefront time, the altitude, and the deviation of the floating conductor from the axis on the breakdown voltage was determined. (2) The physical process of the discharges in long air gaps containing a floating conductor was determined. The reason why the discharge characteristics of long air gaps containing a floating electrode with complex geometrics and sharp protrusions and long air gaps with a rod-shaped floating electrode are similar has been studied. The formation mechanism of the lowest breakdown voltage area of a long air gap containing a floating conductor is explained. (3) A simulation discharge model of long air gaps containing a floating conductor was established, which can describe the physical process and predict the breakdown voltage. The model can realize the accurate prediction of the breakdown voltage of typical long air gaps containing a floating conductor and live-line work combined air gaps in transmission lines. The findings of the study can provide theoretical reference and technical support for improving the safety of live-line work.

A Unified Model for XVA, including Interest Rates and Rating

We start in Chapter 2 to investigate linear matrix-valued SDEs and the Itô-stochastic Magnus expansion. The Itô-stochastic Magnus expansion provides an efficient numerical scheme to solve matrix-valued SDEs. We show convergence of the expansion up to a stopping time τ and provide an asymptotic estimate of the cumulative distribution function of τ. Moreover, we show how to apply it to solve SPDEs with one and two spatial dimensions by combining it with the method of lines with high accuracy. We will see that the Magnus expansion allows us to use GPU techniques leading to major performance improvements compared to a standard Euler-Maruyama scheme. In Chapter 3, we study a short-rate model in a Cox-Ingersoll-Ross (CIR) framework for negative interest rates. We define the short rate as the difference of two independent CIR processes and add a deterministic shift to guarantee a perfect fit to the market term structure. We show how to use the Gram-Charlier expansion to efficiently calibrate the model to the market swaption surface and price Bermudan swaptions with good accuracy. We are taking two different perspectives for rating transition modelling. In Section 4.4, we study inhomogeneous continuous-time Markov chains (ICTMC) as a candidate for a rating model with deterministic rating transitions. We extend this model by taking a Lie group perspective in Section 4.5, to allow for stochastic rating transitions. In both cases, we will compare the most popular choices for a change of measure technique and show how to efficiently calibrate both models to the available historical rating data and market default probabilities. At the very end, we apply the techniques shown in this thesis to minimize the collateral-inclusive Credit/ Debit Valuation Adjustments under the constraint of small collateral postings by using a collateral account dependent on rating trigger.