Stability and stabilization of sampled-data control for lure systems

Este trabalho apresenta um novo método para a análise de estabilidade e estabilização de sistemas do tipo Lure com controle amostrado, sujeitos a amostragem aperiódica e não linearidades que são limitadas em setor e restritas em derivada, em ambos contextos global e regional. Assume-se que os estados da planta estão disponíveis para medição e que as não linearidades são conhecidas, o que leva a uma formulação mais geral do problema. Os estados são adquiridos por um controlador digital que atualiza a entrada de controle em instantes de tempo discretos e aperiódicos, mantendo-a constante entre dois instantes sucessivos de amostragem. A abordagem apresentada neste trabalho é baseada no uso de uma nova classe de looped-functionals e em uma função do tipo Lure generalizada, que leva a condições de estabilidade e estabilização que são escritas na forma de desigualdades matriciais lineares (LMIs) e quasi-LMIs, respectivamente. Com base nestas condições, problemas de otimização são formulados com o objetivo de computar o intervalo máximo entre amostragens ou os limites máximos do setor para os quais a estabilidade assintótica da origem do sistema de dados amostrados em malha fechada é garantida. No caso em que as condições de setor são válidas apenas localmente, a solução desses problemas também fornece uma estimativa da região de atração para as trajetórias em tempo contínuo do sistema em malha fechada. Como as condições de síntese são quasi-LMIs, um algoritmo de otimização por enxame de partículas é proposto para lidar com as não linearidades envolvidas nos problemas de otimização, que surgem do produto de algumas variáveis de decisão. Exemplos numéricos são apresentados ao longo do trabalho para destacar as potencialidades do método.This work presents a new method for stability analysis and stabilization of sampleddata controlled Lure systems, subject to aperiodic sampling and nonlinearities that are sector bounded and slope restricted, in both global and regional contexts. We assume that the states of the plant are available for measurement and that the nonlinearities are known, which leads to a more general formulation of the problem. The states are acquired by a digital controller which updates the control input at aperiodic discrete-time instants, keeping it constant between successive sampling instants. The approach here presented is based on the use of a new class of looped-functionals and a generalized Luretype function, which leads to stability and stabilization conditions that are written in the form of Linear Matrix Inequalities (LMIs) and quasi-LMIs, respectively. On this basis, optimization problems are formulated aiming to compute the maximal intersampling interval or the maximal sector bounds for which the asymptotic stability of the origin of the sampled-data closed-loop system is guaranteed. In the case where the sector conditions hold only locally, the solution of these problems also provide an estimate of the region of attraction for the continuous-time trajectories of the closed-loop system. As the synthesis conditions are quasi-LMIs, a Particle Swarm Optimization (PSO) algorithm is proposed to deal with the involved nonlinearities in the optimization problems, which arise from the product of some decision variables. Numerical examples are presented throughout the work to highlight the potentialities of the method

Late Prehistoric Lithic Economies in the Prairie Peninsula: a Comparison of Oneota and Langford in Southern Wisconsin and Northern Illinois

This thesis is an examination of the environmental settlement patterns and the organization of lithic technology surrounding Upper Mississippian groups in Southeastern Wisconsin and Northern Illinois. The sites investigated in this study are the Washington Irving (11K52) and Koshkonong Creek Village (47JE379) habitation sites, contemporaneous creekside Langford and Oneota sites located approximately 90 kilometers apart. A two-kilometer catchment of Washington Irving is compared to that of the Koshkonong Creek Village to clarify the nature of environmental variation in Langford and Oneota settlement patterns and increase our understanding of Upper Mississippian horticulturalist lifeways. Lithic tool and mass debitage analyses use an assemblage-based approach to understand the lithic economies at each site, accounting for procurement and manufacturing strategies and assemblage diversity and complexity

Exponential input-to-state stability for Lur’e systems via Integral Quadratic Constraints and Zames–Falb multipliers

Absolute stability criteria that are sufficient for global exponential stability are shown, under a Lipschitz assumption, to be sufficient for the a priori stronger exponential input-to-state stability property. Important corollaries of this result are as follows: (i) absolute stability results obtained using Zames–Falb multipliers for systems containing slope-restricted nonlinearities provide exponential input-to-state-stability under a mild detectability assumption; and (ii) more generally, many absolute stability results obtained via Integral Quadratic Constraint methods provide, with the additional Lipschitz assumption, this stronger property

Modeling and forecasting the COVID-19 temporal spread in Greece: an exploratory approach based on complex network defined splines

Within the complex framework of anti-COVID-19 health management, where the criteria of diagnostic testing, the availability of public-health resources and services, and the applied anti-COVID-19 policies vary between countries, the reliability and the accuracy in the modeling of temporal spread can be proven effective in the worldwide fight against the disease. This paper applies an exploratory time-series analysis to the evolution of the disease in Greece, which currently suggests a success story of COVID-19 management. The proposed method builds on a recent conceptualization of detecting connective communities in a time-series and develops a novel spline regression model where the knot vector is determined by the community detection in the complex network. Overall, the study contributes to the COVID-19 research by proposing a free of disconnected past-data and reliable framework of forecasting, which can facilitate decision-making and management of the available health resources

Migration intensity has no effect on peak HIV prevalence: An ecological study

Background: Correctly identifying the determinants of generalized HIV epidemics is crucial to bringing down ongoing high HIV incidence in these countries. High rates of migration are believed to be an important determinant of HIV prevalence. This study has two aims. Firstly, it evaluates the ecological association between levels of internal and international migration and national peak HIV prevalence using thirteen variables from a variety of sources to capture various aspects of internal and international migration intensity. Secondly, it examines the relationship between circular migration and HIV at an individual and population-level in South Africa.Methods: Linear regression was used to analyze the association between the various measures of migration intensity and peak national HIV prevalence for 141 countries and HIV prevalence by province and ethnic group in South Africa.Results: No evidence of a positive ecological association between national migration intensity and HIV prevalence was found. This remained the case when the analyses were limited to the countries of sub-Saharan Africa. On the whole, countries with generalized HIV epidemics had lower rates of internal and external migration. Likewise, no association was found between migration and HIV positivity at an individual or group-level in South Africa.Conclusion: These results do not support the thesis that migration measured at the country level plays a significant role in determining peak HIV prevalence

The Utility of CA125 for the Detection of Ovarian Cancer in Primary Care

Background Ovarian cancer is the 6th most common cancer to affect UK women and has the worst prognosis of any gynaecological cancer. Most women are not diagnosed until the disease is advanced, which leads to poor outcomes. Earlier ovarian cancer diagnosis has the potential to improve these outcomes. Cancer antigen 125 (CA125) is recommended by the National Institute for Health and Care Excellence (NICE) as the first line test for ovarian cancer in symptomatic women presenting to primary care in England. However, the performance of CA125 in this setting is unknown. The overarching aim of this thesis was to determine the diagnostic performance of CA125 for the detection of ovarian cancer when used in primary care, and to develop and evaluate novel approaches to improve its performance and clinical utility. Key methods I used routinely collected primary care and cancer registry data from 50,780 women who underwent CA125 testing in England between 1st May 2011 – 31st December 2014. First, I performed a diagnostic accuracy study, calculating the performance of CA125 within the cohort, at the national cut-off (≥35 U/ml), for the detection of ovarian cancer. Diagnostic accuracy metrics were also calculated for other types of cancer and all cancer types combined (secondary study outcomes). I used logistic regression to estimate the probability of ovarian cancer at specific CA125 levels (1-1000 U/ml) for women of different ages. CA125 levels equating to a 3% ovarian cancer probability (the “risk threshold” at which NICE advocates urgent specialist cancer investigation) were identified. Next, I examined the associations between CA125 test result and time from testing to diagnosis, tumour type and cancer stage, in those women with ovarian cancer. Finally, I developed and internally validated ovarian cancer diagnostic prediction models (of varying complexity) in a sub-group of women with a relevant symptom recorded prior to CA125 testing (n=29,962). To inform the development of these models, I conducted a systematic review of existing ovarian cancer detection tools. Key results CA125 had a sensitivity of 77%, a specificity of 94% and a Positive Predictive Value (PPV) of 10% for ovarian cancer at the national cut-off (≥35 U/ml). The PPV for all cancers combined was 21% overall, and 33% in women ≥50 years of age. 20% of women ≥50 years with a raised CA125 level, but no ovarian cancer, had another type of cancer. A CA125 value of 53 U/ml equated to a 3% probability of ovarian cancer overall, but this varied markedly by age (40- year-old: 104 U/ml, 70-year-old: 32 U/ml). Women with a ‘normal’ CA125 (<35 U/ml) prior to ovarian cancer diagnosis took twice as long to be diagnosed as those with an ‘abnormal’ CA125, but more frequently had indolent tumour types and were more likely to be diagnosed at an early stage. An ovarian cancer prediction model, incorporating patient age and CA125 level, outperformed CA125 alone. This model showed excellent discrimination on internal validation (AUC: 0.94). Including symptoms, baseline risk factors and other routine blood tests did not improve model performance. Conclusions My findings demonstrate that CA125 is a useful test for ovarian cancer detection in primary care. They also indicate that clinicians should consider other types of cancer in women with high CA125 levels, especially if ovarian cancer has been excluded, in order to prevent diagnostic delay. The models presented in this thesis will allow patients and clinicians to determine the estimated probability of ovarian cancer at any given CA125 level and age. This information could inform individual patient decisions on the need for further investigation. If incorporated into the diagnostic pathway, the models would enable patients to be referred on the basis of ovarian cancer risk rather than a generic CA125 cut-off

Derived induction and restriction theory

Let $G$ be a finite group. To any family $\mathscr{F}$ of subgroups of $G$, we associate a thick $\otimes$-ideal $\mathscr{F}^{\mathrm{Nil}}$ of the category of $G$-spectra with the property that every $G$-spectrum in $\mathscr{F}^{\mathrm{Nil}}$ (which we call $\mathscr{F}$-nilpotent) can be reconstructed from its underlying $H$-spectra as $H$ varies over $\mathscr{F}$. A similar result holds for calculating $G$-equivariant homotopy classes of maps into such spectra via an appropriate homotopy limit spectral sequence. In general, the condition $E\in \mathscr{F}^{\mathrm{Nil}}$ implies strong collapse results for this spectral sequence as well as its dual homotopy colimit spectral sequence. As applications, we obtain Artin and Brauer type induction theorems for $G$-equivariant $E$-homology and cohomology, and generalizations of Quillen's $\mathcal{F}_p$-isomorphism theorem when $E$ is a homotopy commutative $G$-ring spectrum. We show that the subcategory $\mathscr{F}^{\mathrm{Nil}}$ contains many $G$-spectra of interest for relatively small families $\mathscr{F}$. These include $G$-equivariant real and complex $K$-theory as well as the Borel-equivariant cohomology theories associated to complex oriented ring spectra, any $L_n$-local spectrum, the classical bordism theories, connective real $K$-theory, and any of the standard variants of topological modular forms. In each of these cases we identify the minimal family such that these results hold.Comment: 63 pages. Many edits and some simplifications. Final version, to appear in Geometry and Topolog