On Local Observer Design for LQR Problems with Tracking

The paper addresses the problem of an observer design for a nonlinear system for which a linear approach is followed for the control synthesis. The linear context driven by the control design allows to focus the observers design in the class of local, i.e. linear, observers. It is shown that when the control contains an external reference, the solution obtained working with the linear approximation to get local solutions produces non consistent results in terms of local regions of convergence for the system and for the observer. The case of a control law which solves a LQR problem with tracking is addressed and two different approaches with respect to the classical one for the observer design are studied. The results are applied to an epidemic spread control to check the differences in the performances for the two different approaches

Evaluation of the effect of different policies in the containment of epidemic spreads for the COVID-19 case

The paper presents a new mathematical model for the SARS-CoV-2 virus propagation, designed to include all the possible actions to prevent the spread and to help in the healing of infected people. After a discussion on the equilibrium and stability properties of the model, the effects of each different control actions on the evolution of the epidemic spread are analysed, through numerical evaluations for a more intuitive and immediate presentation, showing the consequences on the classes of the population

Debits and Credits in Petri Nets and Linear Logic

Exchanging resources often involves situations where a participant gives a resource without obtaining immediately the expected reward. For instance, one can buy an item without paying it in advance, but contracting a debt which must be eventually honoured. Resources, credits and debits can be represented, either implicitly or explicitly, in several formal models, among which Petri nets and linear logic. In this paper we study the relations between two of these models, namely intuitionistic linear logic with mix and Debit Petri nets. In particular, we establish a natural correspondence between provability in the logic, and marking reachability in nets

Vicious circles in contracts and in logic

Contracts are formal promises on the future interactions of participants, which describe the causal dependencies among their actions. An inherent feature of contracts is that such dependencies may be circular: for instance, a buyer promises to pay for an item if the seller promises to ship it, and vice versa. We establish a bridge between two formal models for contracts, one based on games over event structures, and the other one on Propositional Contract Logic. In particular, we show that winning strategies in the game-theoretic model correspond to proofs in the logi

Age Based Modelling of SARS-CoV-2 Contagion: The Italian case

The paper deals with the modelling of the COVID-19 spread among people with different age. The model introduced is a simplified version of a full age based one where the division into age based groups of the population is performed only for distinguishing the initial contagion step. An identification procedure is performed on the basis of the data acquired for the Italian case showing that the model can describe and explain the actual differences between the different aged individuals with respect to the possibility to acquire the virus

Fibromyalgia syndrome : definition and diagnostic aspects

Ever since it was first defined, fibromyalgia (FM) has been considered one of the most controversial diagnoses in the field of rheumatology, to the point that not everybody accepts its existence as an independent entity. The sensitivity and specificity of the proposed diagnostic criteria are still debated by various specialists (not only rheumatologists), whose main criticism of the 1990 American College of Rheumatology criteria is that they identify subsets of particular patients that do not reflect everyday clinical reality. Furthermore, the symptoms characterising FM overlap with those of many other conditions classified in a different manner. Over the last few years, this has led to FM being considered less as a clinical entity and more as a possible manifestation of alterations in the psychoneuroendocrine system (the spectrum of affective disorders) or the stress reaction system (dysfunctional symptoms). More recently, doubts have been raised about even these classifications; and it now seems more appropriate to include FM among the central sensitisation syndromes, which identify the main pathogenetic mechanism as the cause of skeletal and extra-skeletal symptoms of FM and other previously defined "dysfunctional" syndromes

Fibromyalgia syndrome : the pharmacological treatment options

Pharmacological treatment has been gradually enriched by a variety of compounds; however, no single drug is capable of fully managing the constellation of fibromyalgia (FM) symptoms. Currently, it is not possible to draw definite conclusions concerning the best pharmacological approach to managing FM because results of randomized clinical trials present methodological limitations and therapeutic programs are too heterogeneous for adequate comparison. However, a variety of pharmacological treatments including antidepressants, nonsteroidal anti-inflammatory drugs (NSAIDS), opioids, sedatives, muscle relaxants and antiepileptics have been used to treat FM with varying results. In this review, we will evaluate those pharmacological therapies that have produced the most significant clinical results in treating FM patients. The nature of FM suggests that an individualized, multimodal approach that includes both pharmacologic and nonpharmacologic therapies seems to be the most appropriate treatment strategy to date

Non pharmacological treatments in fibromyalgia

Fibromyalgia is a complex syndrome associated with significant impairment in quality of life and function and with substantial financial costs. Once the diagnosis is made, providers should aim to increase patients' function and minimize pain. Fibromyalgia patients frequently use alternative therapies, strongly indicating both their dissatisfaction with and the substantial ineffectiveness of traditional medical therapy, especially pharmacological treatments. At present, pharmacological treatments for fibromyalgia have a rather discouraging cost/benefit ratio in terms of poor symptom control and high incidence of side effects. The interdisciplinary treatment programs have been shown to improve subjective pain with greater success than monotherapy. Physical therapies, rehabilitation and alternative therapies are generally perceived to be more "natural," to have fewer adverse effects, and in some way, to be more effective. In this review, physical exercise and multimodal cognitive behavioural therapy are presented as the more accepted and beneficial forms of nonpharmacological therapy

Symptoms and signs in fibromyalgia syndrome

Fibromyalgia syndrome (FM) is a common chronic pain condition that affects at least 2% of the adult population. Chronic widespread pain is the defining feature of FM, but patients may also exhibit a range of other symptoms, including sleep disturbance, fatigue, irritable bowel syndrome, headaches, and mood disorders. The etiology of FM is not completely understood and the syndrome is influenced by factors such as stress, medical illness, and a variety of pain conditions. Establishing diagnosis may be difficult because of the multifaceted nature of the syndrome and overlap with other chronically painful conditions. A unifying hypothesis is that FM results from sensitization of the central nervous system; this new concept could justify the variety of characteristics of the syndrome. FM symptoms can be musculoskeletal, non-musculoskeletal, or a combination of both; and many patients will also experience a host of associated symptoms or conditions. The ACR classification criteria focus only on pain and disregard other important symptoms; but three key features, pain, fatigue and sleep disturbance, are present in virtually every patient with FM. Several other associated syndromes, including circulatory, nervous, digestive, urinary and reproductive systems are probably a part of the so called central sensitivity or sensitization syndrome. A minority subgroup of patients (30-40%) has a significant psychological disturbance. Psychological factors are an important determinant of any type of pain, and psychological comorbidity is frequent in FM. Psychiatric disorders most commonly described are mood disorders, but psychiatric illness is not a necessary factor in the etiopathogenesis of FM