Formal Analysis of Linear Control Systems using Theorem Proving

Control systems are an integral part of almost every engineering and physical system and thus their accurate analysis is of utmost importance. Traditionally, control systems are analyzed using paper-and-pencil proof and computer simulation methods, however, both of these methods cannot provide accurate analysis due to their inherent limitations. Model checking has been widely used to analyze control systems but the continuous nature of their environment and physical components cannot be truly captured by a state-transition system in this technique. To overcome these limitations, we propose to use higher-order-logic theorem proving for analyzing linear control systems based on a formalized theory of the Laplace transform method. For this purpose, we have formalized the foundations of linear control system analysis in higher-order logic so that a linear control system can be readily modeled and analyzed. The paper presents a new formalization of the Laplace transform and the formal verification of its properties that are frequently used in the transfer function based analysis to judge the frequency response, gain margin and phase margin, and stability of a linear control system. We also formalize the active realizations of various controllers, like Proportional-Integral-Derivative (PID), Proportional-Integral (PI), Proportional-Derivative (PD), and various active and passive compensators, like lead, lag and lag-lead. For illustration, we present a formal analysis of an unmanned free-swimming submersible vehicle using the HOL Light theorem prover.Comment: International Conference on Formal Engineering Method

Formalization of Transform Methods using HOL Light

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover. In particular, we present the motivation of the formalization, which is followed by the related work. Next, we present the task completed so far while highlighting some of the challenges faced during the formalization. Finally, we present a roadmap to achieve our objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201

Characteristics and outcomes of an international cohort of 600 000 hospitalized patients with COVID-19

Background: We describe demographic features, treatments and clinical outcomes in the International Severe Acute Respiratory and emerging Infection Consortium (ISARIC) COVID-19 cohort, one of the world’s largest international, standardized data sets concerning hospitalized patients. Methods: The data set analysed includes COVID-19 patients hospitalized between January 2020 and January 2022 in 52 countries. We investigated how symptoms on admission, co-morbidities, risk factors and treatments varied by age, sex and other characteristics. We used Cox regression models to investigate associations between demographics, symptoms, co-morbidities and other factors with risk of death, admission to an intensive care unit (ICU) and invasive mechanical ventilation (IMV). Results: Data were available for 689 572 patients with laboratory-confirmed (91.1%) or clinically diagnosed (8.9%) SARS-CoV-2 infection from 52 countries. Age [adjusted hazard ratio per 10 years 1.49 (95% CI 1.48, 1.49)] and male sex [1.23 (1.21, 1.24)] were associated with a higher risk of death. Rates of admission to an ICU and use of IMV increased with age up to age 60 years then dropped. Symptoms, co-morbidities and treatments varied by age and had varied associations with clinical outcomes. The case-fatality ratio varied by country partly due to differences in the clinical characteristics of recruited patients and was on average 21.5%. Conclusions: Age was the strongest determinant of risk of death, with a ~30-fold difference between the oldest and youngest groups; each of the co-morbidities included was associated with up to an almost 2-fold increase in risk. Smoking and obesity were also associated with a higher risk of death. The size of our international database and the standardized data collection method make this study a comprehensive international description of COVID-19 clinical features. Our findings may inform strategies that involve prioritization of patients hospitalized with COVID-19 who have a higher risk of death

Long-term (180-Day) outcomes in critically Ill patients with COVID-19 in the REMAP-CAP randomized clinical trial

Importance The longer-term effects of therapies for the treatment of critically ill patients with COVID-19 are unknown. Objective To determine the effect of multiple interventions for critically ill adults with COVID-19 on longer-term outcomes. Design, Setting, and Participants Prespecified secondary analysis of an ongoing adaptive platform trial (REMAP-CAP) testing interventions within multiple therapeutic domains in which 4869 critically ill adult patients with COVID-19 were enrolled between March 9, 2020, and June 22, 2021, from 197 sites in 14 countries. The final 180-day follow-up was completed on March 2, 2022. Interventions Patients were randomized to receive 1 or more interventions within 6 treatment domains: immune modulators (n = 2274), convalescent plasma (n = 2011), antiplatelet therapy (n = 1557), anticoagulation (n = 1033), antivirals (n = 726), and corticosteroids (n = 401). Main Outcomes and Measures The main outcome was survival through day 180, analyzed using a bayesian piecewise exponential model. A hazard ratio (HR) less than 1 represented improved survival (superiority), while an HR greater than 1 represented worsened survival (harm); futility was represented by a relative improvement less than 20% in outcome, shown by an HR greater than 0.83. Results Among 4869 randomized patients (mean age, 59.3 years; 1537 [32.1%] women), 4107 (84.3%) had known vital status and 2590 (63.1%) were alive at day 180. IL-6 receptor antagonists had a greater than 99.9% probability of improving 6-month survival (adjusted HR, 0.74 [95% credible interval {CrI}, 0.61-0.90]) and antiplatelet agents had a 95% probability of improving 6-month survival (adjusted HR, 0.85 [95% CrI, 0.71-1.03]) compared with the control, while the probability of trial-defined statistical futility (HR >0.83) was high for therapeutic anticoagulation (99.9%; HR, 1.13 [95% CrI, 0.93-1.42]), convalescent plasma (99.2%; HR, 0.99 [95% CrI, 0.86-1.14]), and lopinavir-ritonavir (96.6%; HR, 1.06 [95% CrI, 0.82-1.38]) and the probabilities of harm from hydroxychloroquine (96.9%; HR, 1.51 [95% CrI, 0.98-2.29]) and the combination of lopinavir-ritonavir and hydroxychloroquine (96.8%; HR, 1.61 [95% CrI, 0.97-2.67]) were high. The corticosteroid domain was stopped early prior to reaching a predefined statistical trigger; there was a 57.1% to 61.6% probability of improving 6-month survival across varying hydrocortisone dosing strategies. Conclusions and Relevance Among critically ill patients with COVID-19 randomized to receive 1 or more therapeutic interventions, treatment with an IL-6 receptor antagonist had a greater than 99.9% probability of improved 180-day mortality compared with patients randomized to the control, and treatment with an antiplatelet had a 95.0% probability of improved 180-day mortality compared with patients randomized to the control. Overall, when considered with previously reported short-term results, the findings indicate that initial in-hospital treatment effects were consistent for most therapies through 6 months

Respiratory support in patients with severe COVID-19 in the International Severe Acute Respiratory and Emerging Infection (ISARIC) COVID-19 study: a prospective, multinational, observational study

Background: Up to 30% of hospitalised patients with COVID-19 require advanced respiratory support, including high-flow nasal cannulas (HFNC), non-invasive mechanical ventilation (NIV), or invasive mechanical ventilation (IMV). We aimed to describe the clinical characteristics, outcomes and risk factors for failing non-invasive respiratory support in patients treated with severe COVID-19 during the first two years of the pandemic in high-income countries (HICs) and low middle-income countries (LMICs). Methods: This is a multinational, multicentre, prospective cohort study embedded in the ISARIC-WHO COVID-19 Clinical Characterisation Protocol. Patients with laboratory-confirmed SARS-CoV-2 infection who required hospital admission were recruited prospectively. Patients treated with HFNC, NIV, or IMV within the first 24 h of hospital admission were included in this study. Descriptive statistics, random forest, and logistic regression analyses were used to describe clinical characteristics and compare clinical outcomes among patients treated with the different types of advanced respiratory support. Results: A total of 66,565 patients were included in this study. Overall, 82.6% of patients were treated in HIC, and 40.6% were admitted to the hospital during the first pandemic wave. During the first 24 h after hospital admission, patients in HICs were more frequently treated with HFNC (48.0%), followed by NIV (38.6%) and IMV (13.4%). In contrast, patients admitted in lower- and middle-income countries (LMICs) were less frequently treated with HFNC (16.1%) and the majority received IMV (59.1%). The failure rate of non-invasive respiratory support (i.e. HFNC or NIV) was 15.5%, of which 71.2% were from HIC and 28.8% from LMIC. The variables most strongly associated with non-invasive ventilation failure, defined as progression to IMV, were high leukocyte counts at hospital admission (OR [95%CI]; 5.86 [4.83–7.10]), treatment in an LMIC (OR [95%CI]; 2.04 [1.97–2.11]), and tachypnoea at hospital admission (OR [95%CI]; 1.16 [1.14–1.18]). Patients who failed HFNC/NIV had a higher 28-day fatality ratio (OR [95%CI]; 1.27 [1.25–1.30]). Conclusions: In the present international cohort, the most frequently used advanced respiratory support was the HFNC. However, IMV was used more often in LMIC. Higher leucocyte count, tachypnoea, and treatment in LMIC were risk factors for HFNC/NIV failure. HFNC/NIV failure was related to worse clinical outcomes, such as 28-day mortality. Trial registration This is a prospective observational study; therefore, no health care interventions were applied to participants, and trial registration is not applicable

The value of open-source clinical science in pandemic response: lessons from ISARIC

International audienc