Arbitrarily low sensitivity (ALS) in linear distributed systems using pointwise linear feedback

The sensitivity problem is defined for feedback systems with plants described by linear partial differential operators having constant coefficients, in a bounded one-dimensional domain. there are also finitely many observation points and finitely many lumped feedback loops, and a finite number of disturbance inputs. The sensitivity problem is studied in detail for the heat equation, and comments are made about the linearized damped beam equation and the damped wave equation. It is shown that it is possible to reduce arbitrarily the sensitivity over any temporal frequency interval uniformly in the space domain (except for the undamped wave equation, where a limitation in the frequency interval is induced by the plant). This reduction may require a high-gain feedback around the points where the disturbances appear

Modeling and feedback control of a flexible arm of a robot for prescribed frequency-domain tolerances

In this article we solve the problem of achieving quantitative specifications for the tip of a rotating flexible beam with uncertainty in some of its physical and geometric parameters. The frequency-domain design method used here is also helpful in clarifying some limitations on the feedback loop capabilities due to the distributed nature of the problem. Finally, time domain simulations, while proving the validity of the design method suggested in this work, pointed to some interesting mathematical problems concerning the influence of some of the parameters on the plant dynamics with possible physical consequences on the design of flexible beams

Pancreatic surgery outcomes: multicentre prospective snapshot study in 67 countries

Background: Pancreatic surgery remains associated with high morbidity rates. Although postoperative mortality appears to have improved with specialization, the outcomes reported in the literature reflect the activity of highly specialized centres. The aim of this study was to evaluate the outcomes following pancreatic surgery worldwide.Methods: This was an international, prospective, multicentre, cross-sectional snapshot study of consecutive patients undergoing pancreatic operations worldwide in a 3-month interval in 2021. The primary outcome was postoperative mortality within 90 days of surgery. Multivariable logistic regression was used to explore relationships with Human Development Index (HDI) and other parameters.Results: A total of 4223 patients from 67 countries were analysed. A complication of any severity was detected in 68.7 percent of patients (2901 of 4223). Major complication rates (Clavien-Dindo grade at least IIIa) were 24, 18, and 27 percent, and mortality rates were 10, 5, and 5 per cent in low-to-middle-, high-, and very high-HDI countries respectively. The 90-day postoperative mortality rate was 5.4 per cent (229 of 4223) overall, but was significantly higher in the low-to-middle-HDI group (adjusted OR 2.88, 95 per cent c.i. 1.80 to 4.48). The overall failure-to-rescue rate was 21 percent; however, it was 41 per cent in low-to-middle-compared with 19 per cent in very high-HDI countries.Conclusion: Excess mortality in low-to-middle-HDI countries could be attributable to failure to rescue of patients from severe complications. The authors call for a collaborative response from international and regional associations of pancreatic surgeons to address management related to death from postoperative complications to tackle the global disparities in the outcomes of pancreatic surgery (NCT04652271; ISRCTN95140761)