Search for: All records

n this paper, we focus on the problem of shrinking-horizon Model Predictive Control (MPC) in uncertain dynamic environments. We consider controlling a deterministic autonomous system that interacts with uncontrollable stochastic agents during its mission. Employing tools from conformal prediction, existing works derive high-confidence prediction regions for the unknown agent trajectories, and integrate these regions in the design of suitable safety constraints for MPC. Despite guaranteeing probabilistic safety of the closed-loop trajectories, these constraints do not ensure feasibility of the respective MPC schemes for the entire duration of the mission. We propose a shrinking-horizon MPC that guarantees recursive feasibility via a gradual relaxation of the safety constraints as new prediction regions become available online. This relaxation enforces the safety constraints to hold over the least restrictive prediction region from the set of all available prediction regions. In a comparative case study with the state of the art, we empirically show that our approach results in tighter prediction regions and verify recursive feasibility of our MPC scheme. 

Abstract PurposeThis study aims to characterize the dependence of measured retinal arterial and venous saturation on vessel diameter and central reflex in retinal oximetry, with an ultimate goal of identifying potential causes and suggesting approaches to improve measurement accuracy. MethodsIn 10 subjects, oxygen saturation, vessel diameter and optical density are obtained using Oxymap Analyzer software without diameter correction. Diameter dependence of saturation is characterized using linear regression between measured values of saturation and diameter. Occurrences of negative values of vessel optical densities (ODs) associated with central vessel reflex are acquired from Oxymap Analyzer. A conceptual model is used to calculate the ratio of optical densities (ODRs) according to retinal reflectance properties and single and double‐pass light transmission across fixed path lengths. Model‐predicted values are compared with measured oximetry values at different vessel diameters. ResultsVenous saturation shows an inverse relationship with vessel diameter (D) across subjects, with a mean slope of −0.180 (SE = 0.022) %/μm (20 < D < 180 μm) and a more rapid saturation increase at small vessel diameters reaching to over 80%. Arterial saturation yields smaller positive and negative slopes in individual subjects, with an average of −0.007 (SE = 0.021) %/μm (20 < D < 200 μm) across all subjects. Measurements where vessel brightness exceeds that of the retinal background result in negative values of optical density, causing an artifactual increase in saturation. Optimization of model reflectance values produces a good fit of the conceptual model to measured ODRs. ConclusionMeasurement artefacts in retinal oximetry are caused by strong central vessel reflections, and apparent diameter sensitivity may result from single and double‐pass transmission in vessels. Improvement in correction for vessel diameter is indicated for arteries however further study is necessary for venous corrections.