Search

This paper studies the distributed convex optimization of bipartite containment control problem for a class of higher order nonlinear multi-agent systems with uncertain states. For the optimization problem, the penalty function is constructed by summing the local objective function of each agent and combining the penalty term formed by the adjacency matrix. For the unknown nonlinear function and unpredictable states in the system, this paper construct radial basis function Neural-networks and state observer for approaching, respectively. In order to avoid “explosion of complexity,” under the framework of Lyapunov function theory, we propose the dynamic surface control (DSC) technology and design the distributed adaptive backstepping neural network controller to ensure all the signals remain semi-global uniformly ultimately bounded in the closed-loop system and all agents can converge to the convex hull containing each boundary trajectory as well as its opposite trajectory different in sign. Simulation results confirm the feasibility of the proposed control method.

Background: Recent studies have indicated that heart failure (HF) with preserved ejection fraction (HFpEF) within different left ventricular ejection fraction (LVEF) ranges presents distinct morphological and pathophysiological characteristics, potentially leading to diverse prognoses. Methods: We included chronic HF patients hospitalized in the Department of Cardiology at Hebei General Hospital from January 2018 to June 2021. Patients were categorized into four groups based on LVEF: HF with reduced ejection fraction (HFrEF, LVEF ≤40%), HF with mildly reduced ejection fraction (HFmrEF, 41% ≤ LVEF ≤ 49%), low LVEF-HFpEF (50% ≤ LVEF ≤ 60%), and high LVEF-HFpEF (LVEF >60%). Kaplan‒Meier curves were plotted to observe the occurrence rate of endpoint events (all-cause mortality and cardiovascular mortality) within a 2-year period. Cox proportional hazards regression models were employed to predict the risk factors for endpoint events. Sensitivity analyses were conducted using propensity score matching (PSM), and Fine-Gray tests were used to evaluate competitive risk. Results: A total of 483 chronic HF patients were ultimately included. Kaplan‒Meier curves indicated a lower risk of endpoint events in the high LVEF-HFpEF group than in the low LVEF-HFpEF group. After PSM, there were still statistically significant differences in endpoint events between the two groups (all-cause mortality p = 0.048, cardiovascular mortality p = 0.027). Body mass index (BMI), coronary artery disease, cerebrovascular disease, hyperlipidemia, hypoalbuminemia, and diuretic use were identified as independent risk factors for all-cause mortality in the low LVEF-HFpEF group (p < 0.05). Hyperlipidemia, the estimated glomerular filtration rate (eGFR), and β-blocker use were independent risk factors for cardiovascular mortality (p < 0.05). In the high LVEF-HFpEF group, multivariate Cox regression analysis revealed that age, smoking history, hypoalbuminemia, and the eGFR were independent risk factors for all-cause mortality, while age, heart rate, blood potassium level, and the eGFR were independent risk factors for cardiovascular mortality (p < 0.05). After controlling for competitive risk, cardiovascular mortality risk remained higher in the low LVEF-HFpEF group than in the high LVEF-HFpEF group (Fine-Gray p < 0.01). Conclusions: Low LVEF-HFpEF and high LVEF-HFpEF represent two distinct phenotypes of HFpEF. Patients with high LVEF-HFpEF have lower risks of both all-cause mortality and cardiovascular mortality than those with low LVEF-HFpEF. The therapeutic reduction in blood volume may not be the best treatment option for patients with high LVEF-HFpEF.