Hypertension is a potentially unsafe health ailment, which can be indicated directly from the blood pressure (BP). Hypertension always leads to other health complications. Continuous monitoring of BP is very important; however, cuff-based BP measurements are discrete and uncomfortable to the user. To address this need, a cuff-less, continuous, and noninvasive BP measurement system is proposed using the photoplethysmograph (PPG) signal and demographic features using machine learning (ML) algorithms. PPG signals were acquired from 219 subjects, which undergo preprocessing and feature extraction steps. Time, frequency, and time-frequency domain features were extracted from the PPG and their derivative signals. Feature selection techniques were used to reduce the computational complexity and to decrease the chance of over-fitting the ML algorithms. The features were then used to train and evaluate ML algorithms. The best regression models were selected for systolic BP (SBP) and diastolic BP (DBP) estimation individually. Gaussian process regression (GPR) along with the ReliefF feature selection algorithm outperforms other algorithms in estimating SBP and DBP with a root mean square error (RMSE) of 6.74 and 3.59, respectively. This ML model can be implemented in hardware systems to continuously monitor BP and avoid any critical health conditions due to sudden changes.

Respiratory ailments such as asthma, chronic obstructive pulmonary disease (COPD), pneumonia, and lung cancer are life-threatening. Respiration rate (RR) is a vital indicator of the wellness of a patient. Continuous monitoring of RR can provide early indication and thereby save lives. However, a real-time continuous RR monitoring facility is only available at the intensive care unit (ICU) due to the size and cost of the equipment. Recent researches have proposed Photoplethysmogram (PPG) and/ Electrocardiogram (ECG) signals for RR estimation however, the usage of ECG is limited due to the unavailability of it in wearable devices. Due to the advent of wearable smartwatches with built-in PPG sensors, it is now being considered for continuous monitoring of RR. This paper describes a novel approach for RR estimation using motion artifact correction and machine learning (ML) models with the PPG signal features. Feature selection algorithms were used to reduce computational complexity and the chance of overfitting. The best ML model and the best feature selection algorithm combination was fine-tuned to optimize its performance using hyperparameter optimization. Gaussian Process Regression (GPR) with Fit a Gaussian process regression model (Fitrgp) feature selection algorithm outperformed all other combinations and exhibits a root mean squared error (RMSE), mean absolute error (MAE), and two-standard deviation (2SD) of 2.63, 1.97, and 5.25 breaths per minute, respectively. Patients would be able to track RR at a lower cost and with less inconvenience if RR can be extracted efficiently and reliably from the PPG signal.

Stabilizing a flow around an unstable equilibrium is a typical problem in flow control. Model-based designed of modern controllers like LQR/LQG or H∞ compensators is often limited by the large-scale of the discretized flow models. Therefore, model reduction is usually needed before designing such a controller. Here we suggest an approach based on applying balanced truncation for unstable systems to the linearized flow equations usually used for compensator design. For this purpose, we modify the ADI iteration for Lyapunov equations to deal with the index-2 structure of the underlying descriptor system efficiently in an implicit way. The resulting algorithm is tested for model reduction and control design of a linearized Navier-Stokes system describing von Kármán vortex shedding.2010 Mathematics Subject Classification. Primary: 93B40, 93B11; Secondary: 65F30, 65F50. Key words and phrases. balanced truncation, unstable system, differential algebraic system, differential index-2, linearized flow model. 1 2 P. BENNER, J. SAAK AND M. M. UDDIN

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