Experimental blood glucose interval identification of patients with type 1 diabetes

Many problems are confronted when characterizing a type 1 diabetic patient such as model mismatches, noisy inputs, measurement errors and huge variability in the glucose profiles. In this work we introduce a new identification method based on interval analysis where variability and model imprecisions are represented by an interval model as parametric uncertainty.The minimization of a composite cost index comprising: (1) the glucose envelope width predicted by the interval model, and (2) a Hausdorff-distance-based prediction error with respect to the envelope, is proposed. The method is evaluated with clinical data consisting in insulin and blood glucose reference measurements from 12 patients for four different lunchtime postprandial periods each.Following a “leave-one-day-out” cross-validation study, model prediction capabilities for validation days were encouraging (medians of: relative error = 5.45%, samples predicted = 57%, prediction width = 79.1 mg/dL). The consideration of the days with maximum patient variability represented as identification days, resulted in improved prediction capabilities for the identified model (medians of: relative error = 0.03%, samples predicted = 96.8%, prediction width = 101.3 mg/dL). Feasibility of interval models identification in the context of type 1 diabetes was demonstrated.     

Comparison of interval and Monte Carlo simulation for the prediction of postprandial glucose under uncertainty in type 1 diabetes mellitus

In this paper, the problem of tackling uncertainty in the prediction of postprandial blood glucose is analyzed. Two simulation approaches, Monte Carlo and interval models, are studied and compared. Interval simulation is carried out using modal interval analysis. Simulation of a glucoregulatory model with uncertainty in insulin sensitivities, glucose absorption and food intake is carried out using both methods. Interval simulation is superior in predicting all severe and mild hyper- and hypoglycemia episodes. Furthermore, much less computational time is required for interval simulation than for Monte Carlo simulation.     

Development of a multi-parametric model predictive control algorithm for insulin delivery in type 1 diabetes mellitus using clinical parameters

A multi-parametric model predictive control (mpMPC) algorithm for subcutaneous insulin delivery for individuals with type 1 diabetes mellitus (T1DM) that is computationally efficient, robust to variations in insulin sensitivity, and involves minimal burden for the user is proposed. System identification was achieved through impulse response tests feasible for ambulatory conditions on the UVa/Padova simulator adult subjects with T1DM. An alternative means of system identification using readily available clinical parameters was also investigated. A safety constraint was included explicitly in the algorithm formulation using clinical parameters typical of those available to an attending physician. Closed-loop simulations were carried out with daily consumption of 200 g carbohydrate. Controller robustness was assessed by subject/model mismatch scenarios addressing daily, simultaneous variation in insulin sensitivity and meal size with the addition of Gaussian white noise with a standard deviation of 10%. A second-order-plus-time-delay transfer function model fit the validation data with a mean (coefficient of variation) root-mean-square-error (RMSE) of 26 mg/dL (19%) for a 3 h prediction horizon. The resulting control law maintained a low risk Low Blood Glucose Index without any information about carbohydrate consumption for 90% of the subjects. Low-order linear models with clinically meaningful parameters thus provided sufficient information for a model predictive control algorithm to control glycemia. The use of clinical knowledge as a safety constraint can reduce hypoglycemic events, and this same knowledge can further improve glycemic control when used explicitly as the controller model. The resulting mpMPC algorithm was sufficiently compact to be implemented on a simple electronic device.     

Continuous-time system identification of the steering dynamics of a ship on a river

In this study, we consider the parameter estimation problem of a ship dynamics model. We consider two possible approaches to identify a continuous-time model from real data obtained on a river, where the presence of disturbances is a key issue. The first approach is identification through optimisation using a disturbance observer. The second approach corresponds to the refined instrumental variable method for linear parameter varying systems. In addition, we evaluate the accuracy of the parameter estimation through a sensitivity analysis. The obtained results show an improvement in the parameter estimates compared to identification procedures that do not consider the river disturbances. The application of the model for track-keeping control is also illustrated.     

Positive sliding mode control for blood glucose regulation

Biological systems involving positive variables as concentrations are some examples of so-called positive systems. This is the case of the glycemia–insulinemia system considered in this paper. To cope with these physical constraints, it is shown that a positive sliding mode control (SMC) can be designed for glycemia regulation. The largest positive invariant set (PIS) is obtained for the insulinemia subsystem in open and closed loop. The existence of a positive SMC for glycemia regulation is shown here for the first time. Necessary conditions to design the sliding surface and the discontinuity gain are derived to guarantee a positive SMC for the insulin dynamics. SMC is designed to be positive everywhere in the largest closed-loop PIS of plasma insulin system. Two-stage SMC is employed; the last stage SMC2 block uses the glycemia error to design the desired insulin trajectory. Then the plasma insulin state is forced to track the reference via SMC1. The resulting desired insulin trajectory is the required virtual control input of the glycemia system to eliminate blood glucose (BG) error. The positive control is tested in silico on type-1 diabetic patients model derived from real-life clinical data.     

A learning automata-based blood glucose regulation mechanism in type 2 diabetes

This paper proposes a learning automata-based mechanism for blood glucose regulation in type 2 diabetics. The proposed mechanism takes into account the past history of the blood glucose level to determine the correct dosage of the insulin. This method uses the learning automata theory to predict the required dosage of insulin and records the patient history in parameters of a Gaussian probability distribution function. The parameters of the distribution function are updated based on the difference between the actual glucose level regulated by the learning automata and the normal range in such a way that the gap between the actual glucose level and the normal one is minimized. As the proposed algorithm proceeds, it can be seen that it converges to the optimal insulin dosage that keeps the glucose level in normal range for a long time. Convergence of the proposed algorithm to the optimal insulin dosage is theoretically proven. A clinical study is conducted to show the performance of the proposed insulin therapy system for regulation of the blood glucose level of type 2 diabetics.     

Data driven nonparametric identification and model based control of glucose-insulin process in type 1 diabetics

Closed loop control of glucose homeostasis via subcutaneous insulin infusion and continuous glucose monitoring system can give better living to a type 1 diabetic patient. This paper deals with the real time implementation of internal model control (IMC) of subcutaneous insulin infusion. The model based control is applied on the nonparametric model of the patient identified in real time from input–output data. Meal simulation model of the glucose-insulin system of type 1 diabetic patient based on the work of Dalla Man et. al. is considered. This model is constructed in hardware platform that acts as the virtual patient. The data-driven nonparametric model of the virtual patient is identified in real time by computing Volterra kernels. The kernels are solved up to second order using recursive least squares (RLS) algorithm with short memory length of M = 2. The validation results of the identified model output and the actual output have shown good fit in both simulation and real time environments. The frequency domain kernels are used in internal model control to generate insulin dosage. The control algorithm is developed in simulation and implemented in real time with hardware in loop on dSPACE platform. The closed loop system yields good meal disturbance rejection, less undershoots, settling time and more profoundly smaller requirement of insulin infusion as compared to the earlier reported data.     

Selection of input variables for model identification of static nonlinear systems

System identification can be divided into structure and parameter identification. In most system-identification approaches the structure is presumed and only a parameter identification is performed to obtain the coefficients in the functional system. Yet, often there is little knowledge about the system structure. In such cases, the first step has to be the identification of the decisive input variables. In this paper a black-box input variable identification approach using feedforward neural networks is proposed.     

基于NT降阶的乘积型区间二型模糊控制器结构分析

目前区间二型模糊控制器的结构分析主要基于Zadeh的取小推理和KM降阶算法。KM算法是一循环迭代过程,没有解析解,无法进行控制器的稳定性分析,且取小推理需要进行输入空间的划分,过程较为繁琐。提出了一种简化的区间二型模糊控制器分析方法,该方法首先采用乘积推理,模糊规则的激发隶属度为输入变量隶属度的乘积,统一了控制器的表达式形式,避免了输入空间的划分过程,模糊控制器的结构分析更加简单。二型模糊集合采用NT降阶算法,该算法直接利用首隶属度函数的上、下限的平均值来进行解模糊化操作,避免了迭代计算,简化了降阶过程。控制器的表达式等效于一个增量式PI（位置式PD）控制器,其比例增益、积分增益以及补偿项均为非线性可调。而且还能得到控制器的闭环表达式,易于进行区间二型模糊控制器的稳定性分析与设计等。     

基于T-S模型的非线性系统模糊聚类辨识方法

提出一种基于T-S模型的非线性系统模糊聚类辨识方法,对T-S模糊模型的前提部分和结论部分进行分开辨识,既简化该模型的辨识步骤,又提高它的泛化能力,同时也解决了T-S模糊模型随辨识系统复杂程度提高而规则数增大的问题。对一个非线性系统辨识的仿真结果验证了这种模糊聚类辨识方法的有效性。     

Prediction of postprandial blood glucose under uncertainty and intra-patient variability in type 1 diabetes: A comparative study of three interval models

The behavior of three insulin action and glucose kinetics models was assessed for an insulin therapy regime in the presence of patient variability. For this purpose, postprandial glucose in patients with type 1 diabetes was predicted by considering intra- and inter-patient variability using modal interval analysis. Equations to achieve optimal prediction are presented for models 1, 2 and 3, which are of increasing complexity. The model parameters were adjusted to reflect the "same" patient in the presence of variability. The glucose response envelope for model 1, the simplest insulin-glucose model assessed, included the responses of the other two models when a good fit of the model parameters was achieved. Thus, under variability, simple glucose-insulin models may be sufficient to describe patient dynamics in most situations.     

Adaptive control strategy for regulation of blood glucose levels in patients with type 1 diabetes

Current insulin therapy for patients with type 1 diabetes often results in high variability in blood glucose concentrations and may cause hyperglycemic/hypoglycemic episodes. Closing the glucose control loop with a fully automated electro-mechanical pancreas will improve the quality of life for insulin-dependent patients. An adaptive control algorithm is proposed to keep glucose concentrations within normoglycemic range and dynamically respond to glycemic challenges. A model-based control strategy is used to calculate the required insulin infusion rate, while the model parameters are recursively tuned. The algorithm handles delays associated with insulin absorption, time-lag between subcutaneous and blood glucose concentrations, and variations in inter/intra-subject glucose–insulin dynamics. Simulation results for simultaneous meal and physiological disturbances are demonstrated for subcutaneous insulin infusion.     

Tracking and parameter identification for model reference adaptive control

We provide barrier Lyapunov functions for model reference adaptive control algorithms, allowing us to prove robustness in the input‐to‐state stability framework and to compute rates of exponential convergence of the tracking and parameter identification errors to zero. Our results ensure identification of all entries of the unknown weight and control effectiveness matrices. We provide easily checked sufficient conditions for our relaxed persistency of excitation conditions to hold. Our illustrative numerical example demonstrates the performance of the control methods.     

Third-order cumulants based methods for continuous-time errors-in-variables model identification

In this paper, the problem of identifying stochastic linear continuous-time systems from noisy input/output data is addressed. The input of the system is assumed to have a skewed probability density function, whereas the noises contaminating the data are assumed to be symmetrically distributed. The third-order cumulants of the input/output data are then (asymptotically) insensitive to the noises, that can be coloured and/or mutually correlated. Using this noise-cancellation property two computationally simple estimators are proposed. The usefulness of the proposed algorithms is assessed through a numerical simulation.     

区间多目标优化非支配排序云模型算法

针对区间多目标优化问题,利用云模型对NSGA-II算法进行改进,提出一种非支配排序云模型算法（NSCMA）。首先,从初始云团中随机选取一个云滴作为父代,通过正态云算子生成子代云滴,用来替代传统NSGA-II遗传操作中的交叉和变异;其次,用约束条件对生成的云滴进行筛选处理,避免不可行解进入下一步算法;最后,运用区间占优关系对满足约束条件的解进行占优排序,对无法比较的同序值解计算拥挤距离。仿真结果验证了所设计算法的有效性。     

机动目标运动模型动态辨识理论的研究

在对现有机动目标假定模型结构的合理性及现代战场对目标模型需求性综合分析的基础上，完成了机动目标运动模型的辨识理论研究，提出了机动目标运动模型可动态辨识的条件．为解决机动目标运动模型动态辨识提供了新的技术途径．所提出的“参数辨识模型”具有良好的模型结构，对目标的各种运动模态具有广泛的适应能力．