G. De Nicolao

Diabetes: Models, Signals, and Control

The control of diabetes is an interdisciplinary endeavor, which includes a significant biomedical engineering component, with traditions of success beginning in the early 1960s. It began with modeling of the insulin-glucose system, and progressed to large-scale in silico experiments, and automated closed-loop control (artificial pancreas). Here, we follow these engineering efforts through the last, almost 50 years. We begin with the now classic minimal modeling approach and discuss a number of subsequent models, which have recently resulted in the first in silico simulation model accepted as substitute to animal trials in the quest for optimal diabetes control. We then review metabolic monitoring, with a particular emphasis on the new continuous glucose sensors, on the analyses of their time-series signals, and on the opportunities that they present for automation of diabetes control. Finally, we review control strategies that have been successfully employed in vivo or in silico, presenting a promise for the development of a future artificial pancreas and, in particular, discuss a modular architecture for building closed-loop control systems, including insulin delivery and patient safety supervision layers. We conclude with a brief discussion of the unique interactions between human physiology, behavioral events, engineering modeling and control relevant to diabetes.

A stabilizing model-based predictive control algorithm for nonlinear systems

Using distinct prediction and control horizons, nonlinear model-based predictive control can guarantee: (i) computational efficiency, (ii) enlargement of the stability domain and (iii) local optimality.

Stabilizing receding-horizon control of nonlinear time-varying systems

A receding horizon control scheme for nonlinear time-varying systems is proposed which is based on a finite-horizon optimization problem with a terminal state penalty. The penalty is equal to the cost that would be incurred over an infinite horizon by applying a (locally stabilizing) linear control law to the nonlinear system. Assuming only stabilizability of the linearized system around the desired equilibrium, the new scheme ensures exponential stability of the equilibrium. As the length of the optimization horizon goes from zero to infinity, the domain of attraction moves from the basin of attraction of the linear controller toward the basin of attraction of the infinite-horizon nonlinear controller. Stability robustness in the face of system perturbations is also established.

The difference periodic Ricati equation for the periodic prediction problem

Gives a comprehensive treatment of several important aspects of the discrete-time periodic Riccati equation (DPRE) arising from the prediction problem for linear discrete-time periodic systems. The authors analyze the symmetric periodic positive semidefinite (SPPS) solution of the DPRE under appropriate assumptions of stabilizability and detectability of the periodic system. Among the results obtained are necessary and sufficient conditions for the existence and uniqueness of the SPPS solution and the stability of the resulting closed-loop system. Some of these results can be seen as extensions of the corresponding results for the time-invariant case; however, a number of them contain contributions to the time-invariant case as well. The paper also gives a numerical algorithm based on an iterative linearization procedure for computing the SPPS solution. The algorithm is a periodic version of Kleinmans algorithm for the time-invariant case. >

Model predictive control of glucose concentration in type I diabetic patients: An in silico trial

Abstract In this paper, the feedback control of glucose concentration in type I diabetic patients using subcutaneous insulin delivery and subcutaneous continuous glucose monitoring is considered. A recently developed in silico model of glucose metabolism is employed to generate virtual patients on which control algorithms can be validated against interindividual variability. An in silico trial consisting of 100 patients is used to assess the performances of a linear output feedback and a nonlinear state-feedback model predictive controller, designed on the basis of the in silico model. More than satisfactory results are obtained in the great majority of virtual patients. The experiments highlight the crucial role of the anticipative feedforward action driven by the meal announcement information. Preliminary results indicate that further improvements may be achieved by means of a nonlinear model predictive control scheme.

Stability and Robustness of Nonlinear Receding Horizon Control

The main design strategies for ensuring stability and robustness of nonlinear RH (Receding-Horizon) control systems are critically surveyed. In particular, the following algorithms with guaranteed closed-loop stability of the equilibrium are considered: the zero-state terminal constraint, the dual-mode RH controller, the infinite-horizon closed-loop costing, the quasi-infinite method, and the contractive constraint. For each algorithm, we analyse and compare feasibility, performance, and implementation issues. For what concerns robustness analysis and design, we consider: monotonicity-based robustness, inverse optimality robustness margins, nonlinear H ∞ RH design, and a new nonlinear RH design with local H ∞ recovery.

Modular Closed-Loop Control of Diabetes

Modularity plays a key role in many engineering systems, allowing for plug-and-play integration of components, enhancing flexibility and adaptability, and facilitating standardization. In the control of diabetes, i.e., the so-called “artificial pancreas,” modularity allows for the step-wise introduction of (and regulatory approval for) algorithmic components, starting with subsystems for assured patient safety and followed by higher layer components that serve to modify the patients basal rate in real time. In this paper, we introduce a three-layer modular architecture for the control of diabetes, consisting in a sensor/pump interface module (IM), a continuous safety module (CSM), and a real-time control module (RTCM), which separates the functions of insulin recommendation (postmeal insulin for mitigating hyperglycemia) and safety (prevention of hypoglycemia). In addition, we provide details of instances of all three layers of the architecture: the APS© serving as the IM, the safety supervision module (SSM) serving as the CSM, and the range correction module (RCM) serving as the RTCM. We evaluate the performance of the integrated system via in silico preclinical trials, demonstrating 1) the ability of the SSM to reduce the incidence of hypoglycemia under nonideal operating conditions and 2) the ability of the RCM to reduce glycemic variability.

Brief Output feedback and tracking of nonlinear systems with model predictive control

This paper presents an output feedback Receding Horizon (RH) control algorithm for nonlinear discrete-time systems which solves the problem of tracking exogenous signals and asymptotically rejecting disturbances generated by a properly defined exosystem. The regulator is composed by an internal model of the exosystem and a stabilizing RH regulator. Some robustness results are also achieved in the case of constant references.

On the robustness of receding-horizon control with terminal constraints

Robustness properties of nonlinear receding-horizon controllers with zero terminal state constraints are investigated with respect to gain and additive perturbations. Some robustness margins are derived by extending to the receding-horizon case the analysis originally proposed by Geromel and da Cruz for infinite-horizon controllers. In the linear case, it is shown that the zero terminal state receding-horizon controller exhibits worse robustness margins compared to standard infinite-horizon LQ control.

MPC based Artificial Pancreas: Strategies for individualization and meal compensation

This paper addresses the design of glucose regulators based on Model Predictive Control (MPC) to be used as part of Artificial Pancreas devices for type 1 diabetic patients. Two key issues are deeply investigated: individualization, needed to cope with intersubject variability, and meal compensation, interpreted as a disturbance rejection problem. The individualization is achieved either by tuning the cost function, based on few well known clinical parameters (MPC1) or through the use of an individual model obtained via system identification techniques and an optimal tuning of the cost function based on real-life experiments (MPC2). The in silico tests, performed on 4 different scenarios using a simulator equipped with 100 patients, show that the performances of MPC1 are very promising, supporting its current use in an in vivo multicenter trial on 47 patients that is being carried out within the European Research Project AP@home. At the same time, further improvements are achieved by MPC2, showing that there is scope for in vivo experimentation of control strategies employing individually estimated patient models.