Model Predictive Control with Performance-Driven Parameter Tuning using Bayesian Optimisation for Type-1 Diabetes

Abstract

Over the years, the conventional open-loop basal-bolus regiment has proven to be inadequate for long-term glucose management of Type-1 diabetes mellitus (T1DM) patients. The ’artificial pancreas (AP)’, which is characterized by a closed-loop control system that typically relies solely on subcutaneous glucose measurements as a feedback to deliver insulin corrections, is widely regarded as a viable alternative to the former approach. An earlier literature survey showed that model predictive control (MPC) and proportional-integral-derivative (PID) control are the two most commonly employed approaches in APs to treat T1DM, especially the former in recent years, due to its ability to incorporate flexible safety-critical constraints and account for inherent system delays. With most state-of-the art MPC controllers designed to exert direct control on insulin corrections over the patient however, the extent to which closed-loop performance can be maximised greatly depends on how accurately the plant is modelled. In addition to the immense difficulty in identifying certain physical parameters and non-linearities that describe an individual patient’s insulin-glucose pharmacokinetics, practical challenges arising from the collection of open-loop data from the patient hinder the identification process of a prediction model. The resulting model-plant mismatch is detrimental to the closed-loop performance, especially during postprandial periods when hypoglycaemic episodes are most likely to occur. As a countermeasure for the model-plant mismatch, insulin delivery rates are often tightly enforced, which may increase robustness of the MPC controller but comes at a price of reduced, sub-optimal performance due to worse-case conservative assumptions.

This thesis presents a dual-layer control scheme: a lower layer comprising of a control architecture that regulates the rate of insulin delivery for corrections against disturbances, and an upper layer that represents a performance-driven tuning framework using Bayesian Optimisation (BO). The proposed control architecture is hierarchical, consisting of an inner-loop PID controller, and an MPC which serves as the outer-loop controller that governs the reference input signal to the inner-loop control system. The upper layer tuning framework is implemented in two stages, the first on a set of clinical-related parameters, and the second a controller and model parameter, as part of the individualized control objective. In both stages, the BO framework optimises the parameters via a daily query of one parameter set and its corresponding performance value, which is computed based on experimental data. The proposed control scheme is designed and evaluated using a cohort of 10 adult virtual patients of the U.S. Food & Drug Administration (FDA)-accepted University of Virginia/Padova simulator through several in silico scenarios. Numerical evaluation and results show that the proposed hierarchical controller outperforms its baseline counterpart, and that glycaemic performance of all the tested subjects improved using the proposed tuning approach compared to under nominal settings. Notwithstanding the absence of a probabilistic safety-critical constraint in the BO problem, the employment of a barrier-like penalty in the objective function, subjected to a deterministic domain-based constraint that is augmented using a rule-based approach, demonstrated to be an efficient safeguard against hypoglycaemia during the parameter tuning process.