Optimal Periodic Impulsive Strategies in Glycemic Control

Type-1 (insulin-dependent) diabetes is a chronic disease characterized by persistent excessive concentration of glucose in blood due to lack or insufficient secretion of the insulin hormone, which needs to be administered exogenously, possibly with automatic control techniques. In this work, we present a novel approach to glucose regulation for patients with type-1 diabetes, based on optimal impulsive control strategies, in the framework of the so-called multiple daily injections (MDI). In more detail, the optimal (periodic) glucose trajectory is first computed offline in ideal conditions and is then optimally tracked in real-time, with reduced computational effort, based on sparse measurements, so that possible nonidealities can be properly accounted for. The theoretical framework is able to preserve the nonlinear and continuous-time nature of the glucose–insulin model while realistically managing quantization in the actuation and assuming sporadic output measurements, from which the state of the system is estimated online. A preclinical in silico validation campaign based on a different, extended model of the glucose–insulin system shows the effectiveness of the proposed approach.