Sampled-data glucose regulation with reach-and-stay specifications through time-varying contracts

The complexity of the glucose-insulin system makes the glucose control problem a hard task to accomplish. In this context, a decentralized approach can be of help, through the exploitation of contracts theory, which allows to formalize the fulfillment of safety/invariance specifications over a system in terms of set of assumptions and guarantees over the composing subsystems.We here take a compositional modelbased approach considering, as a first attempt, simplified scalar glucose and insulin subsystems. Assumptions and guarantees sets are piecewise-constant time-varying intervals, computed at sampling times, on the basis of the glucose measurements, so they are not completely known a priori. Updating the intervals may lead to temporary violation of the contracts, according to their classical definition, until the system reaches the new target set. By exploiting the property of monotonicity of the involved subsystems, we define a minimum-time reachability problem, which is solved in closed form to minimize the worst-case contract time violation, and such that the insulin subsystem is steered to a controlled invariant set (reachand- stay specification). Simulations performed in a non-ideal scenario confirm the potential of the proposed approach.