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.