Asymmetrical Soft Constraints of the Controlled Variable to Improve the Management of Hypoglycemia in the MPC-Based Artificial Pancreas

An appropriate design of the model predictive control algorithm for the artificial pancreas to control glycemia in patients with type 1 diabetes should ideally take into account the asymmetrical nature of glycemia dynamics that consequently results in asymmetrical requirements on the control performance with respect to normoglycemia. This demand is primarily physiology involved since the state of hypoglycemia is much more dangerous and easier to reach by careless insulin administration than hyperglycemia. As the traditional formulation of model predictive control considers only symmetrical penalization of the control error, a more sophisticated strategy is required. One of the approaches is to apply hard constraints on the controlled variable. However, the issue with this is that the control may become infeasible if there are considered too tight constraints of the manipulated variable and the controlled variable at the same time. Therefore, in order to ensure the control feasibility while constraining the controlled variable, we proposed a soft constraints formulation introducing special slack variables and a quadratic penalty to the corresponding cost function. Independently weighted soft constraints of the controlled variable with asymmetric bounds are considered while anticipating the desired suppression of hypoglycemia during automated glycemia control. The proposed strategy was validated within a simulation experiment, and it turned out that the soft constraint formulation allowed avoiding hypoglycemia at the expense of mild hyperglycemia.