Observer based nonlinear control design for glucose regulation in type 1 diabetic patients: An LMI approach

This paper deals with the design of observer-based nonlinear control of blood glucose concentration (BGC) of Type 1 diabetes mellitus (T1DM) patients in a Linear Matrix Inequality (LMI) framework. The controller design relies on the information of the states obtained from a nonlinear observer. The control law is derived using feedback linearisation and regional pole placement technique. Further, a numerical optimisation method is proposed for the computation of the controller gains by capturing the relationship between transformed domain and original domain dynamics by iteratively tuning the circular LMI region parameters ('q' and 'r') such that the locations of closed-loop poles of the original nonlinear system are attained. The proposed controller can deliver robust closed-loop response of BGC within a specified range of parametric uncertainty and meal disturbances owing to the appropriately tuned bound of LMI region parameters. The performance of the proposed controller is tested for 100 virtual T1DM patients in the presence of parametric uncertainty and uncertain meal disturbance. Both severe hypoglycemia (<50 mg/dl) and post-prandial hyperglycemia are avoided by the proposed scheme for nominal and uncertain parameters.