Inverse Optimal Trajectory Tracking for Discrete Time Nonlinear Positive Systems

In this paper, discrete time inverse optimal trajectory tracking for a class of non-linear positive systems is proposed. The scheme is developed for MIMO (multi-input, multi-output) affine systems. This approach is adapted for glycemic control of type 1 diabetes mellitus (T1DM) patients. The control law calculates the insulin delivery rate in order to prevent hyperglycemia levels. A neural model is obtained from an on-line neural identifier, which uses a recurrent neural network, trained with the extended Kalman filter (EKF); this neural model has an affine form, which permits the applicability of inverse optimal control scheme. The proposed algorithm is tuned to follow a desired trajectory; this trajectory reproduces the glucose absorption of a healthy person. Simulation results illustrate the aplicability of the control law in biological processes.