||Nonlinear Model Predictive Control for an Artificial Pancreas
||Boiroux, Dimitri (Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Jørgensen, John Bagterp (Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
||This thesis deals with nonlinear model control for an artificial pancreas. It
presents two numerical methods to solve discrete-time Bolza problems, namely
the single shooting and the multiple shooting.
First of all, this thesis presents a numerical method to solve a general optimization
problem using a local SQP optimization algorithm with a damped BFGS
update of the Hessian matrix. It also introduces a primal-dual point algorithm
and a linesearch algorithm that are used in the local SQP algorithm. Then, it
shows how to use an explicit Runge-Kutta method to solve the differential equations
involved in the single and multiple shooting methods. The single shooting
is implemented for a linear test problem in which we can compute the optimal
solution in order to validate the method.
This thesis also shows the Powell's modified BFGS update for the multiple
shooting, which produces a sparse and block diagonal Hessian matrix. This
structure is used to simplify the primal-dual interior point algorithm by using
an iterative method, and a comparison between single and multiple shooting for
a test problem.
Finally, the Hovorka model is simulated. After having been linearized around a
steady state and simulated using a linear MPC algorithm, the multiple shooting
has been used in order to find the optimal insulin administration in the Hovorka
model for some 24-hours simulations.
||Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark
Creation date: 2009-08-19
Update date: 2009-11-04