Nonlinear Optimal Control of Oxygen and Carbon Dioxide Levels in Blood

Abstract

Nonlinear H-infinity control is proposed for the regulation of the levels of oxygen and carbon dioxide in the blood of patients undergoing heart surgery and extracorporeal blood circulation. The levels of blood gases are administered through a membrane oxygenator and the control inputs are the externally supplied oxygen and the aggregate gas supply (oxygen plus nitrogen). The proposed control method is based on linearization of the oxygenator’s dynamical model through Taylor series expansion and the computation of Jacobian matrices. The local linearization points are defined by the present value of the oxygenator’s state vector and the last value of the control input that was exerted on this system. The modelling errors due to linearization are considered as disturbances which are compensated by the robustness of the control loop. Next, for the linearized model of the oxygenator an H-infinity control input is computed at each iteration of the control algorithm through the solution of an algebraic Riccati equation. With the use of Lyapunov stability analysis it is demonstrated that the control scheme satisfies the H-infinity tracking performance criterion, which signifies improved robustness against modelling uncertainty and external disturbances. Moreover, under moderate conditions the asymptotic stability of the control loop is also proven. To estimate non-measurable state vector elements of the oxygenator the H-infinity Kalman Filter is proposed and thus state estimation-based control is also applied. The efficient performance of the control scheme is confirmed through simulation experiments.