A flatness-based control approach to drug infusion for cardiac function regulation

Abstract

A new control method based on differential flatness theory is developed in this study, aiming at solving the problem of regulation of haemodynamic parameters. Actually control of the cardiac output (volume of blood pumped out by heart per unit of time) and of the arterial blood pressure is achieved through the administered infusion of cardiovascular drugs such as dopamine and sodium nitroprusside. Time delays between the control inputs and the system's outputs are taken into account. Using the principle of dynamic extension, which means that by considering certain control inputs and their derivatives as additional state variables, a state-space description for the heart's function is obtained. It is proven that the dynamic model of the heart is a differentially flat one. This enables its transformation into a linear canonical and decoupled form, for which the design of a stabilising feedback controller becomes possible. The proposed feedback controller is of proven stability and assures fast and accurate tracking of the reference setpoints by the outputs of the heart's dynamic model. Moreover, by using a Kalman filter-based disturbances' estimator, it becomes possible to estimate in real-time and compensate for the model uncertainty and external perturbation inputs that affect the heart's model.