Observer-based resilient finite-time control of blood gases model during extra-corporeal circulation

Abstract

This study aims at designing an observer-based resilient controller to regulate the amount of oxygen and carbon dioxide in the blood of patients during the extra-corporeal blood circulation process. More precisely, in this study, a suitable observer-based resilient controller is constructed to regulate the levels of patient blood gases in a finite interval of time. The finite-time boundedness with the prescribed $H_{\infty }$ performance index of the considered blood gases control system against modelling uncertainty and external disturbances is ensured by using Lyapunov stability analysis. Moreover, a set of sufficient conditions for obtaining the controller gain is developed in the form of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed robust finite-time control scheme is verified through simulation results. The result reveals that the blood gases are maintained in their physiological ranges during a stable extra-corporeal circulation process via the proposed observer-based resilient controller.

Keywords: CO2; H∞ performance index; LMIs; Lyapunov methods; Lyapunov stability analysis; O2; biomedical equipment; blood; blood gases control system; carbon compounds; carbon dioxide amount; controller gain; controllers; extracorporeal blood circulation process; finite time interval; finite-time boundedness; haemodynamics; linear matrix inequalities; medical control systems; observer-based resilient controller; observer-based resilient finite-time control; oxygen; oxygen amount; patient blood gas levels; physiological ranges.

Fig. 1

Responses of flow rate of oxygen ( $x_1(t)$) and its estimate ( ${\hat{x}}_1(t)$ )

Fig. 2

Responses of flow rate of carbon dioxide ( $x_2(t)$) and its estimate ( ${\hat{x}}_2(t)$ )

Fig. 3

Responses of arterial partial pressure of oxygen ( $x_3(t)$) and its estimate ( ${\hat{x}}_3(t)$ )

Fig. 4

Responses of arterial partial pressure of carbon dioxide ( $x_4(t)$) and its estimate ( ${\hat{x}}_4(t)$ )

Fig. 5

Disturbance

Fig. 6

Commanded flow rates

Fig. 7

Controlled output trajectories

Fig. 8

Response of $x_c^T(t)\mathit{R}{x}_c(t)$