Sensitivity analysis and multi-model generalised predictive control of uncertain intravenous general anaesthesia system

Feedback control of anaesthesia may offer a number of benefts. However,the design of the feedback controller is complicated by the presence of uncertainty due to inter-individual variability. As such, systematic analysis on the inter-individual variability is important to create better understanding on the system. This thesis aims to analyse the uncertainty in the dose-efect relationship and develop suitable controller(s) for intravenous general anaesthesia under the presence of uncertainty. Throughout the research, the propofol infusion rate and Bispectral Index (BIS) were considered as the control input and controlled variable, respectively.The dose-efect relationship in biological systems is best described by the pharmacokinetic pharmacodynamic (PKPD) model. Inter-individual variability may arise from PK, PD or both. To quantify the efect of parametric variability in the propofol PKPD model on BIS uncertainty, a Sobol' variance based global sensitivity analysis was performed. Nine input factors were evaluated:patient's age, body weight, height, four PK model parameters and two PD model parameters. Result indicates that variability of PK model has a much smaller efect on BIS values compared to PD model. Among the input factors,Ce50 was the most signifcant variable in the PKPD model.Inter-patient variability may lead to system instability. Therefore, it is important to know the uncertainty bounds acceptable by a controller to maintain system stability. While the variability in the nonlinear PD is much higher than the linear PK, most of the stability analyses have only considered modelling error that exists linearly. By employing circle criterion approach, the sector of nonlinearity that guarantees absolute stability of a closed-loop anaesthesia system was identifed. It was found that the robust stability bound of the specifed control system is sufciently large against the possible ariability of nonlinearity among patients.The PK model is a positive system. Imposing states positiveness in a closed loop system allows one to greatly simplify the stability analysis. Consequently,the controller design can be treated as a positive stabilisation problem. By making use of the positive nature of PK model, an observer-based output feedback controller was designed using a linear programming (LP) approach for uncertain PK models. However, simulation results show that the response of this controller was slow; a long induction phase duration (ID) was observed.Finally, a multi-model generalised predictive controller with switching (MMGPC)was proposed. The idea is that, upon linearisation, important parameters variability can be reduced to one single factor, the process gain. Therefore,inter-individual variability among patient can be tackled by switching within models with diferent gain. The performance of MMGPC was evaluated and compared with three other extensions of GPC: the GPC with T polynomial (GPCT), the independent model GPC (GPCI), and the adaptive GPC (AGPC). Among these four controllers, MMGPC is found to perform the best; it has the lowest mean values for integral absolute error (IAE), the percentage of time of BIS outside 10 units from set point (T±10) as well as input signal's total variation (TV).

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