Nonlinear Control Analysis of an ICU Model for Tight Glycaemic Control Levente KovÆcs*, PØter Szalay*, BalÆzs Beny*, J. Geoffrey Chase** *Budapest University of Technology and Economics, Dept. of Control Engineering and Information Technology Magyar tudsok krt. 2, Budapest, H-1117 Hungary (Tel: +36-1-463-4027; e-mail: {lkovacs, szalaip, bbenyo}@iit.bme.hu) ** Dept. of Mechanical Engineering, Centre for Bio-Engineering, University of Canterbury, Christchurch, New Zealand (e-mail: geoff.chase@canterbury.ac.nz) Abstract: Intensive care is one of the most challenging areas of modern medicine. Maintenance of glucose levels in intensive care unit (ICU) patients via control of insulin inputs is an active research field. Accurate metabolic system models are a critical element of automatic control. Different ICU models appeared in the literature some of them already validated in clinical trials. The current paper analyzes and gives a nonlinear synthesis of a frequently used ICU metabolic system models redefined version. The model has been already validated in clinical trials. Global control characteristics are determined using nonlinear analysis. Results of reachability and observability are explained regarding physiological meanings, and then exact linearization is computed. Finally, quasi affine linear parameter varying (qALPV) modeling methodology is applied and compared with results obtained by exact linearization. It is demonstrated that inside the chosen scheduling parameters vertex the qAPLV model represents the nonlinear system itself without any approximation. Conclusions are drawn from this analysis for further robust nonlinear model based controller design. Keywords: Intensive Care Unit, tight glycaemic control, nonlinear analysis, exact linearization, qALPV, scheduling parameter. 1. INTRODUCTION Critically ill patients admitted to the Intensive Care Unit (ICU) often display hyperglycaemia and insulin resistance (Krinsley (2004)), which are associated with increased morbidity and mortality (Capes et al. (2000)). Tight glycaemic control (TGC) can reduce these adverse outcomes (Chase et al. (2008)), as well as reducing economic costs (Van den Berghe (2006)). Hence, TGC using model-based methods has become an active research field (Chase et al. (2006)). Several studies have shown that TGC can reduce mortality (Chase et al. (2008)), but several others have reported difficulty repeating these results (Griesdale (2009)). This difficulty is caused in large part due to the significant metabolic variability of ICU patients (Lin et al. (2008)). It presents an ideal application for model-based automation of insulin infusions for TGC. Accurate metabolic system models are a critical element. The best known model is the minimal model of Bergman et al. (1981), used primarily for clinical research studies. However, the models simplicity is a disadvantage, with significant important components of glucose-insulin interaction neglected in its formulation. Consequently, different models were derived to generalize to the ICU case. Wong et al. (2006) and Lotz et al. (2006) presented a third order model that better captured insulin losses and saturation dynamics. Van Herpe et al. (2007) created a fourth order model that accounted for further typical features of the ICU patient. Pielmeier et al. (2009) created the Glucosafe model that integrates a range of physiological models and parameters. Of these models, only Wong et al. (2006) and Lotz et al. (2006) (named in the followings as Canterbury-model) have been clinically applied and validated in TGC for ICU patients, as well as in other clinical experiments. An updated version of this model has recently appeared (Suhaimi et al. (2010)). The goal of this paper is to make a nonlinear control analysis and synthesis on this modified Canterbury-model and compare the results with the qALPV nonlinear model-based methodology for the same model. 2. THE CANTERBURY-MODEL Wong et al. (2006) developed a series of models based on a fundamental system with three compartments (Wong et al. (2006); Lin et al. (2008)) with recent redefinition in Suhaimi et al. (2010): G b G I G V CNS EGP t P t Q t Q t G t S t G p ) t ( G D 1 (1/a) t kQ t kI t Q (1/b) V t u V t u t I t nI t I end ex I D 1 (1/c) t P d t D t P 1 1 1 (1/d) ^ ‘ max P , t P d min t P d t P 2 2 1 1 2 (1/e) ^ ‘ max P , t P d min t P 2 2 (1/f) ‚ ‚ „ • ¤ ¤ ' § 3 2 1 k t I k exp k t u end (1/g) Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011 Copyright by the International Federation of Automatic Control (IFAC) 1739