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Vol: 51(65) No: 1 / March 2006      

On the Use of Robust Servo Control In Diabetes Under Intensive Care
Levente Kovacs
Department of Control Engineering and Information Technology, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, H-1117 Budapest, Magyar Tudósok krt. 2, Hungary, phone: (36-1) 463-4027, e-mail: lkovacs@iit.bme.hu
Balazs Kulcsar
Department of Transport Automation, Budapest University of Technology and Economics, Faculty of Transportation Engineering, H-1111 Budapest, Bertalan Lajos u. 2, Hungary, phone: (36-1) 463-2255, e-mail: kulcsar@kaut.kka.bme.hu
Zoltan Benyo
Department of Transport Automation, Budapest University of Technology and Economics, Faculty of Transportation Engineering, H-1111 Budapest, Bertalan Lajos u. 2, Hungary


Keywords: diabetes mellitus, glucose-insulin control, robust control, multiplicative uncertainty, μ-synthesis method.

Abstract
The robust servo control of a model-based biomedical application, namely the glucose-insulin control of diabetes patients under intensive care, is presented in the paper. The synthesis and analysis is based on a modified two compartment Bergman model and realized with a two degree of freedom controller structure permitting to assure insulin tracking. The augmented Δ − P − K structure is described with the necessary weighting functions. A non-conservative complex μ-synthesis method is applied. Using the controller, not only the robust stability is met under multiplicative uncertainty, but also the nominal performance i.e. the disturbance rejection is fulfilled. Food (sugar) intake is considered as disturbance. Closed loop simulation results are edged for optimizing the insulin amount.

References
[1] G. van den Berghe, “Insulin therapy for the critically ill patient”, Clinical Cornerstone, vol. 5/2, pp. 56 – 63, 2003.
[2] B. N. Bergman, Y. Z. Ider, C. R. Bowden and C. Cobelli, “Quantitive estimation of insulin sensitivity”, American Journal of Physiology, vol. 236, pp. 667 – 677, 1979.
[3] R. N.Bergman, L. S. Philips and C. Cobelli, “Physiologic evaluation of factors controlling glucose tolerance in man”, Journal of Clinical Investigation, vol. 68; pp.1456 – 1467, 1981.
[4] J. T. Sorensen, A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes, Ph.D. thesis, Massachusetts Institute of Technology (MIT), 1985.
[5] I. M. Tolic, E. Mosekilde and J. Sturis, “Modeling the Insulin-Glucose Feedback System: The Signification of Pulsatile Insulin Selection”, Journal of Theoretical Biology, vol. 207/3, pp. 361 – 375, 2000.
[6] D. L. Benett and S. A. Gourley, “Asymptotic properties of a delay differential equation model for the interaction of glucose with plasma and interstitial insulin”, Elsevier, Applied Mathematics and Computation, vol. 151/1, pp. 189 – 207, 2003.
[7] M. E. Fischer and K. L. Teo, “Optimal Insulin Infusion Resulting from a Mathematical Model of Blood Glucose Dynamics”, IEEE Trans. Biomed. Eng., vol. 36/3, pp. 479 – 486, 1989.
[8] Cs. Juhász and B. Asztalos, “AdASDiM: An Adaptive Control Approach to Diabetic Management”, Innovation et Technologie en Biologie et Medicine, vol. 17/1, 1996.
[9] A. Sano, “Adaptive and optimal schemes for control of blood glucose levels”, Biomedical Measurements, Informatics and Control, vol. 1/1, pp. 16 – 22, 1986.
[10] Z. Benyó, B. Paláncz, Cs. Juhász and P. Várady, “Design of Glucose Control via Symbolic Computation”, In Proc. of 20th Ann. Int. Conf. of the IEEE Engineering in Medicine and Biology Society, Hong Kong, vol. 20/6, pp. 3116 – 3119, 1998.
[11] R. Hovorka, V. Canonico, L. J. Chassin, U. Haueter, M. Massi-Benedetti, M. Orsini Federici, T. R. Pieber, H. C. Schaller, L. Schaupp, T. Vering and M. E. Wilinska, “Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes”, Physiological measurement, vol. 25, pp. 905 – 920, 2004.
[12] S. M. Lynch and B. W. Bequette, “Model predictive control of blood glucose in type I diabetics using subcutaneous glucose measurements”, American Control Conference, Anchorage (USA), vol. 5, pp. 4039 – 4043, 2002.
[13] R. S. Parker, F. J. Doyle III and N. A. Peppas, “A model-based algorithm for blood glucose control in type I diabetics patients”, IEEE Transactions on Biomedical Engineering, vol. 46, pp. 148 – 157, 1999.
[14] M. Fernandez, D. Acosta, M. Villasana and D. Streja, “Enhancing Parameter Precision and the Minimal Modeling Approach in Type I Diabetes”, In Proc. of 26th Ann. Int. Conf. of IEEE Eng. in Biomedicine Soc., San Francisco, USA, pp. 797 – 800, 2004.
[15] J. Lin, J. G. Chase, G. M. Shaw, C. V. Doran, C. E. Hann, M. B. Robertson, P. M. Browne, T. Lotz, G. C. Wake and B. Broughton, “Adaptive Bolus-Based Set-Point Regulation of Hyperglycemia in Critical Care”, In Proc. of 26th Ann. Int. Conf. of IEEE Eng. in Biomedicine Soc., San Francisco, USA, pp. 3463 – 3466, 2004.
[16] H. C. Morris, B. O’Reilly and D. Streja, “A New Biphasic Minimal Model”, In Proc. of 26th Ann. Int. Conf. of IEEE Eng. in Biomedicine Soc., San Francisco, USA, pp. 782 – 785, 2004.
[17] B. Benyó, Z. Benyó, B. Paláncz, L. Kovács and L. Szilágyi, “A Fully Symbolic Design and Modeling of Nonlinear Glucose Control with Control System Professional Suite (CSPS) of Mathematica”, In Proc. of the World Congress on Medical Physics and Biomedical Engineering, Sydney, Australia, electronic publication #2813, 2003.
[18] R. S. Parker, F. J. Doyle III, J. H. Ward and N. A. Peppas, “Robust H∞ Glucose Control in Diabetes Using a Physiological Model”, AIChE Journal, vol. 46/12, pp. 2537 – 2549, 2000.
[19] L. Kovács, B. Paláncz and Z. Benyó, “Classical and Modern Control Strategies in Glucose-Insulin Stabilization”, In Proc 16th IFAC World Congress, Prague, Czech Republic, electronic publication #04165, 2005.
[20] Cs. Juhász, Medical Application of Adaptive Control, Supporting Insulin-Therapy in case of Diabetes Mellitus, PhD thesis, Budapest University of Technology and Economics, Hungary, 1993.
[21] L. Kovács and B. Paláncz, “Linear and Non-linear Approach of the Glucose-Insulin Control using Mathematica”, Periodica Politechnica, Transactions On Automatic Control and Computer Science, Timisoara, Romania, vol. 49/63, pp. 65 – 70, 2004.
[22] J. C.Doyle, K. Glover, P. P. Khargonekar and B. A. Francis, “State-Space Solutions to Standard H2 and H∞ Control Problems”, IEEE Transactions on Automatic Control, vol. 34/8, pp. 831 – 847, 1989.
[23] G. J.Balas, J. C. Doyle, K. Glover, A. Packard and R. Smith, μ analysis and synthesis toolbox, MUSYN Inc. and Mathworks Inc, 1991.
[24] K. Zhou, Robust and Optimal Control, Prentice Hall, New Jersey, 1996.
[25] L. Kovács, B. Kulcsár, J. Bokor and Z. Benyó, “LPV Fault Detection of Glucos-Insulin System”, In Proc. 14th Mediterranean Conference on Control and Automation, Ancona, Italy, electronic publication #TLA2-4, 2006.
[26] A. Edelmayer, J. Bokor, F. Szigeti and L. Keviczky, “Robust detection filter design in the presence of time-varying system perturbation”, Automatica vol. 33, pp. 471 – 475, 1997.