Fuzzy Logic Strategy for Solving an Optimal Control Problem of Glucose and Insulin in Diabetic Human

Jean Marie Ntaganda

Department of Applied Mathematics, School of Pure and Applied Science, College of Science and Technology, University of Rwanda (Huye Campus), Butare, Rwanda.

DOI: 10.4236/ojapps.2013.37052                

Abstract

This paper aims at the development of an approach integrating the fuzzy logic strategy for a glucose and insulin in diabetic human optimal control problem. To test the efficiency of this strategy, the author proposes a numerical comparison with the indirect method. The results are in good agreement with experimental data.

Keywords

Fuzzy Logic; Optimal Control; Membership Function; Membership Degree; Glucose; Insulin; Numerical Simulation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. N. Bergman, D. T. Finegood and S. E. Kahn, “The Evolution of Beta-Cell Dysfunction and Insulin Resistance in Type 2 Diabetes,” European Journal of Clinical Investigation, Vol. 32, Suppl. 3, 2002, pp. 35-45. http://dx.doi.org/10.1046/j.1365-2362.32.s3.5.x
[2]	V. W. Bolie, “Coefficients of Normal Blood Glucose Regulation,” Journal of Applied Physiology, Vol. 16, No. 5, 1961, pp. 783-788.
[3]	R. N. Bergman, L. S. Phillips and C. Cobelli, “Physiologic Evaluation of Factors Controlling Glucose Tolerance in Man: Measurement of Insulin Sensitivity and Beta-Cell Glucose Sensitivity from the Response to Intravenous Glucose,” The Journal of Clinical Investigation, Vol. 68, No. 6, 1981, pp. 1456-1467. http://dx.doi.org/10.1172/JCI110398
[4]	C. Cobelli, G. Pacini, G. Toffolo and L. Sacca, “Estimation of Insulin Sensitivity and Glucose Clearance from Minimal Model: New Insights from Labeled IVGTT,” American Journal of Physiology, Vol. 250, No. 5, 1986, pp. E591-E598.
[5]	C. Cobelli, A. Caumo and M. Omenetto, “Minimal Model SG Overestimation and SI Underestimation: Improved Accuracy by a Bayesian Two-Compartment Model,” American Journal of Physiology, Vol. 277, No. 3, 1999, pp. E481-E488.
[6]	R. Hovorka, F. Shojaee-Moradie, P. V. Carroll, L. J. Chassin, I. J. Gowrie, N. C. Jackson, R. S. Tudor, A. M. Umpleby and R. H. Jones, “Partitioning Glucose Distribution/Transport, Disposal, and Endogenous Production during IVGTT,” American Journal of Physiology: Endocrinology and Metabolism, Vol. 282, No. 5, 2002, pp. E992-E1007.
[7]	M. S. Anirban Roy and R. S. Parker, “Dynamic Modeling of Exercise Effects on Plasma Glucose and Insulin Levels,” Journal of Diabetes Science and Technology, Vol. 1, No. 3, 2007, pp. 338-347.
[8]	J. M. Ntaganda and B. Mampassi, “Modelling Glucose and Insulin in Diabetic Human during Physical Activity,” 2012 Proceeding of the 4th International Conference on Mathamatical Sciences (ICM), United Arab Emirates University, 11-14 March 2012, pp. 331-344.
[9]	S. J. Yakowitz, “The Stagewise Kuhn-Tucker Condition and Differential Dynamic Programming,” IEEE Transactions on Automatic Control, Vol. 31, No. 1, 1986, pp. 25-30.http://dx.doi.org/10.1109/TAC.1986.1104123
[10]	N. K. Masmoudi, C. Rekik, M. Djemel and N. Derbel, ‘‘Decomposition and Hierarchical Control for Discrete Complex Systems by Fuzzy Logic Controllers,” SSD '09. 6th International Multi-Conference on Systems, Signals and Devices, Djerba, 23-26 March 2009, pp. 1-6.
[11]	M. Sugeno and K. Murakami, “Fuzzy Parking Control of Model Car,” The 23rd IEEE Conference on Decision and Control, Vol. 23, 1984, pp. 902-903.
[12]	T. Takagi and M. Sugeno, “Fuzzy Identification of Systems and Its Applications to Modeling and Control,” IEEE Transactions on Systems, Man and Cybernetics, Vol. 15, No. 1, 1985, pp. 116-132. http://dx.doi.org/10.1109/TSMC.1985.6313399
[13]	M. I. Park, E. Kim, S. Ji and M. Park, “A New Approach to Fuzzy Modeling,” IEEE Transactions on Fuzzy Systems, Vol. 5, No. 3, 1987, pp. 328-337.
[14]	D. Jacobson, D. Lele and J. L. Speyer, “New Necessary Conditions of Optimality for Control Problems with State-Variable Inequality Constraints,” Journal of Mathematical Analysis and Applications, Vol. 35, No. 2, 1971, pp. 255-284. http://dx.doi.org/10.1016/0022-247X(71)90219-8
[15]	H. Kwakernaak and R. Savan, “Linear Optimal Control Systems,” Wiley Inter-Science, New York, 1972.
[16]	E. Trélat, “Contrôle Optimal: Théorie et Applications,” Vuibert, Collection Mathématiques Concrètes, Paris, 2005.
[17]	J. M. Ntaganda, B. Mampassi and D. Seck, “Modelling Blood Partial Pressures of the Human Cardiovascular/ Respiratory System,” Applied Mathematics and Computation, Vol. 187, No. 2, 2007, pp. 1100-1108. http://dx.doi.org/10.1016/j.amc.2006.09.016