Fuzzy Logic for Solving an Optimal Control Problem of Hypoxemic Hypoxia Tissue Blood Carbon Dioxide Exchange during Physical Activity
Affiliation(s)
1 Department of Applied Mathematics, School of Pure and Applied Sciences, College of Science and Technology, University of Rwanda, Kigali, Rwanda. 2 N’Djamena University, N’Djamena, Chad. 3 Cheikh Anta Diop University, Dakar, Senegal.
1 Department of Applied Mathematics, School of Pure and Applied Sciences, College of Science and Technology, University of Rwanda, Kigali, Rwanda. 2 N’Djamena University, N’Djamena, Chad. 3 Cheikh Anta Diop University, Dakar, Senegal.
ABSTRACT
This paper aims at using of an approach integrating the fuzzy logic strategy for hypoxemic hypoxia tissue blood carbon dioxide human optimal control problem. To test the efficiency of this strategy, the authors propose a numerical comparison with the direct method by taking the values of determinant parameters of cardiovascular-respiratory system for a 30 years old woman in jogging as her regular physical activity. The results are in good agreement with experimental data.
This paper aims at using of an approach integrating the fuzzy logic strategy for hypoxemic hypoxia tissue blood carbon dioxide human optimal control problem. To test the efficiency of this strategy, the authors propose a numerical comparison with the direct method by taking the values of determinant parameters of cardiovascular-respiratory system for a 30 years old woman in jogging as her regular physical activity. The results are in good agreement with experimental data.
KEYWORDS
Fuzzy Logic, Optimal Control, Membership Function, Membership Degree, Hypoxemic-Hypoxia, Pressure, Carbon Dioxide, Oxygen, Numerical Simulation
Fuzzy Logic, Optimal Control, Membership Function, Membership Degree, Hypoxemic-Hypoxia, Pressure, Carbon Dioxide, Oxygen, Numerical Simulation
Cite this paper
Ntaganda, J. , Daoussa Haggar, M. and Mampassi, B. (2014) Fuzzy Logic for Solving an Optimal Control Problem of Hypoxemic Hypoxia Tissue Blood Carbon Dioxide Exchange during Physical Activity. Open Journal of Applied Sciences, 4, 501-514. doi: 10.4236/ojapps.2014.411049.
Ntaganda, J. , Daoussa Haggar, M. and Mampassi, B. (2014) Fuzzy Logic for Solving an Optimal Control Problem of Hypoxemic Hypoxia Tissue Blood Carbon Dioxide Exchange during Physical Activity. Open Journal of Applied Sciences, 4, 501-514. doi: 10.4236/ojapps.2014.411049.
References
[1] Cymerman, A. and Rock, P.B. (2009) Medical Problems in High Mountain Environments. A Handbook for Medical of Ficers. USARIEM-TN94-2. US Army Research Institute of Environmental Medicine Thermal and Mountain Medicine Division Technical Report. [2] Gutierrez, G. (2004) A Mathematical Model of Tissue-Blood Carbon Dioxide Exchange during Hypoxia. American Journal of Respiratory and Critical Care Medicine, 169, 525-533. [3] Timischl, S., Batzel, J. J. and Kappel, F. (2000) Modeling the Human Cardiovascular-Respiratory Control System: An Optimal Control Application to the Transition to Non-REM Sleep. Spezialforschungsbereich F-003 Technical Report 190, Karl-Franzens-Universitat, Graz. [4] Severinghaus, J.W. (1979) Simple, Accurate Equations for Human Blood O2 Dissociation Computations. Journal of Applied Physiology, 46, 599-602. [5] Giovannini, I., Chiarla, C., Boldrini, G. and Castagneto, M. (1993) Calculation of Venoarterial CO2 Concentration Difference. Journal of Applied Physiology, 74, 959-964. [6] Douglas, A.R., Jones, N.L. and Reed, J.W. (1988) Calculation of Whole Blood CO2 Content. Journal of Applied Physiology, 65, 473-477. [7] Yakowitz, S.J. (1986) The Stagewise Kuhn-Tucker Condition and Differential Dynamic Programming. IEEE Transactions on Automatic Control, 31, 25-30. [8] Masmoudi, N.K. and Derbel, N. (2003) Optimal Control of Nonlinear Systems by Fuzzy Logic. ISCIII, Nabeul,. [9] Sugeno, M. and Murakami, K. (1984) Fuzzy Parking Control of Model Car. 23rd IEEE Conferences on Decision and Control, Las Vegas, 12-14 December 1984, 902-903.
http://dx.doi.org/10.1109/CDC.1984.272144 [10] Takagi, T. and Sugeno, M. (1985) Fuzzy Identification of Systems and Its Applications to Modeling and Control. IEEE Transactions on Systems Man and Cybernetics, 15, 116-132.
http://dx.doi.org/10.1109/TSMC.1985.6313399 [11] Park, M.I., Kim, E., Ji, S. and Park, M. (1987) A New Approach to Fuzzy Modeling. IEEE Transactions on Fuzzy Systems, 5, 328-337. [12] Jacobson, D., Lele, D. and Speyer, J.L. (1971) New Necessary Conditions of Optimality for Control Problems with State-Variable Inequality Constraints. Journal of Mathematical Analysis and Applications, 35, 255-284.
http://dx.doi.org/10.1016/0022-247X(71)90219-8 [13] Kwakernaak, H. and Savan, R. (1972) Linear Optimal Control Systems. Wiley, Inter-Science, New York. [14] Trélat, E. (2005) Controle Optimal: Théeorie et Applications, Vuibert, Collection, Mathématiques Concrètes. [15] Ntaganda, J.M. and Mampassi, B. (2007) Modelling Blood Partial Pressures of the Human Cardiovascular Respiratory System. Applied Mathematics and Computation, 187, 1100-1108.
http://dx.doi.org/10.1016/j.amc.2006.09.016
[1] Cymerman, A. and Rock, P.B. (2009) Medical Problems in High Mountain Environments. A Handbook for Medical of Ficers. USARIEM-TN94-2. US Army Research Institute of Environmental Medicine Thermal and Mountain Medicine Division Technical Report. [2] Gutierrez, G. (2004) A Mathematical Model of Tissue-Blood Carbon Dioxide Exchange during Hypoxia. American Journal of Respiratory and Critical Care Medicine, 169, 525-533. [3] Timischl, S., Batzel, J. J. and Kappel, F. (2000) Modeling the Human Cardiovascular-Respiratory Control System: An Optimal Control Application to the Transition to Non-REM Sleep. Spezialforschungsbereich F-003 Technical Report 190, Karl-Franzens-Universitat, Graz. [4] Severinghaus, J.W. (1979) Simple, Accurate Equations for Human Blood O2 Dissociation Computations. Journal of Applied Physiology, 46, 599-602. [5] Giovannini, I., Chiarla, C., Boldrini, G. and Castagneto, M. (1993) Calculation of Venoarterial CO2 Concentration Difference. Journal of Applied Physiology, 74, 959-964. [6] Douglas, A.R., Jones, N.L. and Reed, J.W. (1988) Calculation of Whole Blood CO2 Content. Journal of Applied Physiology, 65, 473-477. [7] Yakowitz, S.J. (1986) The Stagewise Kuhn-Tucker Condition and Differential Dynamic Programming. IEEE Transactions on Automatic Control, 31, 25-30. [8] Masmoudi, N.K. and Derbel, N. (2003) Optimal Control of Nonlinear Systems by Fuzzy Logic. ISCIII, Nabeul,. [9] Sugeno, M. and Murakami, K. (1984) Fuzzy Parking Control of Model Car. 23rd IEEE Conferences on Decision and Control, Las Vegas, 12-14 December 1984, 902-903.
http://dx.doi.org/10.1109/CDC.1984.272144 [10] Takagi, T. and Sugeno, M. (1985) Fuzzy Identification of Systems and Its Applications to Modeling and Control. IEEE Transactions on Systems Man and Cybernetics, 15, 116-132.
http://dx.doi.org/10.1109/TSMC.1985.6313399 [11] Park, M.I., Kim, E., Ji, S. and Park, M. (1987) A New Approach to Fuzzy Modeling. IEEE Transactions on Fuzzy Systems, 5, 328-337. [12] Jacobson, D., Lele, D. and Speyer, J.L. (1971) New Necessary Conditions of Optimality for Control Problems with State-Variable Inequality Constraints. Journal of Mathematical Analysis and Applications, 35, 255-284.
http://dx.doi.org/10.1016/0022-247X(71)90219-8 [13] Kwakernaak, H. and Savan, R. (1972) Linear Optimal Control Systems. Wiley, Inter-Science, New York. [14] Trélat, E. (2005) Controle Optimal: Théeorie et Applications, Vuibert, Collection, Mathématiques Concrètes. [15] Ntaganda, J.M. and Mampassi, B. (2007) Modelling Blood Partial Pressures of the Human Cardiovascular Respiratory System. Applied Mathematics and Computation, 187, 1100-1108.
http://dx.doi.org/10.1016/j.amc.2006.09.016