Spectral collocation-based optimization in parameter estimation for nonlinear time-varying dynamical systems

2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007

Volumn 5 PART B, Issue , 2008, Pages 853-862

  Deshmukh, Venkatesh ^a,b  

^a Villanova University

^b VILLANOVA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DESIGN; PARAMETER ESTIMATION; QUADRATIC PROGRAMMING;

CHEBYSHEV SPECTRAL COLLOCATIONS; CONSTRUCTIVE OPTIMIZATION; DYNAMIC SYSTEM MODELS; OPTIMISATIONS; OPTIMIZATION ALGORITHMS; PARAMETER SET; PARAMETERS ESTIMATION; SPECTRAL COLLOCATION; TIME VARYING; TIME-VARYING DYNAMICS;

DYNAMICAL SYSTEMS;

EID: 44849095365     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/1.2815335     Document Type: Conference Paper

References (28)

1. Voit, E. O., Marino, S. and Lall, R., 2005, "Challenges for the Identification of Biological Systems from in vivo Time Series Data", In Silico Biology, 5, 83-92.
2. Cruz-Pacheco, G., Esteva, L., Montano-Hirose, J. A. and Vargas, C., 2005, "Modelling the dynamics of West Nile virus", Bulletin of Mathematical Biology, 67, 1157-1172.
3. Bowman, C., Gumel, A.B., van den Driessche, P., Wu, J. and Zhu, H., 2005, "Mathematical model of assessing control strategies against West Nile virus", Bulletin of Mathematical Biology, 61, 1107-1133.
4. Capasso, V. and Morale, D., 2005, "Mathematical models for HIV transmission among injecting drug users", Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, Tan, W.-Y. and Wu, H., (Ed.), 1-30.
5. Bajaria, S. H. and Kirschner, D. E., 2005, "CTL Action during HIV-I is Determined via Interactions with Multiple Cell Types", Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, Tan, W.-Y. and Wu, H., (Ed.), 219-254.
6. Kansal, A. R., 2004, "Modelling Approaches to Type 2 diabetes", Diabetes Technology and Therapeutics, 6(1), 39-47.
7. Cobelli, C., Bier, D.M. and Ferraninni, E., 1990, "Modelling glucose metabolism in man: Theory and practice", Harmone and Metabolic Research: Supplement series, 24, 1-10.
8. Topp, B., Promislow, K., DE Vries, G., Miura, R.M. and Finegood D. T., 2006, "A model of beta-cell mass, insulin and glucose kinetics: Pathways to Diabetes", Journal of Theoretical Biology, 206, 605-619.
9. Goldbeter, A., 1995, "A model for circadian oscillations in the Drosophila period protein", Proceedings of the Royal Society of London B, 261, 319-324.
10. Chen, L. and Wang, R., 2004, "Dynamics of Gene Regulatory Networks with Cell Division Cycle", Physical Review E, 70, 011909, 1-13.
11. Smolen, P., Baxter, D. A. and Byrne, J. H., 2000, "Mathematical Modeling of Gene Networks", Neuron, 26, 567-580.
12. Covert, M. W., Schilling, C. H. and Palsson, B., 2001, "Regulation of Gene Expression in Flux Balance Models of Metabolism", Journal of Theoretical Biology, 213, 73-88.
13. Bradshaw, P. C. and Samuels, D. C., 2005, "A computational model of mitochondrial deoxynucleotide metabolism and DNA replication", American Journal of Physiology - Cell Physiology, 288, 989-1002.
14. Mendes, P. and Kell, D. B., 1998, "Nonlinear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation", Bioinformatics, 14(10), 869-883.
15. de Mottoni, P. And Schiaffino, A., 1981, "Competetion Systems with Periodic Coefficients: A Geometric Approach", Journal of Mathematical Biology, 11, 319-335.
16. Butcher, E. C., Berg, E. L. and Kunkel, E. J., "Systems Biology in Drug Discovery", Nature Biotechnology, 22(10), 1253-1259.
17. Grass, G. M., 1997, "Simulation models to predict oral drug absorption from in vitro data", Advanced Drug Delivery Reviews, 23, 199-219.
18. Tan W.-Y. and Huang, Y., 2005, " Bayesian Estimation of Individual Parameters in an HIV Dynamic Model using Long Term Viral Load Data", Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, Tan, W.-Y. and Wu, H., (Ed.), 361-384.
19. Mendes, P., 2001, "Modeling Large Biological Ssyetms From Functional Genomic Data: Parameter Estimation", Foundations of Systems Biology, Kitano, H., (Ed.), 163-186.
20. www.vbi.vt.edu/mendes
21. Vera, J. And Torres, N. V., 2004, "MetMAP: An Integrated Matlab Package for Analysis and Optimization of Metabolic Systems", In Silico Biology, 4, 97-108.
22. Chalidze, P. and Cusumano, J. P., 2004, "A dynamical systems approach to failure prognosis", ASME Journal of Vibration and Acoustics, 126(1), 2-8.
23. Yin, S. H. and Epureanu, B. I., 2005, "Enhanced nonlinear dynamics and monitoring bifurcation morphing for the identification of parameter variations", Journal of Fluids and Structures, 21, 543-559.
24. Tunali E. T. and Tarn T. J., 1987, "New results for identifiability of nonlinear systems", IEEE Transactions on Automatic Control, 32, 146-154.
25. Trefethen, L. N., 2000, Spectral Methods in MATLAB, SIAM, Philadelphia.
26. Hulme, B. L., 1972, "One-step Piecewise Polynomial Galerkin Methods for Initial Value Problems", Mathematics of Computations, 26(118), 415-426.
27. Weiss, R., 1974, "The Application of Implicit Runge-Kutta and Collocation Methods to Boundary Value Problems", Mathematics of Computation, 28(126), 449-464.
28. de Boor, C. and Swartz, B., 1973, "Collocation at Gaussian Points", SIAM Journal on Numerical Analysis, 10(4), 582-606.