International Journal of Intelligent Systems and Applications (IJISA)
IJISA Vol. 12, No. 1, 8 Feb. 2020
Cover page and Table of Contents: PDF (size: 551KB)
Structural Identifiability of Nonlinear Dynamic Systems under Uncertainty
Full Text (PDF, 551KB), PP.12-22
Views: 0 Downloads: 0
Author(s)
Nikolay N. Karabutov
1,2,*
Index Terms
Framework, nonlinear dynamic system, phase portrait, structural identification, nonlinearity, structural identifiability, synchronizability
Abstract
Approach to the analysis of nonlinear dynamic systems structural identifiability (SI) under uncertainty proposed. This approach has a difference from methods applied to SI estimation of dynamic systems in the parametrical space. Structural identifiability interpreted as of the structural identification possibility a nonlinear system part. We show that the input has S-synchronization property for the solution of the SI task. The identifiability method based on the analysis of structures. The input parameter effect on the possibility of the system SI estimation is studied.
Cite This Paper
Nikolay Karabutov, "Structural Identifiability of Nonlinear Dynamic Systems under Uncertainty", International Journal of Intelligent Systems and Applications(IJISA), Vol.12, No.1, pp.12-22, 2020. DOI:10.5815/ijisa.2020.01.02
Reference
[1]R. E. Kalman, “On the general theory of control systems,” in Proceeding first IFAC Congress on Automatic Control, Moscow, 1960; Butterworths, London, vol. 1, pp. 481-492, 1961.
[2]R. ะก. K. Lee, Optimal estimation, identification, and con-trol. Cambridge, Mass: MIT Press, 1964.
[3]O. I. Elgerd, Control Systems Theory. N.Y.: McGraw-Hill, 1967.
[4]E. Walter, Identifiability of state space models. Berlin Germany: Springer-Verlag, 1982.
[5]S. Audoly, L. D’Angio, M. P. Saccomany, C. Cobelli, “Global identifiability of linear compartmental models – a computer algebra algorithm,” IEEE Trans. Automat. Contr., vol. 45, pp. 36-47, 1998.
[6]T. V. Avdeenko, “Identification of linear dynamic systems with use parametrical space separators,” Automatics and program engineering, no. 1(3), pp. 16-23, 2013.
[7]N. A. Bodunov, "Introduction to the theory of local par-ametrical identifiability," Differential equations and man-agement processes, no. 2, 137 p, 2012.
[8]N. A. Balonin, Theorems of identifiability. St. Petersburg: Politekhnika publishing house, 2010.
[9]Reference book on automatic control theory. Ed. A. A. Krasovsky. Moscow: Nauka, 1987.
[10]J. D. Stigter, R. L. M. Peeters, “On a geometric approach to the structural identifiability problem and its application in a water quality case study,” Proceedings of the European Control Conference 2007 Kos, Greece, July 2-5, pp. 3450-3456, 2007.
[11]O.-T. Chis, J. R. Banga, “E. Balsa-Canto, Structural iden-tifiability of systems biology models: a critical comparison of methods,” PLOS ONE, vol. 6, is. 4, pp. 1-16, 2011.
[12]M. P. Saccomani, K. Thomaseth, “Structural vs practical identifiability of nonlinear differential equation models in systems biology. Bringing mathematics to life,” in Dy-namics of mathematical models in biology, Ed. A. Rogato, V. Zazzu, M. Guarracino. Springer pp. 31-42, 2010.
[13]S. A. Aivazyan, I. S. Yenyukov, L. D. Meshalkin, Applied statistics. Study of relationships. Moscow: Finansy i statistika, 1985.
[14]N. N. Karabutov, Frameworks in identification problems: Design and analysis. Moscow: URSS/Lenand, 2018 (in Russian).
[15]Y. E. Kazakov, B. G. Dostupov, Statistical dynamics of nonlinear automatic systems. Moscow: Fizmatgis, 1962.
[16]V. D. Furasov, Stability of motion, estimation and stabili-zation. Moscow: Nauka, 1977.
[17]G. Choquet, L'enseignement de la geometrie. Paris: Her-mann, 1964.
[18]S. V. Bozhokin, D. A. Parshin, Fractals and Multifractals. Moscow-Izhevsk: Scientific Publishing Centre “Regular and Chaotic Dynamics”, 2001.