On Role of S-Synchronizability and Excitation Constancy in Structural Identifiability Problem of Nonlinear Systems
https://doi.org/10.17587/mau.22.59-70
Abstract
A class of dynamical systems with a single nonlinearity considered. The S-synchronizability concept of input introduced. It is shown that S-synchronizability is a condition for the structural identifiability of a nonlinear system. The decisionmaking on structural identifiability based on the properties analysis for a special class of geometric frameworks. Geometric frameworks reflect properties of the nonlinear dynamic system. Requirements for the model allowed us to obtain a geometric structure based on the input and output data considered. The constant excitation effect of input on the structural identifiability of the system is studied. The constant excitation effect of input studied on the structural identifiability of the system. Nonfulfillment the constant excitation condition gives a nonsignificant geometric framework. Various types of structural identifiability based on structure analysis considered. The concept of d-optimality described properties of the geometric structure introduced. Conditions for non-identifiability of nonlinear system structure obtained if the d-optimality of the geometric framework does not hold for the given properties of the input. Methods for estimating identifiability of the system and determining the identifiability area under uncertainty proposed. The proposed approach is generalized to the system having two nonlinearities. Conditions for partial structural identifiability obtained. Structural identifiability features of this class systems noted. The method for estimating the structure of the system proposed when the condition of structural identifiability satisfied. It has shown how the phase portrait used to estimate the system non-identifiability. A method proposed for constructing the structural identifiability domain of the system. Proposed methods and procedures are applied to study systems with Bouc-Wen hysteresis and two nonlinearity.
About the Author
N. N. Karabutov
MIREA—Russian Technological University
Russian Federation
Moscow, 119454
Russian Federation
Moscow, 119454
References
1. Kalman R. E. On the general theory of control systems. Proceeding first IFAC Congress on Automatic Control, Moscow, 1960; Butterworths, London, 1961, vol. 1, pp. 481—492.
2. Lee R. С. K. Optimal estimation, identification, and control, MIT Press, Cambridge, Mass, 1964. 176 p.
3. Elgerd O. I. Control systems theory, N. Y., McGraw-Hill, 1967. 562 p.
4. Walter E. Identifiability of state space models, Berlin, Germany, Springer-Verlag, 1982, 197 p.
5. Audoly S., D’Angio L., Saccomany M. P., Cobelli C. Global identifiability of linear compartmental models — a computer algebra algorithm, IEEE Trans. Automat. Contr., 1998, vol. 45, pp. 36—47.
6. Avdeenko T. V. Identification of linear dynamic systems with use parametrical space separators, Automatics and Program Engineering, 2013, no. 1(3), pp. 16—23 (in Russian).
7. Bodunov N. A. Introduction to the theory of local parametrical identifiability, Differential Equations and Management Processes, 2012, no. 2, 137 p.
8. Balonin N. A. Theorems of identifiability. St. Petersburg, Politekhnika publishing house, 2010, 49 p.
9. Reference book on automatic control theory, Ed. A. A. Krasovsky, Moscow, Nauka, 1987, 712 p.
10. Stigter J. D., Peeters R. L. M. 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, 2007, pp. 3450—3456.
11. Chis O.-T., Banga J. R., Balsa-Canto E. Structural identifiability of systems biology models: a critical comparison of methods, PLOS ONE, 2011, vol. 6, iss. 4, pp. 1—16.
12. Saccomani M. P., Thomaseth K. Structural vs practical identifiability of nonlinear differential equation models in systems biology. Bringing mathematics to life, Dynamics of Mathematical Models in Biology. Ed. A. Rogato, V. Zazzu, M. Guarracino. Springer, 2010, pp. 31—42.
13. Villaverde A., Barreiro A., Papachristodoulou A. Structural identifiability of dynamic systems biology models, PLOS Computational Biology, 2016, vol. 12, no. 10, pp. 1—22.
14. Raue A., Karlsson J., Saccomani M. P., Jirstrand M., Timmer J. Comparison of approaches for parameter identifiability analysis of biological systems, Bioinformatic, 2014, vol. 30, no. 10, pp. 1440—1448.
15. Karabutov N. About structural identifiability of nonlinear dynamic systems under uncertainty, Global Journal of Science Frontier Research: A Physics and Space Science, 2018, vol. 18, iss. 11 (vers. 1.0), pp. 51—61.
16. Karabutov N. Structural identification of dynamic systems with hysteresis, International Journal of Intelligent Systems and Applications, 2016, vol. 8, no. 7, pp. 1—13.
17. Karabutov N. Structural methods of design identification systems. In Nonlinearity Problems, Solutions and Applications. Vol. 1. Ed. L. A. Uvarova, A. B. Nadykto, A. V. Latyshev. New York. Nova Science Publishers, Inc. 2017, pp. 233—274.
18. Karabutov N. Structural identification of nonlinear dynamic systems. International Journal of Intelligent Systems and Applications, 2015, vol. 7, no. 9, pp. 1—11.
19. Choquet G. L’enseignement de la geometrie. Paris: Hermann, 1964. 173 p.
20. Ismail M., Ikhouane F., Rodellar J. The hysteresis Bouc-Wen model, a survey, Arch Comput Methods Eng, 2009, vol. 16, pp. 161—188.
21. Karabutov N. N. S-synchronization structural identifiability and identification of nonlinear dynamic systems, Mekhatronika, Avtomatizatsiya, Upravlenie. 2020, vol. 21, no. 6 (2020), pp. 323—336.
22. Karabutov N. N. Structural analysis and modifications of system with Bouc-Wen hysteresis, The Bulletin of Voronezh State Technical University, 2020, vol. 16, no. 2, pp. 57—64.
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For citations:
Karabutov N.N. On Role of S-Synchronizability and Excitation Constancy in Structural Identifiability Problem of Nonlinear Systems. Mekhatronika, Avtomatizatsiya, Upravlenie. 2021;22(2):59-70. (In Russ.) https://doi.org/10.17587/mau.22.59-70
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