Conditions of local parameter identifiability for systems of differential equations with an infinite-dimensional parameter

Authors

  • Sergei Yu. Pilyugin St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
  • Vladimir S. Shalgin St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2023.411

Abstract

The problem of parameter identification (determining parameters of a system by observing solutions or functions of them) is one of the main problems of the applied theory of differential equations. The property of local identifiability plays the most important role in solving this problem. The presence of this property means that one can uniquely determine values of parameters of a system in a neighborhood of a particular parameter by observing solutions. Earlier the case of a finite-dimensional parameter was mostly studied in this issue. The problem of local parameter identifiability in the case of an infinite-dimensional parameter is less studied. In this paper we propose a new method for obtaining sufficient conditions for local parameter identifiability in the case of an infinite-dimensional parameter. Under these conditions an infinite-dimensional parameter belonging to certain classes is locally identifiable by observing a solution at a finite set of points. For system with linear dependence on a parameter we establish the genericity of the mentioned conditions. 

Keywords:

differential equation, local parameter identifiability, genericity​​

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References

Литература

1. Бодунов Н. А. Введение в теорию локальной параметрической идентифицируемости. Санкт-Петербург, Изд-во С.-Петерб. ун-та (2006).

2. Бодунов Н. А., Вольфсон Г. И. Локальная идентифицируемость систем с переменным параметром. Дифференциальные уравнения и процессы управления 2, 17-31 (2009). URL: https://diffjournal.spbu.ru/pdf/volfson.pdf (дата обращения: 03.02.2023).

3. Бодунов Н. А., Колбина С. А., Пилюгин С. Ю. Локально параметрически идентифицируемые системы типичны. Вестник Санкт-Петербургского университета. Сер. 1, вып. 2, 16-20 (2012).

4. Бодунов Н. А., Колбина С. А., Пилюгин С. Ю. Превалентность локально параметрически идентифицируемых систем. Вестник Санкт-Петербургского университета. Сер. 1 2 (60), вып. 4, 517-523 (2015).

5. Хирш М. Дифференциальная топология, пер. с англ. Москва, Мир (1979).

References

1. Bodunov N.A. An introduction to the theory of local parameter identifiability. St. Petersburg, St. Рetersburg University Press (2006). (In Russian)

2. Bodunov N.A., Volfson G. I. Local identifiability of systems with a variable parameter. Differential Equations and Control Processes 2, 17-31 (2009). Available at: https://diffjournal.spbu.ru/pdf/volfson.pdf (accessed: February 3, 2023). (In Russian)

3. Bodunov N.A., Kolbina S.A., Pilyugin S.Yu. Locally parameter identifiable systems are generic. Vestnik St. Petersburgskogo Universiteta. Ser. 1, iss. 2, 16-20 (2012). (In Russian)

4. Bodunov N.A., Kolbina S.A., Pilyugin S.Yu. Prevalence of locally parameter identifiable systems. Vestnik St. Petersburg University Ser. 1 2 (60), iss. 4, 517-523 (2015). (In Russian)

5. Hirsch M.W. Differential topology. New York, Springer (1976). doi.org/10.1007/978-1-4684-94495 [Rus. ed.: Hirsch M. Differencial’naya topologiya. Moscow, Mir Publ. (1979)].

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Published

2023-12-23

How to Cite

Pilyugin, S. Y., & Shalgin, V. S. (2023). Conditions of local parameter identifiability for systems of differential equations with an infinite-dimensional parameter. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(4), 749–761. https://doi.org/10.21638/spbu01.2023.411

Issue

Vol. 10 No. 4 (2023)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.