Abstract
This paper discusses a method for constructing Volterra polynomials in the case of a vector input signal. The key idea behind the new approach to constructing integral polynomials is based on the identification of integrals from Volterra kernels. We describe in detail the numerical modeling of a multi-input dynamic system using the cubic Volterra polynomial. This approach is based on solving a specific system of linear algebraic equations (SLAE) obtained by approximating multidimensional convolutions by the product integration method (pi-method). The pi-approximation makes it possible to avoid essential difficulties arising in the solution of multidimensional Volterra equations of the first kind. The numerical efficiency is tested for the problem of modeling the nonlinear dynamics of a heat exchanger element. The results of the computational experiment showed that in most cases the new approach increases the accuracy of modeling.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Raibman, N.S.: Identification of control objects (a rewiew). Avtomatika i telemekhanica 6, 80–93 (1979)
Kleiman, E.G.: Identification of input signals in dynamic systems. Avtomatika i telemekhanica 12, 3–15 (1999)
Karelin, A.E., Maistrenko, A.V., Svetlakov, A.A., Kharitonov, S.A.: Synthesis of the method of automatic control of processes that is based on the concept of inverse dynamics problems. Omsk Sci. Bull. 4(154), 83–86 (2017)
Verlan’, A.F., Sizikov, V.S.: Integral Equations: Methods, Algorithms, Programs. Naukova Dumka, Kiev (1986)
Brunner, H.: Volterra Integral Equations: An Introduction to Theory and Applications. Cambridge University Press, Cambridge (2017)
Volterra, V.: Theory of Functionals and of Integral and Integro-Differential Equations. Dover Publications, New York (1959)
Cheng, C.M., Peng, Z.K., Zhang, W.M., Meng, G.: Volterra-series-based nonlinear system modeling and its engineering applications: a state-of-the-art review. Mech. Syst. Signal Process. 87, 340–364 (2017). https://doi.org/10.1016/j.ymssp.2016.10.029
Solodusha, S.V.: New classes of Volterra integral equations of the first kind related to the modeling of the wind turbine dynamics. In: 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference) (STAB) (2020). https://doi.org/10.1109/STAB49150.2020.9140662
Solodusha, S.V., Spiryaev, V.A., Tairov, E.A.: Numerical modeling of dynamics of thermal power equipment of the power unit at the Nazarovo power station by Volterra polynomial. In: XXI International Conference Complex Systems: Control and Modeling Problems (CSCMP) (2019). https://doi.org/10.1109/CSCMP45713.2019.8976749
Solodusha, S.V.: Quadratic and cubic Volterra polynomials: identification and application. Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr. 14, 131–144 (2018). https://doi.org/10.21638/11702/spbu10.2018.205
Apartsyn, A.S., Spiryaev, V.A.: On an approach to the identification of Volterra polynomials. Optimizaciya, upravlenie, intellekt. 2, 109–117 (2005)
Linz, P.: Product integration method for Volterra integral equations of the first kind. BIT Numer. Math. 11, 413–421 (1971)
Apartsyn, A.S.: Nonclassical Linear Volterra Equations of the First Kind. VSP, Utrecht (2003)
Tairov, E.A.: Nonlinear modeling of heat exchange dynamics in a duct with one-phase heat carrier. Bull. Acad. Sci. USSR. Ser. Energy Transport. 1, 150–156 (1989)
Solodusha, S.V.: Software package “Dynamics” for studying dynamic processes by Volterra series. Bull. South Ural State Univ. Ser. Comput. Technol. Autom. Control Radio Electron. 17, 83-92 (2017). https://doi.org/10.14529/ctcr170207
Acknowledgements
The research was carried out under State Assignment of the Ministry of Science and Higher Education of the Russian Federation (Project FWEU-2021-0006, theme No. AAAA-A21-121012090034-3).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Solodusha, S. (2022). Identification of Integral Models of Nonlinear Multi-input Dynamic Systems Using the Product Integration Method. In: Smirnov, N., Golovkina, A. (eds) Stability and Control Processes. SCP 2020. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-87966-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-030-87966-2_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-87965-5
Online ISBN: 978-3-030-87966-2
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)