 |
S.V. Solodusha, E.D. Antipina On Some Properties of Nonlinear Integral Models of Dynamic Processes |
 |
|
Abstract.
The paper presents algorithms for constructing dynamic models of technical (energy) systems in conditions of noisy data. We consider a class of nonlinear systems of Volterra-type integral equations of the first kind with an input signal consisting of two components. The problem of identifying the input signal of linear systems is well known when reduction to a system of equations of the second kind is performed by differentiating Volterra integral equations of the first kind. When constructing models, a control input action is formed that provides the specified response of the dynamic system. Identification algorithms based on the theory of Volterra polynomial equations are used. The paper considers the case with noisy initial data, including when the condition of non-degeneracy of matrices in front of the main part is violated at some fixed points in time.
Keywords:
identification, dynamic processes, integral models, Volterra polynomial equations of the first kind.
DOI 10.14357/20718632240209
EDN XQUEEY
PP. 92-99. References
1. Volterra V. Theory of functionals and of integral and integro-differential equations. Moscow: Nauka; 1982. 302 p. (In Russ). 2. Giannakis G.B., Serpedin E. A bibliography on nonlinear system identification // Signal Processing. 2001. Vol. 81. №3. P. 533-580. 3. Volkov N.V. Functional series in the problems of dynamics of automated systems. Moscow: Janus-K; 2001. 98 p. (In Russ). 4. Boykov I.V., Krivulin N.P. Identification of parameters of nonlinear dynamical systems simulated by Volterra polynomials // Sib. Zh. Ind. Mat. 2018; 21(2): 17-31 (In Russ). doi: 10.17377/sibjim.2018.21.201 5. Apartsin A.S., Solodusha S.V. Mathematical Simulation of Linear Dynamic Systems by Volterra Series // Engineering Simulation. 2000. Vol. 17. №2. P. 143-153. 6. Methods for research and control of energy systems. A.P. Merenkov, Yu.N. Rudenko (eds.). Novosibirsk: Nauka; 1987. 369 p. (In Russ). 7. Bakhtadze N.N., Lototsky V.A., Maksimov E.M., Maksimova N.E. Intelligent algorithms of power grid's state identification // Informatsionnye Tekhnologii i Vychslitel'nye Sistemy. 2011; 3: 45-50 (In Russ). 8. Bakhtadze N.N., Chereshko A.A., Kushnarev V.N. Scenario forecasting based on digital smart models of dynamic processes // Informatsionnye Tekhnologii i Vychslitel'nye Sistemy. 2023; 3: 70-78 (In Russ). doi: 10.14357/20718632230308 9. Solodusha S.V. Automatic control systems modeling by Volterra polynomials // Modelirovanie i Analiz Informatsionnykh Sistem, 2012; 19(1): 60-68 (In Russ). 10. Solodusha S.V. Modeling Heat Exchangers by Quadratic Volterra Polynomials // Automation and Remote Control. 2014. Vol. 75. №1. P. 87-94. 11. Apartsyn A.S. Polynomial Volterra equations of the first kind and the Lambert function // Trudy Inst. Mat. i Mekh. UrO RAN. 2012. Vol. 18. № 1. P. 69-81. 12. Bulatov M.V., Budnikova O.S. On Stable Algorithms for Numerical Solution of Integral-Algebraic Equations // Vestnik YuUrGU. Ser. Mat. Model. Progr. 2013; 6(4): 5-14 (In Russ). 13. Tairov E.A., Loginov A.A., Chistyakov V.F. Mathematical model, numerical methods and software of the simulator for the generating unit of the Irkutsk CHP-10. Irkutsk: SEI SB RAS; 1999. 43 p. Preprint no. 11 (In Russ). 14. Voskoboynikov Yu.E., Boeva V.A. An estimation of optimal scalar and vector parameters of a smoothing bicubic spline // International Research Journal. 2022; 4(118): 31-39 (In Russ). doi: 10.23670/IRJ.2022.118.4.006. 15. Voskoboinikov Yu.E., Preobrazhensky N.G., Sedelnikov A.I. Mathematical processing of experiment in molecular gas dynamics. Novosibirsk: Nauka; 1984 (In Russ). 16. Voskoboynikov Yu.E., Boeva V.A. L-curve method for evaluating the optimal parameter of a smoothing cubic spline // International Research Journal. 2021; 11(113), pt. 1: 6-13 (In Russ). doi: 10.23670/IRJ.2021.113.11.003.
|
