Identification of Parameters of Nonlinear Dynamical Systems Simulated by Volterra Polynomials

• Published in: Journal of applied and industrial mathematics Vol. 12; no. 2; pp. 220 - 233
• Main Authors: Boikov, I. V., Krivulin, N. P.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.04.2018; Springer Nature B.V
• Subjects: Computer simulation; Discrete systems; Dynamical systems; Identification methods; Integral transforms; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Nonlinear systems; Parameter identification; Polynomials; Theorems; Volterra kernel; identification; Volterra series; nonlinear system; simulation; dynamical system
• ISSN: 1990-4789; 1990-4797
• DOI: 10.1134/S1990478918020035

We study the identification methods for the nonlinear dynamical systems described by Volterra series. One of the main problems in the dynamical system simulation is the problem of the choice of the parameters allowing the realization of a desired behavior of the system. If the structure of the model is identified in advance, then the solution to this problem closely resembles the identification problem of the system parameters. We also investigate the parameter identification of continuous and discrete nonlinear dynamical systems. The identification methods in the continuous case are based on application of the generalized Borel Theorem in combination with integral transformations. To investigate discrete systems, we use a discrete analog of the generalized Borel Theorem in conjunction with discrete transformations. Using model examples, we illustrate the application of the developed methods for simulation of systems with specified characteristics.