MATEC Web Conf.
Volume 226, 2018XIV International Scientific-Technical Conference “Dynamic of Technical Systems” (DTS-2018)
|Number of page(s)||6|
|Section||4 Fundamental methods of system analysis, modeling and optimization of dynamic systems|
|Published online||07 November 2018|
The theory of nonlinear systems as an instrument for solving engineering problems
1 Don State Technical University, 344002 Rostov-on-Don, Russian Federation
2 Russian State Agrarian University named after K.A. Timiryazev, 127550 Moscow, Russia
* Corresponding author: firstname.lastname@example.org
The article outlines theoretical, methodological and practical issues of modern control and optimization theory, as well as the problems of nonlinear systems theory. Theoretical conclusions and results allowed to build mathematical models applicable to the management of objects of different nature with different principles of action, in particular, to the management of complex technical and technological objects that can be considered as nonlinear dynamic systems. The authors find it appropriate to consider nonlinear dynamic integral models as Volterra integro-power series from many functional arguments with multidimensional weight functions and a certain finite set of inputs to the system. The set of multidimensional kernels of integral Volterra operators completely characterizes the nonlinear and dynamic properties, and, consequently, the technical state of the initial system. The application of Volterra series based models allows to take into account the nonlinear and inertial properties of the initial nonlinear dynamic system more fully and accurately, it also makes the model diagnostic of a technical system more universal, raises the reliability of the forecast. The diagnostic procedure in this case is aimed at defining Volterra kernels based on the data of “input-output” experiment and building the diagnostic system of attribute in the space of which the decisive rule of optimal classification is created.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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