UDC 519.6
PSEUDO-INVERSION OF THE MATHEMATICAL MODELS
OF DISTRIBUTED DIFFERENTIAL SYSTEMS
WITH ADDITIVELY DEFINITE NONLINEARITY
Abstract. The author considers spatially distributed dynamic systems whose linear mathematical model
is complemented by a nonlinear differential term, obtained as the product of linear differential transformations
of state function or by replacing such transformations of coefficients of the linear approximation of the model.
Pseudo-inversions of the considered mathematical models, which are consistent with their differential representation
according to the root-mean-square criteria, are generated.
Keywords: pseudo-inversion, nonlinear dynamic systems, distributed-parameter systems, spatially distributed dynamic systems.
FULL TEXT
REFERENCES
- Skopetsky V.V., Stoyan V.A., Krivonos Iu.G. Mathematical modeling of direct and inverse problems of dynamics of systems with distributed parameters [in Ukrainian]. Kyiv: Nauk. Dumka, 2002. 361 p.
- Skopetsky V.V., Stoyan V.A., Zvaridchuk V.B. Mathematical modeling of the dynamics of distributed space-time processes [in Ukrainian]. Kyiv: Stal Publishing House, 2008. 316 p.
- Stoyan V.A. Mathematical modeling of linear, quasilinear and nonlinear dynamical systems [in Ukrainian]. Kyiv: VPC "Kyiv University", 2011. 320 p.
- Stoyan V.A., Dvirnychuk V.B. Before constructing the integral equivalent of linear differential models. Dop. NAN of Ukraine. 2012. N 9. P.36-43.
- Stoyan VA Methods of linear algebra in the problems of studying some classes of nonlinear discrete transforming systems. I. Multiplicatively nonlinear systems. Kibernetika i sistemnyj analiz. 2019. Vol. 54, N 1. P.127-134.
- Stoyan V.A. Methods of linear algebra in the problems of studying some classes of nonlinear discrete transforming systems. II. Systems with additively selected nonlinearity. Kibernetika i sistemnyj analiz. 2019. Vol. 54, N 2. P.102-107.
- Stoyan V.A. To the construction of integral mathematical models of two classes of nonlinear spatially distributed systems. I. The case of discretely defined external dynamic disturbances. Kibernetika i sistemnyj analiz. 2019. Vol. 55, N 5. P.115-127.
- Stoyan V.A. To the construction of integral mathematical models of two classes of nonlinear spatially distributed systems. II. The case of continuously defined external dynamic perturbations. Kibernetika i sistemnyj analiz. 2020. Vol. 56, N 1. P.118-128.
- Bulavatsky V.M., Krivonos Iu.G., Skopetsky V.V. Nonclassical mathematical models of heat and mass transfer processes [in Ukrainian]. Kyiv: Nauk. Dumka, 2005. 282 p.
- Bomba A.Y., Bulavatsky V.M., Skopetsky V.V. Nonlinear mathematical models of geohydrodynamic processes [in Ukrainian]. Kyiv: Nauk. Dumka, 2007. 291 p.
- Markovic B.M. Equation of mathematical physics [in Ukrainian]. Lviv: Vyd-vo NU В«LК№vivsК№ka politekhnikaВ», 2010. 383 p.
- Kirichenko N.F., Stoyan V.A. Analytical representation of matrix and integral linear transformations. Kibernetika i sistemnyj analiz. 1998. N 3. P. 90-104.
