ON EQUIVALENCE OF LINEAR CONTROL SYSTEMS AND ITS USAGE TO VERIFICATION OF THE ADEQUACY OF DIFFERENT MODELS FOR A REAL DYNAMIC PROCESS

Autor:	Vasiliy Ye. Belozyorov, Danylo V. Dantsev, Svetlana A. Volkova
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	linear time-invariant control system system of ordinary autonomous differential equations complete linear group special linear group exterior degree algebraic invariant null-form neural network activation function Mathematics QA1-939
Zdroj:	Journal of Optimization, Differential Equations and Their Applications, Vol 28, Iss 1, Pp 43-97 (2020)
Druh dokumentu:	article
ISSN:	2617-0108 2663-6824
DOI:	10.15421/142002
Popis:	A problem of description of algebraic invariants for a linear control system that determine its structure is considered. With the help of these invariants, the equivalence problem of two linear time-invariant control systems with respect to actions of some linear groups on the spaces of inputs, outputs, and states of these systems is solved. The invariants are used to establish the necessary equivalence conditions for two nonlinear systems of differential equations generalizing the well-known Hopfield neural network model. Finally, these conditions are applied to establish the adequacy of two neural network models designed to describe the behavior of a real dynamic process given by two different sets of time series.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/a002332826d4444d847e0e1b2783d8d8 Zobrazit plný text záznamu View record in DOAJ