DOI
10.34229/KCA2522-9664.26.5.8
UDC 355/359.07:519.816
I.B. Chepkov
Central Scientific Research Institute of Armament and Military Equipment of Armed
Forces of Ukraine, Kyiv, Ukraine, 
chepkov@gmail.com
I.V. Borokhvostov
Central Scientific Research Institute of Armament and Military Equipment of Armed
Forces of Ukraine, Kyiv, Ukraine, borohvostov@icloud.com
V.S. Komarov
Scientific and Research Institute of Military Intelligence, Kyiv, Ukraine,
komarvlad@ukr.net
M.P. Sen
Central Scientific Research Institute of Armament and Military Equipment of Armed
Forces of Ukraine, Kyiv, Ukraine, M.Sen@mil.ua
TOPOLOGY AND METRIC OF THE CHARACTERISTIC SPACE OF COMPLEX TECHNICAL
SYSTEMS IN THE CONTEXT OF THE COUPLED LAGRANGIAN–EULERIAN MODEL
OF THEIR DEVELOPMENT DYNAMICS
Abstract. The paper establishes the topological and metric foundation for a mathematically rigorous formalization of the coupled Lagrangian–Eulerian (CLE)
model of complex technical system (CTS) development dynamics. The characteristic space of a CTS is defined as a
compact topological manifold with boundary, embedded in a finite-dimensional Euclidean
space subject to nonlinear constraints that include resource bounds for each characteristic; under the boundary regularity condition (LICQ), the space is a topological manifold with boundary. For probabilistic-functional CTS — including unmanned robotic systems, cybersecurity systems, and adaptive communication networks — the canonical choice of the Fisher–Rao metric is justified via the Chentsov uniqueness theorem; the weighted Euclidean metric is discussed for deterministic systems. A minimal set of differential-geometric objects is introduced — tangent space, Riemannian speed norm, Riemannian gradient of an efficiency function — and on this basis an exact mathematical definition of the material derivative is obtained as the central operator of the CLE model. This article is the first in a series of four papers on the mathematical theory of CTS evolution dynamics.
Keywords: complex technical systems, characteristic space, Riemannian manifold, Fisher–Rao metric, material derivative, coupled Lagrangian–Eulerian model.
full text
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