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Phased Analytical Modeling of "One-vs-All" Combat Operations Based on the "Mean Dynamics" Model
https://doi.org/10.17587/mau.27.361-372
Abstract
An analytical method for the step-by-step modeling of "one-versus-all" combat operations based on the "mean-field dynamics" model is proposed. It is shown that finding the functions describing the change in the number of groups on each side does not require solving the general eigenvalue problem for the lethality matrix, which is necessary in the classical operator method. Instead, the images of the group sizes are formed based on an algorithm for expanding the characteristic determinant, enabling a selective search for the necessary transfer functions of the system based on computational efficiency. The original functions describing the change in the number of groups on each side are found using residues for images of a repeating standard form, invariant to the model order. The pole values required for the calculations are found using elementary operations. The modeling takes into account the objective necessity of dividing the confrontation process into stages as the participating groups of the "all" side are eliminated, in contrast to the situation where the "one" side is destroyed first. Calculation formulas are provided for conditional time points that characterize either the end of the battle or the moment of transition to a new stage with model reduction upon the destruction of one of the components of the "all" side. The conjugation of the functions describing the change in the number of groups, calculated step-by-step, is performed with a shift in conditional time. The proposed analysis procedures are illustrated by a modeling example in Mathcad 14.0, including a comparison with known numerical methods. It is shown that the built-in numerical integration functions in Mathcad 14.0 are "incapable" of solving the problem and lead to rough results. At the same time, the approximation of the matrix exponential using the method of functionally transformed matrices leads to estimates that practically coincide with those obtained analytically.
About the Author
A. V. Zemskov
Federal State Budgetary Educational Institution of Higher Education "Admiral S. O. Makarov State University of Maritime and Inland Shipping"
Russian Federation
Russian Federation
Zemskov A. V., Dr. of Tech. Sc., Professor
Saint Petersburg
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Review
For citations:
Zemskov A.V. Phased Analytical Modeling of "One-vs-All" Combat Operations Based on the "Mean Dynamics" Model. Mekhatronika, Avtomatizatsiya, Upravlenie. 2026;27(7):361-372. (In Russ.) https://doi.org/10.17587/mau.27.361-372
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