A possible approach to ensuring the necessary qualitative properties of analytical models by adapting their parameters to probable changes in the course of complex processes is considered. The approach involves the use of a polymodel description of processes with the aim of mutual compensation of the objective shortcomings of heterogeneous models, as well as the use of simulation modeling capabilities to adjust the parameters of analytical models in cases where the use of the latter is due to strict limitations on the time of obtaining calculation results and developing control influences based on them. The considered example of parametric adaptation of the Lanchester-type model reflects probable changes in the number of opposing sides during the conduct of hostilities.
This study provides a brief overview of the application of possible modifications of Lanchester-type models, namely, the representation of differential equations of such models in stochastic form. The stochastic setting of differential levels is used in Dynamic models if it is necessary to take into account the influence of random fluctuations (in particular, in radio engineering, thermodynamics, population dynamics models, etc.). As for Lanchester-type models, their stochastic appearance would allow considering the influence of random factors and elements of uncertainty, which are present to a certain extent in any combat operations. At the same time, unlike deterministic models, the numerical solution of systems of stochastic differential equations in such models requires the use of special methods, the choice of a specific one may be based on the requirements for the need to obtain an unambiguous approximate solution, or the probability distribution of the desired quantities. The possibility of obtaining different types of solutions is due to a characteristic feature of the developed methods for numerical integration of stochastic differential equations, namely, the existence of weak and strong approximate methods for solving them. For Lanchester equations, as models for predicting the probable course and results of combat operations, it seems appropriate to obtain a solution precisely in the form of parameters for distributions of random variables, which is possible after processing the results of using weak numerical methods. In addition, such methods are considered easier to implement in practice. Of particular note are the issues of estimating the stability of solutions (in the sense of Lyapunov) of stochastic models. While for Lanchester-type models, approximate practical methods for estimating stability can be considered, especially in relation to the simplest, linear statements of basic equations. The study considers an example of using the stochastic Lanchester-type model based on a system of linear inhomogeneous differential equations, with assumptions about the stability of solutions to the stochastic formulation of such equations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.