Abstract
A two-level hierarchical organization system is used to consider a model for the optimal control of funds and competitive ability of an information–communication company. The model is based on a control problem for ordinary differential equations (that characterize the dynamics of funds) and on an initial–boundary-value problem for multidimensional quasilinear parabolic Lotka–Volterra equations (that describe the sales dynamics of competitive companies) and uses methods of optimal control for distributed-parameter systems. The sufficient existence conditions are established for the optimal control and a stable numerical algorithm is developed to search for optimal control functions.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
N. N. Moiseyev, Mathematical Problems of Systems Analysis [in Russian], Nauka, Moscow (1986).
M. Mesarovic, D. Macko, and Y. Takahara, Theory of Hierarchical Multilevel Systems, Acad. Press, New York (1997).
M. G. Singh and A. Titli (ed.), Systems: Decomposition, Optimization and Control, Pergamon Press, Oxford (1984).
D. A. Novikov, Network Structures and Organizational Systems [in Russian], IPURAN, Moscow (2003).
M. D. Intriligator, Mathematical Optimization and Economic Theory, Prentice Hall (1971).
A. G. Nakonechny and I. I. Sugonyak, “Optimal control processes modeling under uncertainty in economic systems with hierarchy,” J. Autom. Inform. Sci., 39, Issue 2, 62–72 (2007).
Y. Takeuchi, Global Dynamical Properties of Lotka–Volterra Systems, World Sci. Publ., Singapore (1996).
V. V. Akimenko and I. I. Sugonyak, “A model of optimal control over a nonlinear multidimensional innovation diffusion process,” Cybern. Syst. Analysis, 44, No. 4, 564–574 (2008).
V. V. Akimenko and I. I. Sugonyak, “Dynamic models of the lifecycle of innovations under uncertainty,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauk, No. 3, 149–155 (2007).
J. L. Menaldi, E. Rofman, and A. Sulem, Optimal Control and Partial Differential Equations—Innovations & Applications, IOS Press, Amsterdam (2001).
K. Kunisch, G. Leugering, J. Sprekels, and F. Troltzsch, “Control of coupled partial differential equations,” in: Intern. Series of Numerical Math., Vol. 155, Issue VI, Springer (2007).
E. B. Lee and L. Markus, Foundations of Optimal Control Theory, J. Wiley, New York (1967).
V. V. Akimenko and A. G. Nakonechnyi, “Optimal control models for interregional migration under social risks,” Cybern. Syst. Analysis, 42, No. 3, 398–410 (2006).
V. V. Akimenko, A. G. Nakonechnyj, and O. Yu. Trofimchuk, “An optimal control model for a system of degenerate parabolic integro-differential equations,” Cybern. Syst. Analysis, 43, No. 6, 838–847 (2007).
A. N. Tikhonov and V. Ya. Arsenin, Methods to Solve Ill-Posed Problems [in Russian], Nauka, Moscow (1986).
A. N. Kolmogorov and S. V. Fomin, Element of the Function Theory and Functional Analysis [in Russian], Nauka, Moscow (1989).
A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1989).
V. V. Akimenko and A. A. Yefimenko, “Numerical method for solving the diffusive Lotke–Volterra model with discontinuous coefficients for the problem of companies competition,” J. Autom. Inform. Sci., 44, Issue 4, 71–80 (2012).
O. K. Cheremnykh, “Modeling of vertical flows on the background of two-dimensional process of convective heat and mass transfer,” J. Autom. Inform. Sci., 36, Issue 3, 35–45 (2004).
V. V. Akimenko, A. G. Nakonechnyi, and S. D. Voloshchuk, “Scenarios of optimal control of transregional migration processes under risk,” Cybern. Syst. Analysis, 43, No. 1, 12–24 (2007).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2012, pp. 94–111.
Rights and permissions
About this article
Cite this article
Akimenko, V.V., Yefimenko, A.A. Model of the optimal control of funds and competitiveness of the information-communication company. Cybern Syst Anal 48, 722–735 (2012). https://doi.org/10.1007/s10559-012-9452-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-012-9452-5