Peer-reviewed articles 17,970 +


Title: OPTIMAL CONTROL OF ECOLOGICAL SYSTEMS NEAR THE EQUILIBRIUM POSITION
OPTIMAL CONTROL OF ECOLOGICAL SYSTEMS NEAR THE EQUILIBRIUM POSITION

PlumX Article Metrics by Elsevier
L. K. Babadzanjanz; I. Yu. Pototskaya; Yu. Yu. Pupysheva; V. S. Korolev
10.5593/sgem2023/5.1/s20.23
10.5593/sgem2023/5.1
1314-2704
978-619-7603-60-6
English
23
5.1
•    Prof. DSc. Oleksandr Trofymchuk, UKRAINE 
•    Prof. Dr. hab. oec. Baiba Rivza, LATVIA
Ecology and Environmental Protection
The problem of the ecological system long-term keeping near the equilibrium position with minimization of control resources is considered. A mathematical formulation of this problem and a method for optimal expenditure control constructing are presented. While deviations from the equilibrium point are very small, its controlled dynamics can be described by linear differential equations with constant coefficients. The control actions are modeled by piecewise-constant unidirectional functions with a finite number of switching points. The choice of this control class is due to the characteristic features of environmental tasks: control actions on living systems are unidirectional and often have a periodic character [3], [5-11]. It can be individuals catching from the population, feeding, watering, thinning, etc. Therefore, the chosen control class takes into account both the unidirectionality and the periodicity of the control actions. Two types of regulation are discussed: adding to the system any substances promoting the population growth (substrates, fertilizers, etc.), and removal of any volumes (catching individuals from the population, thinning, etc.). As a minimizable functional, the expenditure criterion is used, that is proportional in practice to the consumption of resources used for controlling [1], [4]: pesticides, fertilizers, medicines, etc. In some cases, this criterion minimizing, in addition to the economic one, also gives a direct environmental effect. For example, the constructed optimal control allows the pest population to be destroyed with the minimum quantity of toxic chemicals that adversely affect the environment. The method for solving the problem is based on the mechanical systems optimal control problems methods of solution developed by the authors (e.g. [2]). In this paper, taking into account the ecological specifics of the problem, the system of transcendental equations is obtained. Numerical solution of this system allows us to find the control switching points that satisfy the necessary conditions of the expenditure criterion extremum. To find an adequate initial approximation for the standard numerical methods for solving the equations system an original algorithm is presented.
[1] Afanasyev V.N, Kolmanovsky V.B., Nosov V.R., Mathematical theory of control system construction, Russia, 2003, pp. 614.
[2] Alesova I.M., Babadzanjanz L.K., A.M. Bregman A.M., K.M. Bregman K.M., Pototskaya I.Yu., Pupysheva Yu.Yu., Saakyan A.T., Piecewise constant control of linear mechanical systems in the general case, Greece, AIP Conference Proceedings 1978, pp. 1-4, 2018.
[3] Alexandrov A.Yu., Platonov A.V., Starkov V. N., Stepenko N. Ah., Mathematical modeling and research of biological communities stability, Russia, 2016, pp. 272.
[4] Athans M., Falb P.L., Optimal Control: An Introduction to the Theory and Its Applications, USA, 2007, pp. 896.
[5] Bazykin A. D., Mathematical Biophysics of Interacting Populations, Russia, 1985, pp. 181.
[6] Crespo L.G., Sun J. Q., Optimal Control of Populations of Computing Species, Nonlinear Dynamics, Netherlands, vol.27/issue 2, pp. 197-210, 2002.
[7] Murray J. D., Mathematical Biology I: An Introduction, Germany, 2002, pp. 576.
[8] Riznichenko G. Yu., Mathematical Models in Biophysics and Ecology, Russia, 2003, pp. 184.
[9] Riznichenko G. Yu., Rubin A. B., Mathematical Models of Biological Production Processes, Russia, 2004, pp. 302.
[10] Smith J.M., Models in Ecology, UK, 1974, pp. 146.
[11] Zaslavsky B. G., Poluektov R. A., Ecological Systems Control, Russia,1988, pp. 296
conference
https://doi.org/10.5593/sgem2023/5.1/s20.23
Download PDF
Proceedings of 23rd International Multidisciplinary Scientific GeoConference SGEM 2023
23rd International Multidisciplinary Scientific GeoConference SGEM 2023, 03 - 09 July, 2023
Proceedings Paper
STEF92 Technology
International Multidisciplinary Scientific GeoConference SGEM
SWS Scholarly Society; Acad Sci Czech Republ; Latvian Acad Sci; Polish Acad Sci; Serbian Acad Sci and Arts; Natl Acad Sci Ukraine; Natl Acad Sci Armenia; Sci Council Japan; European Acad Sci, Arts and Letters; Acad Fine Arts Zagreb Croatia; Croatian Acad Sci and Arts; Acad Sci Moldova; Montenegrin Acad Sci and Arts; Georgian Acad Sci; Acad Fine Arts and Design Bratislava; Turkish Acad Sci.
185-192
03 - 09 July, 2023
website
9291
optimal control of ecological systems, control with expenditure criterion, an ecological system near equilibrium position, controlled linear ODE system