TY - GEN

T1 - Quality-cost optimal control in Lotka-Volterra populations model

AU - Babadzanjanz , L. K.

AU - Pototskaya, I. Y.

AU - Pupysheva , Y. Y.

AU - Saakyan , M. A. T.

N1 - Conference code: 19

PY - 2019

Y1 - 2019

N2 - The aim of this article is the studying of the “predator-prey” populations controlled interaction. The well-known Lotka-Volterra system ([1], [3], [5-15]) with control is used as a mathematical model. A complete research of this model is done: From its parameters identification to the choice of optimal control. The identification numerical algorithms are based on the Taylor series method. This method application is reasonable in this case, because right sides of the considered ODEs system can be presented in polynomial form. To select the best control, a number of algorithms based on the direct search are proposed. They allow to find the optimal ratio between the time, cost and accuracy of the perturbed system's returning to the equilibrium point. These algorithms are: The control's work areas constructing algorithm; the algorithm for the constructing a dependence the control’s cost of the distance to the target point; the algorithm for the constructing a dependence the distance of the control’s cost. The algorithms are implemented in the Matlab package and are tested on model examples. Analysis of the test results allows us to see changes in the system dynamics because of control, to compare control influences and choose from them the optimal one for the “quality-cost” balance.

AB - The aim of this article is the studying of the “predator-prey” populations controlled interaction. The well-known Lotka-Volterra system ([1], [3], [5-15]) with control is used as a mathematical model. A complete research of this model is done: From its parameters identification to the choice of optimal control. The identification numerical algorithms are based on the Taylor series method. This method application is reasonable in this case, because right sides of the considered ODEs system can be presented in polynomial form. To select the best control, a number of algorithms based on the direct search are proposed. They allow to find the optimal ratio between the time, cost and accuracy of the perturbed system's returning to the equilibrium point. These algorithms are: The control's work areas constructing algorithm; the algorithm for the constructing a dependence the control’s cost of the distance to the target point; the algorithm for the constructing a dependence the distance of the control’s cost. The algorithms are implemented in the Matlab package and are tested on model examples. Analysis of the test results allows us to see changes in the system dynamics because of control, to compare control influences and choose from them the optimal one for the “quality-cost” balance.

KW - ODE numerical integration

KW - Optimal control

KW - Parameters identification

KW - The Lotka-Volterra model

KW - The Taylor series method

UR - http://www.scopus.com/inward/record.url?scp=85073367908&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=42460142

U2 - 10.5593/sgem2019/5.1/S20.001

DO - 10.5593/sgem2019/5.1/S20.001

M3 - Conference contribution

T3 - International Multidisciplinary Scientific GeoConference-SGEM

SP - 3

EP - 10

BT - 19th International Multidisciplinary Scientific GeoConference SGEM 2019

PB - STEF92 Technology Ltd.

CY - София

T2 - 19th International Multidisciplinary Scientific Geoconference, SGEM 2019

Y2 - 9 December 2019 through 11 December 2019

ER -