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"QUALITY - COST" OPTIMAL CONTROL IN LOTKA-VOLTERRA POPULATIONS MODEL
Abstract
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.
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