SEARCH FOR AN APPROXIMATE SOLUTION TO A NONLINEAR PROBLEM OF OPTIMALPERFORMANCE BASED ON EVOLUTIONARY COMPUTATIONS
E. V. Antipina1, S. A. Mustafina1, A. F. Antipin2
1Ufa University of Science and Technology, Ufa, Russia
2Sterlitamak Branch of Ufa University of Science and Technology, Sterlitamak, Russia
Keywords: optimal performance problem, artificial immune systems, nonlinear controllable systems, evolutionary methods
Abstract
The article problem of optimal performance for a process described by a system of nonlinear differential equations is considered. To determine an approximate solution to the problem, it is proposed to apply the evolutionary method of artificial immune systems, which offers an advantage of the lack of sensitivity to the choice of the initial approximation. To find a numerical solution to the problem of optimal performance, a step-by-step algorithm is formulated, whose operation is tested on a model problem. Suboptimal control in terms of response time is obtained, and the algorithm parameters are determined that allow one to calculate the problem solution with the least computational costs. The efficiency of the developed algorithm is demonstrated by comparing the results of numerical calculations with the results of applying the fixed-point method.
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