Numerical Method of Synthesized Control for Solution of the Optimal Control Problem

The new computing method of solution of a classical problem of optimum control is considered. The method demands preliminary transformation of right part of a system of differential equations of mathematical model of an object of control to a form of the contracting mapping. The decision represents piecewise constant vector function which switches the provision of the fixed points of the contraction mapping. As a result, we receive sustainable solutions to a problem of optimum control. Received solutions are less sensitive to indignation of model and to an integration step. For ensuring property of the contraction mapping the evolutionary method of symbolical regression is used. Numerical examples of the solution of a problem of optimum control of group of mobile robots with phase restrictions are reviewed. © 2020, Springer Nature Switzerland AG.