Conditions for the Optimality of the Averaged Problem of Nonlinear Programming and Synthesis of the Philippov's Theorem on Speed of Motion of Systems with the Discontinued Right Part of Differential Equations
Abstract
A generalization of the Filippov's velocity averaging method in the problem of determining the slip velocity of a dynamical system with discontinuous right-hand sides is proposed. It is shown that in the multidimensional case such an extension is reduced to the solution of the averaged nonlinear programming problem and the methods of averaged optimization can be used to calculate the slip velocity. Problems with various dimensions
