Using the averaging method optimization problem of determining the velocity of the slip

A generalization of the method of averaging rates of A.F. Filippov to extend the definition of the problem of the sliding speed of the dynamic system with discontinuous right-hand sides. It is shown that in the multidimensional case, it reduces to the solution of the homogenized problem of nonlinear programming to calculate the speed of sliding methods may be used to optimize the average. The problems with the various dimensions of the vector speed limits and the number of gap control surfaces.