Methods of averaged optimization in the problem of extending the rate of sliding of the right side discontinuity surface

For the problem of extending the rate of sliding of a dynamic system with discontinuous right sides, a generalization of the A. F. Filippov method of speed averaging was proposed. In the multidimensional case, this extension was shown to be reducible to the averaged problem of nonlinear programming. The methods of averaged optimization were shown to be applicable to calculation of the sliding rate. Consideration was given to the problems with different dimensions of the vector of admissible rates and number of control discontinuity surfaces.