Solving a Class of Non-Smooth Optimal Control Problems

Abstract

In this paper, we first propose a new generalized derivative for non-smooth functions and then we utilize this generalized derivative to convert a class of non-smooth optimal control problem to the corresponding smooth form. In the next step, we apply the discretization method to approximate the obtained smooth problem to the nonlinear programming problem. Finally, by solving the last problem, we obtain an approximate optimal solution for main problem

On the Validity of Nonlinear and Nonsmooth Inequalities

“…A similar approach is g iven [13] to solve the nonsmooth optimizat ion problems. Also, some other types of GDs are presented in [14,15].…”

“…Assume (see [6,7]). Here, by assumption (where M is a sufficiently big number), the infinite dimensional nonsmooth optimization problem (11) can be approximated to the follo wing finite d imensional smooth problem (see [12]): (12) Further, in [11,12] , to obtain the optimal solution of the NLP problem (15), and then obtain an approximate optimal solution for the nonsmooth optimization problem (2) to determine the validity of nonsmooth inequality (1).…”