Optimal Control with Sweeping Processes: Numerical Method

This paper focuses on numerical methods for a class of optimal control problems involving sweeping processes. We consider a problem, where the sweeping set is constant and coincides with the 0 level set of a C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^2$$\end{document} convex function. For such problems, we propose a numerical method based on a sequence of approximating standard optimal control problems. We illustrate our method treating numerically an example.