New smoothing techniques for solving bang–bang optimal control problems – numerical results and statistical interpretation

In this paper, we investigate the solution of bang-bang optimal control problems by shooting methods. We will show how modifying the performance index by a term depending on a small parameter ϵ yields more regular controls and shooting functions. A continuation procedure on ϵ will lead us to a good approximation of the initial solution. Then, a statistical interpretation of the method is given, providing us with a general framework for building new regular controls. Finally, two numerical examples are solved illustrating the interest of our method.