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

Abstract

Abstract 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. Copyright © 2002 John Wiley & Sons, Ltd.