A modified control parametrization method for the numerical solution of bang–bang optimal control problems

Abstract

In the present paper, an efficient computational method for the solution of bang–bang optimal control problems is investigated. The method is based on control parametrization and belongs to the direct methods for numerical solution of optimal control problems. In this method, control functions are considered to be piecewise constant with values and switching points taken as decision variables. Thereby, the problem is converted into a mathematical programming problem which can be solved by well-developed parameter optimization algorithms. The main advantages of the present method are that: (i) it obtains good results and the switching points can be captured accurately; and (ii) an incorrectly guessed number of switching points can be detected by the results of the method. These are illustrated through three examples and the efficiency of the method is reported.