On a class of optimal control problems with variable time points in the objective and constraint functionals

Abstract

We develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on a set of variable time points. Control parametrization and a time scaling transformation are used to approximate this type of optimal control problem by an optimal parameter selection problem. This approximate optimal parameter selection problem can be viewed as a finite dimensional optimization problem. On this basis, gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be applied. For illustration, a numerical example is solved.