Density Functions for Mesh Refinement in Numerical Optimal Control

This paper introduces an efficient and simple method for mesh point distribution for solving optimal control problems using direct methods. The method is based on density (or monitor) functions, which have been used extensively for mesh refinement in other areas such as partial differential equations and finite element methods. Subsequently, the problem of mesh refinement is converted to a problem of finding an appropriate density function. It is shown that an appropriate choice of density functionmay help increase the accuracy of the solution and improve numerical robustness.