Direct numerical solution of optimal control problems

A class of optimization problems is the state change of a dynamic system while minimizing a functional as a quality criterion. Such problems may be solved with the help of the Hamiltonian function, which allows to find an optimal control variable for the process. Given the boundary conditions for the system state variables x, it is necessary to find initial conditions for the adjunct variables ψ. Then the adjunct system can be solved in an iterative manner with classic ODE solvers. In this paper an alternative method based on recently developed methods for a direct numerical solution of such a problem is presented. The advantages are that it is not necessary to calculate an exponential matrix, and furthermore the approach is better suited for stiff systems than classical solvers.