Computation of consistent initial values for optimal control problems with DAE systems of higher index

In recent years direct methods have been favored for solving optimal control problems with ODE systems. These approaches reduce the "infinite-dimensional" optimization problem to a finite-dimensional optimization problem by approximating the control and the state over a fixed grid. Because of special problems arising from differential-algebraic equation systems (DAE systems), e.g. the calculation of consistent initial values, the transfer of these ideas to DAE optimal control problems (DOCP) can not be done without further ado. Hence we suggest ideas for a direct solution of DOCP taking these problems into account and present numerical methods for the solution of higher index systems. A high dimensional example is discussed which shows the efficiency and robustness of the proposed methods.