Computation of derivatives for structure preserving optimal control using automatic differentiation

In this work we combine a recently developed method, Discrete Mechanics and Optimal Control (DMOC), with the well established Automatic Differentiation package ADOL-C. DMOC is based on the discretization of the variational structure of the mechanical system which leads to structure (symplectic-momentum) preserving time-stepping equations. The discretized equations provide equality constraints for the resulting finite dimensional nonlinear optimization problem. For the solution of this problem standard nonlinear optimization techniques like sequential quadratic programming (SQP) are used. To ensure robustness of these techniques the computation of derivatives of the objective function and the constraints is of great importance. The concept of Automatic Differentiation (AD) is used to improve the performance of the SQP method. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)