Full algorithmic differentiation of a Rosenbrock-type method for direct single shooting

Direct single shooting for optimal control by means of gradient-based numerical optimizers requires sensitivity information. We provide this sensitivity information by means of the full algorithmic differentiation (AD), also referred to as first-discretize-then-differentiate, of a stiffly accurate Rosenbrock-type method with variable step size. In this context, full algorithmic differentiation means that the model equation and the numerical integrator, including the step control mechanism, are simultaneously processed by an AD tool. The fully differentiated Rosenbrock type integrator is interfaced to the nonlinear programming (NLP) solver SNOPT. We compare the robustness of the fully algorithmically differentiated solver with the sensitivity integrator IDAS which represents the approach of first-differentiate-then-discretize. With respect to the optimization by means of SNOPT the numerical experiments with a small nonlinear optimal control problem indicate that the first-discretize-then-differentiate approach is more robust and may reduce the overall computational costs.