Numerical Sensitivity Analysis for Parametric Ordinary Differential Equations

Dr. Ralf Hannemann-Tamás

RWTH Aachen

Monday, January 11, 2016, 10:30

Room 02-014, Georges-Koehler-Allee 103, Freiburg 79110, Germany

Nonlinear model-predictive control algorithms for continuous ODE models are often based on direct shooting methods. In general the associated numerical optmization algorithm has to be fed with first- and possibly second-order derivatives of the objective and constraint functions. One possibility to efficiently compute first-order derivatives is the newly developed NMPC-tailored Rosenbrock-type sensitivity integrator Rosi. Rosi features variable step-size, stiffly accurate, A- and L-stable integration. Additionally, Rosi implements internal numerical differentiation for the computation of exact first-order sensitivities and implements a recording/replay-strategy to guarantee continuity and differentiability for small parameter changes. The required derivatives of the model residuals are obtained by algorithmic differentiation, where we provide an easy-to-use interface to the algorithmic differentiation software “dcc” of Uwe Naumann. The “Rosi-dcc” framework has been successfully tested on an embedded platform. In addition to the presentation of Rosi, some recent results on (higher-order) adjoint sensitivity analysis of (non-smooth) differential-algebraic equation systems are presented.