This talk focuses on different aspects of variational integrators (so-called geometric integrators) and their use for numerical optimal control methods.
The key feature of variational integrators is that the time-stepping schemes are derived from a discrete variational principle based on a discrete action function that approximates the continuous one. The resulting schemes are structure preserving, i.e. they are symplectic-momentum conserving and exhibit good energy behaviour, meaning that no artificial dissipation is present and the energy error stays bounded over longterm simulations.
For the numerical solution of optimal control problems, direct methods are based on a discretization of the underlying differential equations which serve as equality constraints for the resulting finite dimensional nonlinear optimization problem. For the case of mechanical systems, the presented method, denoted by DMOC (Discrete Mechanics and Optimal Control), is based on the discretization of the variational structure of the system directly and thus inherits the structure preservation properties of variational integrators.
Different approaches are discussed to obtain integration schemes of higher accuracy such as higher order variational methods and multirate integrators. Furthermore, we will demonstrate how to exploit inherent properties of the dynamical system to find good initial guesses such that the global optimal solution can be approximated. The applicability of the algorithms is demonstrated by different examples from mechanical and electrical engineering.
2004 Dipl. Math., Diploma in Technomathematics, University of Paderborn
2008 Dr. rer. nat, PhD in Applied Mathematics, University of Paderborn
2008-2009 Postdoctorial Scholar, California Institute of Technology
2009 -
Jun.-Professor, Computational Dynamics and Optimal Control, Department of Mathematics, University of Paderborn
2011-2012 substitute professorship (W2) for Applied Mathematics, Zentrum Mathematik, Technische Universität München