## Systems and Control Seminars for the Summer Semester 2013

### Geometric Integration and Numerical Optimal Control Methods

### Speaker

Sina Ober-Blöbaum
Computational Dynamics and Optimal Control

Department of Mathematics

University of Paderborn

### Time and Place

The presentation will be given on September 9, 2013 at 2.00 p.m. in building 07, room 208.

### Abstract

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.

### Information about the Speaker

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

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