Jerrold E. Marsden received his PhD from Princeton University in 1968 in Applied Mathematics and is now the Carl F. Braun Professor of Engineering and Control and Dynamical Systems at Caltech. His primary current interests are in applied dynamics, control theory, and multiscale systems, especially how these subjects relate to dynamical and mechanical systems with symmetry, to numerical algorithms in computational mechanics, as well as to the dynamics and control of underwater vehicles in a dynamic ocean environment, and to astrodynamics and space mission design. He received the AMS-SIAM Norbert Wiener prize (1990), a Humboldt Senior Scientist award (1991, 1999), a Fairchild Fellowship (1992), a Max Planck Research Award (2000), and the SIAM von Neumann prize (2005). He is a fellow of the Royal Society of Canada and the American Academy of Arts and Science. He is an Editor of Springer-Verlag's Applied Mathematical Sciences Series and is on the editorial boards for a number of prominent journals in applied dynamics and mechanics. He currently serves as director of CIMMS, the Center for Integrative Multiscale Modeling and Simulation at Caltech, is on the Board of Trustees of SIAM, is on the Scientific Advisory board of the DFG Research Center ~SMathematics for Key Technologies~T, Berlin and is the scientific co-chair of ICIAM 2011.
This talk will outline new methods from discrete mechanics for stabilization and optimization of mechanical systems. The idea of discrete mechanics is to replace Hamilton's principle, possibly including dissipative or control forces, by a corresponding discrete version. These methods have led to the development of successful variational integrators for the dynamics of mechanical systems, including continuum mechanics. After reviewing this methodology for dynamics, we show how it is also useful for control. Optimization is illustrated using a fleet of hovercraft, underwater vehicles and spacecraft (with Oliver Junge and Sina Ober-Bloebaum) and for locomotion problems (with Eva Kanso).