Optimal control on Lie groups: The projection operator approach

Alessandro Saccon (Instituto Superior Tecnico (IST), Lisbon, Portugal )

SYSTEMS AND CONTROL SERIES

DATE: 2011-04-11
TIME: 16:30:00 - 17:20:00
LOCATION: Engineering Lecture Theatre
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ABSTRACT:
Many nonlinear systems of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. Examples range from aircraft and underwater vehicles to quantum mechanical systems. The Lie group projection operator approach is an iterative algorithm for solving continuous-time optimal control problems on Lie groups. In the talk, we will discuss the main ideas that defines this approach and, in particular, the formulas to compute the time-varying linear quadratic problem required in computing the optimal descent direction. A numerical example will be provided to demonstrate the effectiveness of the method and to highlight the second order converge rate.

BIO:
Alessandro Saccon received the laurea degree "summa cum laude" in computer engineering from the University of Padova, Italy, in October 2002 and received a PhD degree in control system theory from the same institution on March 2006, with a scholarship from MSC.Software Corporation. From April 2006 to December 2008, he has been a postdoc at the Department of Information Engineering, University of Padova, Italy, working on control and optimization methods for the exploration of the dynamics of racing motorcycles for virtual prototyping studies. Currently, he is a postdoctoral scholar at the Institute for Systems and Robotics, Instituto Superior Tecnico, Lisbon, Portugal, working on dynamic motion planning algorithms and identification methods for autonomous underwater vehicles (AUV). His research interests include optimal control theory, applied optimization, motorcycle dynamics and control, underwater vehicle dynamics and control, geometric mechanics, variational integrators, maneuver regulation of nonlinear systems, and receding horizon control.