Structural Properties of Spatially Distributed Systems

Dr. Nader Motee
California Institute of Technology

Friday, February 20, 2009 at 3:00pm
Engr IV Room 57-124

Abstract
Spatially distributed dynamical systems appear in several domains of engineering and science. Examples include multi-agent robotic systems, networks of embedded systems, arrays of mobile sensor networks for monitoring environment, platoon of vehicles in automated highways, deflection of beams and membranes, and the temperature distribution of thermally conductive materials. These systems can be described by a finite or infinite number of coupled subsystems that are possibly heterogeneous and of low dimensions. Even when each individual subsystem has a predictable behavior, the resulting spatially distributed dynamical system displays a rich and complex behavior when viewed as a whole. In this talk, we present a mathematical framework to study the structural properties of optimal control of linear spatially distributed dynamical systems with arbitrary interconnection topologies. Our aim is to determine to what extent the optimal control law is localized in space and that how much information from far away subsystems is required. Specifically, we prove that global features of spatially distributed dynamical systems such as stability and optimal performance are inherently localized in space. In this talk, we develop a mathematical framework using tools from functional analysis and operator theory to analyze the locality properties of optimal control problems involving infinite-horizon linear quadratic criteria and constrained receding horizon control. We will also briefly discuss how to apply the developed framework to design global state feedback controllers by using approximation methods and spatial interpolation of local controllers.

Biography
Nader received the M.Sc. and Ph.D. degrees in electrical and systems engineering from the University of Pennsylvania, Philadelphia, in 2006 and 2007, respectively. He is currently a Postdoctoral Scholar at the Control and Dynamical Systems at Caltech. He is the recipient of the 2008 O Hugo Schuck Award for theory of the American Automatic Control Council.