Sparsity Measures in Spatially Distributed Systems

February 28, 2014, Webb 1100

Nader Motee

Lehigh University, Mechanical Engineering & Mechanics


A new theory of compressive feedback control (CFC) design for spatially distributed systems within the areas of distributed control systems, operational research, and machine learning is emerging. The CFC theory asserts that feedback control design for a certain class of spatially distributed systems can be spatially localized using far less sensor measurements than traditional control design techniques. Moreover, the CFC theory exploits the fact that the quadratically optimal state feedback controllers for many real-world systems are sparse and spatially localized in the sense that they have near-optimal sparse information structures. In this talk, I will introduce an important and omnipresent class of spatially distributed systems, so called spatially decaying systems. Examples of spatially decaying systems include spatially distributed power networks with sparse interconnection topologies, multi-agent systems with nearest neighbor coupling structures, arrays of micro-mirrors, micro-cantilevers, and sensor networks. The common fundamental property of all these systems is that there is a notion of spatial distance with respect to which couplings between the subsystems can be quantified using a class of coupling weight functions. Then, I will describe a newly developed mathematical framework, based on notions of quasi-Banach algebras of spatially decaying matrices, to relate spatial decay properties of spatially decaying systems to sparsity features of their underlying information structures. The bridge connecting these two notions is built upon several cornerstones. I will discuss some of the fundamental insights and tools that will allow us to exploit architectural properties of the underlying systems in order to introduce system-oriented sparsity measures for spatially distributed systems.

Speaker's Bio

Nader Motee is a P.C. Rossin assistant professor in the Mechanical Engineering and Mechanics Department at Lehigh University. Before joining Lehigh, he was a postdoctoral scholar at the Control and Dynamical Systems Department at Caltech and a visiting scholar at UCSB. He received a PhD degree in electrical and systems engineering from the University of Pennsylvania in 2007. His research interests include theoretical foundation of distributed control systems and optimization with applications to power grid, network of autonomous vehicles, and biological systems. Motee received an AFOSR Young Investigator Award in 2013, the 2008 O. Hugo Schuck Award for Theory of the American Automatic Control Council, the Student Best Paper Award at the American Control Conference in 2007, the Joseph and Rosaline Wolf Award for Best PhD Dissertation in 2008, and was a finalist for the Student Best Paper Award at the American Control Conference in 2006, and the IEEE Region 8 Student Paper Contest in 2000.

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