CSCAMM Day 2010

Distributed optimizations and Banach algebras

Radu Balan

University of Maryland

The classical Wiener lemma states that the reciprocal of an absolutely Fourier series that does not vanish is also an absolutely convergent Fourier series. Using Banach algebras techniques, a non-commutative version of this result involving algebras of infinite matrices with certain off-diagonal decay has been obtained. In a different context, an interesting question arises in connexion to optimal control of large-scale systems. Specifically one would like to obtain solutions to Liapunov and Riccati equations that are well-localized. In this framework, localization is equivalent to distributed implementation of optimal controllers. The talk will present some results on this topic.