Graph Decomposition for Large-Scale Dynamical System Analysis

The DBAI Group will host a talk by James Anderson on April 24, 2015.

ABSTRACT

In this talk I will consider the problem of stability verification of large-scale dynamical systems using techniques from convex optimization and algebraic graph theory. Two approaches will be presented that rely on an appropriate graph decomposition scheme. In the first case, a dynamical system will be represented as a graph and we will decompose the system into a set of interacting subsystems using a max-cut approach and then pursue a composite stability analysis. The second approach exploits a relationship between sparse positive semidefinite matrices and chordal graphs to reduce the dimension of the constraint space in a semidefinite optimization programme. Motivating examples, including optimization over the (relaxed) space of positive polynomials will be given.