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.
James Anderson is currently a Junior Research Fellow at St. John’s College, University of Oxford. He completed his D.Phil in Engineering Science at Oxford in 2012. Prior to this he obtained a B.Sc and M.Sc in engineering from the University of Reading. His research deals with the analysis and design of large-scale networked systems. Using techniques from robust control theory, dynamical systems, graph theory and convex optimisation he is interested in developing mathematical and algorithmic techniques capable of taking into account the underlying nonlinearities and uncertainty that real world systems exhibit. The goal of this research is to design feedback control laws that can optimise the performance of a network of interacting systems subject to noise from the environment. Such methods must provide guaranteed robust stability certificates and at the same time be computationally efficient to derive. Application areas of interest include power system networks, technological networks and synthetic biology.
This talk is organized by the Database & Artificial Intelligence Group at the Institute of Information Systems.