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SySOS: Systems of Systems and Sum of Squares

Our group develops tools and algorithms for the analysis and design of technological and biological systems and applies them in a range of areas, from fluid mechanics to Synthetic Biology. In particular, we have been developing theory to understand how nonlinear networked systems (System of Systems) operate how to design control laws for them, using computational tools based on the Sum of Squares decomposition and Semidefinite Programming. We have been applying this theory to understanding and (re)designing of biological systems (Systems and Synthetic Biology) but also the analysis and design of control laws for fluid flows, robust synchronization, multi-agent system consensus, smart power networks and congestion control for the Internet. Here is a short summary of the areas we work on - please follow the links below for more details.

  • Nonlinear systems analysis, Sum of Squares optimization and Lyapunov techniques. In this spirit, we have developed methods for stability analysis of systems described by Ordinary, Delay and Partial Differential Equations, as well as switched/hybrid systems.
  • Systems and Synthetic Biology. We collaborate closely with groups in biochemistry for understanding biological pathways through mathematical modelling using experimental data and designing new experiments for model invalidation (Systems Biology), as well as proposing and implementing redesigns for existing biological systems for improved performance (Synthetic Biology).
  • Software Development (SOSTOOLS). This can be found here.
  • Large-scale Networked Systems analysis with communication and structural constraints. Examples in this field come from synchronization phenomena in oscillator networks, Network Congestion Control for the Internet and Power System analysis/Smart grid. We are also looking at multi-agent systems consensus under communication and structural constraints such as the effect of time delays and switching topologies.
  • Fluid mechanics and Heat transfer, from a control perspective. We are taking a control engineering approach to understand questions in Hydrodynamic Stability and mechanisms for background noise energy amplification and subsequent reduction. We are also using a Sum of Squares approach for the stability analysis and control design of systems described by Partial Differential Equations.
  • Complexity reduction of networked systems. We are investigating methods based on model decomposition and reduction to facilitate computational analysis and identification of large-scale and nonlinear systems. Systems of interest include biochemical reaction networks, power systems and consensus networks.

Current Members

  • Mr Thomas Folliard - PRS student, October 2013-. Co-supervised with Professor Judith Armitage.

Current Externally Funded Projects



  • Antonis Papachristodoulou awarded an EPSRC Fellowship for Growth in Synthetic Biology.
  • Richard Mason's paper Chordal Sparsity, Decomposing SDPs and the Lyapunov Equation has received the best student paper award at the 2014 American Control Conference. Download the PDF here.

Joining SySOS

  • If you find what we do interesting, and you want to apply for a DPhil (PhD) or MSc by Research in our group, then please contact us sooner than later to discuss possible projects. Note that there are several Centres of Doctoral Training that are relevant to our research, especially the EPSRC & BBSRC CDT in Synthetic Biology as well as the EPSRC CDT in Autonomous Intelligent Machines and Systems. If you have a strong academic background, the chances of securing funding for your studies are higher the earlier you apply. Note that applications need to follow the Postgraduate Admissions guidelines.
  • There are several other routes for joining SySOS, mainly through fellowships.

Previous Members

  • Dr Bing Chu - Postdoctoral Research Assistant, June 2010-March 2012
  • Dr Yo-Cheng (Mark) Chang DPhil, co-supervised with Professor Judith Armitage, Department of Biochemistry, January 2007-January 2011.
  • Dr Bence Mélykúti, DPhil, co-supervised with Professor Alison Etheridge, Department of Statistics, January 2008-February 2011.
  • Miss Nassia Inglessis, September 2009 - October 2009
  • Mr Christoph Maier, April 2009 - July 2009

Completed Projects

  • European Space Agency project with GMV (Spain), NGC (Canada) and the University of Leicester, "Worst-Case and Safety Analysis Tools for Autonomous Rendezvous Systems".

Useful Links