# Antonis

### From SYSOS

# Teaching

- Academic Year 2006-2007
- Michaelmas 2006: C5A, Control and Optimization of Operations
- Hilary 2007: C4A, Networked Systems

- Academic Year 2007-2008
- Michaelmas 2007: C4A, Networked Systems
- Hilary 2008: C5B, Biosystem Modelling

- Academic Year 2008-2009
- Hilary 2009: C4A: Networked Systems, C5B: Biosystem Modelling.

# Publications

## Systems Biology

- E. August and A. Papachristodoulou. Efficient, sparse biological network determination. BMC Systems Biology 2009, 3:25.
- E. August and A. Papachristodoulou. A new computational tool for establishing model parameter identifiability. Awaiting publication in Journal of Computational Biology.
- E. August, A. Papachristodoulou, B. Recht, M. A. J. Roberts and A. Jadbabaie. Determining Interconnections in Biochemical Networks Using Linear Programming. In Proc. of the IEEE CDC, 2008.
- A. Papachristodoulou and B. Recht. Determining Interconnections in Chemical Reaction Networks. In Proc. of the American Control Conference, 2007.
- A. Papachristodoulou and H. El-Samad. Algorithms for Discriminating between Biochemical Reaction Network Models: Towards Systematic Experimental Design. In Proc. of the American Control Conference, 2007.
- H. El-Samad, S. Prajna, A. Papachristodoulou, J. C. Doyle, and M. Khammash. Advanced Methods and Algorithms for Biological Networks Analysis. Proceedings of the IEEE, 94(4): 832 – 853, 2006.
- H. El-Samad, M. Fazel, X. Liu, A. Papachristodoulou, S. Prajna. Stochastic Reachability Analysis in Complex Biological Networks. In Proc. of the American Control Conference, 2006.
- T.-M. Yi, M. Fazel, X. Liu, O. Otitoju, J. Gonçalves, A. Papachristodoulou, S. Prajna, J. C. Doyle. Application of Robust Model Validation Using SOSTOOLS to the Study of G-Protein Signaling in Yeast. In Proc. of Foundations of Systems Biology in Engineering, 2005.
- H. El-Samad, S. Prajna, A. Papachristodoulou, M. Khammash, and J.C. Doyle. Model invalidation and robustness analysis of the bacterial heat shock response using SOSTOOLS. In Proc. of the IEEE CDC, 2003.

## Sum of Squares Techniques for Systems Analysis

- A. Papachristodoulou and S. Prajna. Robust stability analysis of nonlinear hybrid systems. Awaiting publication in IEEE Transactions in Automatic Control.
- A. Papachristodoulou, M. M. Peet and S. Lall. Analysis of polynomial systems with time delays via the sum of squares decomposition. Awaiting publication in IEEE Transactions in Automatic Control.
- M. M. Peet, A. Papachristodoulou and S. Lall. Positive forms and the stability of linear time-delay systems. Awaiting publication in SIAM Journal on Control and Optimization.
- M. M. Peet and A. Papachristodoulou. Using polynomial semi-separable kernels to construct infinite-dimensional Lyapunov functions. In Proc. of the IEEE CDC, 2008.
- A. Papachristodoulou, M. M. Peet and S.-I. Niculescu. Stability Analysis of Linear Systems with Time-Varying Delays: Delay Uncertainty and Quenching. In Proc. of the IEEE CDC, 2007.
- M. M. Peet and A. Papachristodoulou. Positivity of Kernel Functions for Systems with Communication Delay. In Proc. of the IEEE CDC, 2007.
- M. M. Peet, A. Papachristodoulou, and S. Lall. Positive Forms and Stability of Linear Time-Delay Systems. In Proc. of the IEEE CDC, 2006.
- A. Papachristodoulou and M. M. Peet. On the Analysis of Systems Described by Classes of Partial Differential Equations. In Proc. of the IEEE CDC, 2006.
- A. A. Salinas-Varela, A. Papachristodoulou and J. Gonçalves. On L2 Error Bounds between Systems. In Proc. of the International Symposium on Mathematical Theory of Networks and Systems, 2006.
- A. Papachristodoulou. Robust stabilization of nonlinear time delay systems using convex optimization. In Proc. of the IEEE CDC, 2005.
- A. Papachristodoulou, M. M. Peet and S. Lall. Constructing Lyapunov-Krasovskii Functionals for Linear Time Delay Systems. In Proc. of the American Control Conference, 2005.
- A. Papachristodoulou and S. Prajna. Analysis of non-polynomial systems using the sum of squares decomposition. In Positive Polynomials in Control, Springer-Verlag, 2005.
- S. Prajna, A. Papachristodoulou, and F. Wu. Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based approach. In Proc. of the Asian Control Conference, 2004.
- A. Papachristodoulou. Analysis of nonlinear time delay systems using the sum of squares decomposition. In Proc. of the American Control Conference, 2004.
- S. Prajna and A. Papachristodoulou. Analysis of switched and hybrid systems – beyond piecewise quadratic methods. In Proc. of the American Control Conference, 2003.
- A. Papachristodoulou and S. Prajna. On the construction of Lyapunov functions using the sum of squares decomposition. In Proc. of the IEEE CDC, 2002.

## Large Scale Systems Analysis and Design

- U. Münz, A. Papachristodoulou and F. Allgöwer. Consensus Reaching in Multi-Agent Packet-Switched Networks with Nonlinear Coupling. Awaiting publication in International Journal of Control.
- U. Münz, A. Papachristodoulou and F. Allgöwer. Delay-dependent rendezvous and flocking of large scale multi-agent systems with communication delays. In Proc. of the IEEE CDC, 2008.
- U. Münz, A. Papachristodoulou and F. Allgöwer. Nonlinear Multi-Agent System Consensus with Time-Varying Delays. In Proc. of the IFAC World Congress, 2008.
- A. Papachristodoulou and M. M. Peet. Global Stability Analysis of Primal Internet Congestion Control Schemes with Heterogeneous Delays. In Proc. of the IFAC World Congress, 2008.
- Y. Li, A. Papachristodoulou, M. Chiang and A. R. Calderbank. Stability of Congestion Control Schemes with Delay Sensitive Traffic. In Proc. of the American Control Conference, 2008.
- U. Münz, A. Papachristodoulou and F. Allgöwer. Multi-Agent System Consensus in Packet-Switched Networks. Proc. of the European Control Conference, 2007.
- A. Papachristodoulou, A. Jadbabaie. Synchronization in Oscillator Networks with Heterogeneous Delays, Switching Topologies and Nonlinear Dynamics. In Proc. of the IEEE CDC, 2006.
- A. Papachristodoulou, A. Jadbabaie. Synchronization in Oscillator Networks: Switching Topologies and Non-homogeneous Delays. In Proc. of the IEEE CDC, 2005.
- A. Papachristodoulou, L. Li and J. C. Doyle. Methodological Frameworks for Large-scale Network Analysis and Design. ACM SIGCOMM Comp. Comm. Reviews, 34(3): 7 – 20, 2004.
- A. Papachristodoulou. Global stability analysis of a TCP/AQM protocol for arbitrary networks with delay. In Proc. of the IEEE CDC, 2004.

## Software

- S. Prajna, A. Papachristodoulou, and P. A. Parrilo. SOSTOOLS – Sum of Squares Optimization Toolbox, User’s Guide. Available at http://www.cds.caltech.edu/sostools, 2002.
- S. Prajna, A. Papachristodoulou, and P. A. Parrilo. Introducing SOSTOOLS: A general purpose sum of squares programming solver. In Proc. of the IEEE CDC, 2002.
- S. Prajna, A. Papachristodoulou, P. Seiler, and P. A. Parrilo. New developments in sum of squares optimization and SOSTOOLS. In Positive Polynomials in Control, Springer-Verlag, 2005.

## Applications

- A. Papachristodoulou and M. M. Peet. SOS for Nonlinear Delayed Models in Biology and Networking. In Topics in Time-Delay Systems: Analysis, Algorithms and Control, Springer-Verlag, 2008.
- S. Glavaski, D. Subramanian, K. Ariyur, R. Ghosh, N. Lamba and A. Papachristodoulou. A Nonlinear Hybrid Life Support System: Dynamic Modelling, Control Design, and Safety Verification. IEEE Transactions on Control Technology, 15(6): 1003 – 1017, 2007.
- A. Papachristodoulou, S. Prajna and S. Glavaski. Sum of Squares in Industry: An Algorithmic Analysis Approach. Tutorial Session at the American Control Conference, 2005.
- K. Krishnaswamy, G. Papageorgiou, S. Glavaski, and A. Papachristodoulou. Analysis of aircraft pitch axis stability augmentation system using sum of squares optimization. In Proc. of the American Control Conference, 2005.
- A. Papachristodoulou and C. Papageorgiou. Robust stability and performance analysis of a longitudinal aircraft model using sum of squares techniques. In Proc. of the Mediterranean Control Conference, 2005.
- S. Glavaski, A. Papachristodoulou and K. Ariyur. Computational challenges of controlled hybrid system safety verification. In Hybrid Systems: Computation and Control, Springer-Verlag, 2005.
- A. Papachristodoulou, J. C. Doyle, and S. H. Low. Analysis of nonlinear delay differential equation models of TCP/AQM protocols using sums of squares. In Proc. of the IEEE CDC, 2004.
- A. Papachristodoulou and F. E. C. Culick. Flight Mechanics of the Wright Aircraft 1903-1912. In AIAA 41st Aerospace Sciences Meeting and Exhibit, Paper number AIAA-2003-0097, 2003.

## Theses

- A. Papachristodoulou. Scalable Analysis of Nonlinear Systems Using Convex Optimization. PhD Thesis, California Institute of Technology, Pasadena CA, 2005.