Mathematics and Theory

SOSTOOLS
Theory papers:
- Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization .
  P. A. Parrilo
  Ph.D. Thesis. Caltech. 2000.
- Semidefinite Programming Relaxations for Semialgebraic Problems.
  P. A. Parrilo
  In Mathematical Programming Ser. B 96(2):293-320. 2003.
- An explicit construction of distinguished representations of polynomials nonnegative over finite sets
  P.A. Parrilo,
  IfA Technical Report AUT02-02, March 2002.
- Minimizing polynomial functions
  P.A. Parrilo, B. Sturmfels,
  In Algorithmic and quantitative real algebraic geometry ,
  DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 60, pp. 83--99, AMS.
- Symmetry groups, semidefinite programs, and sums of squares
  K. Gatermann, P.A. Parrilo,
  Journal of Pure and Appl. Algebra, Vol. 192, No. 1-3, pp. 95-128, 2004.
- Nonlinear control synthesis by convex optimization
  S. Prajna, P.A. Parrilo, A. Rantzer,
  IEEE Transactions on Automatic Control, Vol. 49, No. 2, 2004
- Semidefinite programming relaxations and algebraic optimization in Control
  P.A. Parrilo, S. Lall,
  European Journal of Control, Vol. 9, No. 2-3, 2003.
- Primal-Dual Tests for Safety and Reachability.
  S. Prajna, A. Rantzer.
  To appear in Hybrid Systems: Computation and Control. Springer-Verlag. 2005.
- Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition.
  A. Papachristodoulou, S. Prajna.
  To appear in Positive Polynomials in Control. Springer-Verlag. 2005.
- Safety Verification of Hybrid Systems Using Barrier Certificates.
  S. Prajna, A. Jadbabaie.
  In Hybrid Systems: Computation and Control. Springer-Verlag. 2004.
- On the Necessity of Barrier Certificates.
  S. Prajna, A. Rantzer.
  To appear in Proceedings of the IFAC World Congress, Prague, Czech Republic. 2005.
- Stochastic Safety Verification Using Barrier Certificates.
  S. Prajna, A. Jadbabaie, G. J. Pappas.
  Proceedings of the IEEE Conference on Decision and Control (CDC), Paradise Island, Bahamas. 2004.
- S.O.S. for Safety.
  H. Yazarel, S. Prajna, G. J. Pappas.
  Proceedings of the IEEE Conference on Decision and Control (CDC), Paradise Island, Bahamas. 2004.
- On Analysis and Synthesis of Safe Control Laws.
  A. Rantzer, S. Prajna.
  Proceedings of the Allerton Conference on Communication, Control, and Computing, Champaign-Urbana, IL. 2004.
- Nonlinear Control Synthesis by Sum of Squares Optimization: A Lyapunov-based Approach.
  S. Prajna, A. Papachristodoulou, F. Wu.
  Proceedings of the Asian Control Conference (ASCC), Melbourne, Australia. 2004.
- A New Solution Approach to Polynomial LPV System Analysis and Synthesis.
  F. Wu, S. Prajna.
  Proceedings of the American Control Conference (ACC), Boston, MA. 2004.
- Barrier Certificates for Nonlinear Model Validation.
  S. Prajna.
  Proceedings of the IEEE Conference on Decision and Control (CDC), Maui, HI. 2003.
  The proofs can be found in this technical report.
- Analysis of Switched and Hybrid Systems - Beyond Piecewise Quadratic Methods.
  S. Prajna, A. Papachristodoulou.
  Proceedings of the American Control Conference (ACC), Denver, CO. 2003.
- On the Construction of Lyapunov Functions using the Sum of Squares Decomposition.
  A. Papachristodoulou, S. Prajna.
  Proceedings of the IEEE Conference on Decision and Control (CDC), Las Vegas, NV. 2002.
- Analysis of Nonlinear Time Delay Systems Using the Sum of Squares Decomposition.
  A. Papachristodoulou.
  Proceedings of the American Control Conference (ACC), Boston, MA. 2004.
SOSTOOLS papers:
- SOSTOOLS: Control Applications and New Developments.
  S. Prajna, A. Papachristodoulou, P. Seiler, P. A. Parrilo.
  Proceedings of the IEEE Conference on Computer Aided Control Systems Design (CACSD), Taipei, Taiwan. 2004.
- Introducing SOSTOOLS: A General Purpose Sum of Squares Programming Solver.
  S. Prajna, A. Papachristodoulou, P. A. Parrilo.
  Proceedings of the IEEE Conference on Decision and Control (CDC), Las Vegas, NV. 2002.
- SOSTOOLS and Its Control Applications.
  S. Prajna, A. Papachristodoulou, P. Seiler, P. A. Parrilo.
  To appear in Positive Polynomials in Control. Springer-Verlag. 2005
SOS application papers:
- Safety Verification of Controlled Advanced Life Support System Using Barrier Certificates.
  S. Glavaski, A. Papachristodoulou, K. Ariyur.
  In Hybrid Systems: Computation and Control. Springer-Verlag. 2005.
- Model Validation and Robustness Analysis of the Bacterial Heat Shock Response using SOSTOOLS.
  H. El-Samad, S. Prajna, A. Papachristodoulou, M. H. Khammash, J. C. Doyle.
  Proceedings of the IEEE Conference on Decision and Control (CDC), Maui, HI. 2003.
- Analysis of Nonlinear Delay Differential Equation Models of TCP/AQM Protocols Using Sums of Squares.
  A. Papachristodoulou, J. C. Doyle, S. H. Low.
  Proceedings of the IEEE Conference on Decision and Control (CDC), Paradise Island, Bahamas. 2004.
Collaborators:
- Pablo A. Parrilo