Taught at NASA Langley Research Center by Gary Balas (U of Minnesota), Andy Packard (UC Berkeley), Peter Seiler (U of Minnesota), and Ufuk Topcu (Caltech).
Introduction slides
Nonlinear analysis slides are available here.
Worst-case simulation slides are available here.
GTM report: Worst-case simulation and Region of attraction.
Reachability example, pdf version.
(UPDATED - OCT 1, 2009, 9:48AM (EDT)) Demo (on basic use of multipoly, SOSOPT, and S-procedure) presented on the second day of the workshop. exercise, solutions
SeDuMi is maintained by Lehigh University. See their website for downloads, installation instructions, etc. Notes on SeDuMi installation.
You can download all the nonlinear analysis software (except SeDuMi) in one package here.
You can also download the individual packages
Script file to configure the MATLAB path for these packages (sosaddpath.m)
Multipoly: Package used to represent multivariate polynomials.
Polysys: Package used to model, simulate, and analyze nonlinear systems with polynomial dynamics.
Worstcase: Package to compute the induced gain of nonlinear systems using an iterative algorithm.
SOSOPT: General SOS optimization utility.
Other nonlinear analysis code: The rest of the routines discussed in the workshop.
Worst-case simulation code.
Demo files
Details for the software packages listed above can be found in the following publications:
J. Tierno, R. Murray, and J. C. Doyle, “An efficient algorithm for performance analysis of nonlinear control systems,” Proceedings of the 1995 American Control Conference, pp. 2717-2721.
P. A. Parrilo, “Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization” Ph.D. Dissertation, California Institute of Technology, 2000. pdf
W. Tan, “Nonlinear control analysis and synthesis using Sum-of-Squares programming,” Ph.D. Dissertation, University of California, Berkeley, 2006. pdf
U. Topcu, “Quantitative local analysis of nonlinear systems,” Ph.D. Dissertation, University of California, Berkeley, 2008. pdf
Special issue on positive polynomials in control, IEEE Transactions on Automatic Control, May, 2009 (issue 5).
This work is supported by the NASA NRA Grant/Cooperative Agreement NNX08AC80A, Analytical Validation Tools for Safety Critical Systems, Dr. Christine Belcastro, Technical Monitor, 01/01/2008 - 12/31/2010.