Robustness Analysis of Nonlinear Systems

Gary Balas (U of Minnesota), Andy Packard (UC Berkeley), Peter Seiler (U of Minnesota), and Ufuk Topcu (Caltech)

Previous Workshop Slides

Short Course at NASA Langley Research Center (September 30 - October 1, 2009) : Slides

MATLAB Software

You can download the software packages
- Multipoly : Package used to represent multivariate polynomials.
  Version 2.02
  Date: April 16, 2014
  Description: Updated to Matlab's new object format and added new functionality. The complete list of functions can be found in the documentation in the doc/ folder.
- SOSOPT : General SOS optimization utility.
  Version 2.02
  Date: April 16, 2014
  Description: Added new interface for specifying polynomial constraints and options. This is described in the documentation in the doc/ folder. Also added functionality for polynomial equality constraints.
- SOSAnalysis : Complete software package with iteration algorithms for nonlinear analysis.
  Version 2.02
  Date: April 16, 2014
  Description: Updated the nonlinear analysis code to integrate with the new SOSOPT and Multipoly toolboxes. Also, there are new iteration algorithms for region of attraction, I/O gain, and reachability analysis.
Script file to configure the MATLAB path for these packages (sosaddpath.m )
SeDuMi is maintained by Lehigh University. See their website for downloads, installation instructions, etc. The tools have been tested with
version 1.1 of Sedumi so this version should be selected for installation.

A. Chakraborty, P. Seiler, and G. Balas, “Susceptibility of F/A-18 Flight Controllers to the Falling-Leaf Mode: Linear Analysis,” AIAA Journal of Guidance, Control, and Dynamics, Vol.34 No.1, 2011, 57-72. [pdf] [Mfiles]
A. Chakraborty, P. Seiler, and G. Balas, “Susceptibility of F/A-18 Flight Controllers to the Falling-Leaf Mode: Nonlinear Analysis,” AIAA Journal of Guidance, Control, and Dynamics, Vol.34 No.1, 2011, 73-85. [pdf] [Mfiles]
A. Chakraborty, P. Seiler, and G. Balas, “Nonlinear Region of Attraction Analysis for Flight Control Verification and Validation,” Control Engineering Practice, Vol.19, Issue 4, April 2011, Pages 335-345. [pdf] [link] [Mfiles]
A. Chakraborty, P. Seiler, and G. Balas, “Applications of Linear and Nonlinear Robustness Analysis Tehniques to the F/A-18 Flight Control Laws,” AIAA Guidance, Navigation, and Control Conference, Chicago, Illinois, Aug. 10-13, 2009. [pdf]
R. Pandita, A. Chakraborty, P. Seiler, and G. Balas, “Reachability and Region of Attraction Analysis Applied to GTM Dynamic Flight Envelope Assessment ,”AIAA Guidance, Navigation, and Control Conference, Chicago, Illinois, Aug. 10-13, 2009. [link]