A numerical algebraic geometry approach to regional stability analysis of polynomial systems
Name
Tedrake_A numerical.pdf
Size
405.05 KB
Format
Adobe PDF
Checksum (MD5)
97746a9a1155c01b1ca9ec6d6dfe9a4f
Author(s)
Wampler, Charles
Permenter, Frank Noble
Tedrake, Russell Louis
Date Issued
June 2013
Journal
Proceedings of the 2013 American Control Conference
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Permenter, Frank, Charles Wampler, and Russ Tedrake. “A Numerical Algebraic Geometry Approach to Regional Stability Analysis of Polynomial Systems.” 2013 American Control Conference (June 2013).
Version
Author's final manuscript
Abstract
We explore region of attraction (ROA) estimation for polynomial systems via the numerical solution of polynomial equations. Computing an optimal, stable sub-level set of a Lyapunov function is first posed as a polynomial optimization problem. Solutions to this optimization problem are found by solving a polynomial system of equations using techniques from numerical algebraic geometry. This system describes KKT points and singular points not satisfying a regularity condition. Though this system has exponentially many solutions, the proposed method trivially parallelizes and is practical for problems of moderate dimension and degree. In suitably generic settings, the method can solve the underlying optimization problem to arbitrary precision, which could make it a useful tool for studying popular semidefinite programming based relaxations used in ROA analysis.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/ACC.2013.6580150
