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Published July 10, 2013 | public
Journal Article

Quantitative local L_2-gain and Reachability analysis for nonlinear systems

Abstract

This paper develops theoretical and numerical tools for quantitative local analysis of nonlinear systems. Specifically, sufficient conditions are provided for bounds on the reachable set and L_2 gain of the nonlinear system subject to norm-bounded disturbance inputs. The main theoretical results are extensions of classical dissipation inequalities but enforced only on local regions of the state and input space. Computational algorithms are derived from these local results by restricting to polynomial systems, using convex relaxations, for example the S-procedure, and applying sum-of-squares optimizations. Several pedagogical and realistic examples are provided to illustrate the proposed approach.

Additional Information

© 2013 John Wiley & Sons, Ltd. Received 2 November 2011; Revised 3 October 2012; Accepted 2 December 2012. Published online 3 January 2013. The authors would like to thank Professor Craig Evans and Dr. Ryan Hynd for several helpful discussions. This material is based upon work supported under a National Science Foundation Graduate Research Fellowship, the NASA Harriet Jenkins Predoctoral Fellowship, the Amelia Earhart Fellowship, the University of Minnesota Doctoral Dissertation Fellowship, the Boeing Corporation, the NASA Langley NRA contract NNH077ZEA001N entitled 'Analytical Validation Tools for Safety Critical Systems' and the AFOSR award FA9550-12-1-0339 entitled 'A Merged IQC/SOS Theory for Analysis of Nonlinear Control Systems'.

Additional details

Created:
August 22, 2023
Modified:
October 26, 2023