Quantitative local L2-gain and Reachability analysis for nonlinear systems

Erin Summers, Abhijit Chakraborty, Weehong Tan, Ufuk Topcu, Peter J Seiler Jr, Gary Balas, Andrew Packard

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 L2 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.

Original languageEnglish (US)
Pages (from-to)1115-1135
Number of pages21
JournalInternational Journal of Robust and Nonlinear Control
Volume23
Issue number10
DOIs
StatePublished - Jul 10 2013

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Nonlinear systems
Polynomials

Keywords

  • dissipation inequalities
  • local L gain
  • nonlinear systems
  • reachability
  • sum-of-squares polynomial

Cite this

Quantitative local L2-gain and Reachability analysis for nonlinear systems. / Summers, Erin; Chakraborty, Abhijit; Tan, Weehong; Topcu, Ufuk; Seiler Jr, Peter J; Balas, Gary; Packard, Andrew.

In: International Journal of Robust and Nonlinear Control, Vol. 23, No. 10, 10.07.2013, p. 1115-1135.

Research output: Contribution to journalArticle

Summers, Erin ; Chakraborty, Abhijit ; Tan, Weehong ; Topcu, Ufuk ; Seiler Jr, Peter J ; Balas, Gary ; Packard, Andrew. / Quantitative local L2-gain and Reachability analysis for nonlinear systems. In: International Journal of Robust and Nonlinear Control. 2013 ; Vol. 23, No. 10. pp. 1115-1135.
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