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Computation of a contraction metric for a periodic orbit using meshfree collocation

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posted on 2023-06-09, 18:20 authored by Peter GieslPeter Giesl
Contraction analysis uses a local criterion to prove the long-term behaviour of a dynamical system. We consider a contraction metric, i.e. a Riemannian metric with respect to which the distance between adjacent solutions contracts. If adjacent solutions in all directions perpendicular to the flow are contracted, then there exists a unique periodic orbit, which is exponentially stable. In this paper we propose a construction method using meshfree collocation to approximately solve a matrix-valued PDE problem. We derive error estimates and show that the approximation is itself a matrix-valued PDE problem. We derive error estimates and show that the approximation is itself a contraction metric if the collocation points are sufficiently dense. We apply the method to several examples.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

SIAM Journal on Applied Dynamical Systems

ISSN

1536-0040

Publisher

Society for Industrial and Applied Mathematics

Issue

3

Volume

18

Page range

1536-1564

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-07-09

First Open Access (FOA) Date

2019-09-12

First Compliant Deposit (FCD) Date

2019-07-05

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