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- Title
Construction of contraction metrics for discrete-time dynamical systems using meshfree collocation.
- Authors
Pokkakkillath, Sareena; Giesl, Peter
- Abstract
A contraction metric for a discrete-time dynamical system given by an autonomous iteration is a Riemannian metric such that the distance between adjacent solutions contracts over time. A contraction metric can be used to determine the basin of attraction of a fixed point and it is robust to small perturbations of the system, including those varying the position of the fixed point.In this paper, we prove a converse theorem, showing the existence of a contraction metric, which is the solution of a matrix-valued equation. We then develop a construction method based on meshless collocation to approximate the solution of this equation. Error estimates imply that a sufficiently close approximation is itself a contraction metric. The method is applied to several examples.
- Subjects
DISCRETE-time systems; DYNAMICAL systems; RIEMANNIAN metric; MESHFREE methods
- Publication
Discrete & Continuous Dynamical Systems - Series B, 2024, Vol 29, Issue 4, p1
- ISSN
1531-3492
- Publication type
Article
- DOI
10.3934/dcdsb.2023166