Computation of a Contraction Metric for a Periodic Orbit Using Meshfree Collocation

DOI10.1137/18M1220182zbMath1453.34061OpenAlexW2964712166WikidataQ127312424 ScholiaQ127312424MaRDI QIDQ5238244

Peter Giesl

Publication date: 28 October 2019

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1220182

zbMATH Keywords

error estimatesperiodic orbitcontraction metricmeshfree collocationmatrix-valued partial differential equation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Periodic solutions to ordinary differential equations (34C25) Error bounds for boundary value problems involving PDEs (65N15) Periodic orbits of vector fields and flows (37C27)

Related Items (3)

Review on contraction analysis and computation of contraction metrics ⋮ On a matrix-valued PDE characterizing a contraction metric for a periodic orbit ⋮ Computation and verification of contraction metrics for periodic orbits

Cites Work

• Construction of a CPA contraction metric for periodic orbits using semidefinite optimization
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• Necessary conditions for a limit cycle and its basin of attraction.
• Converse theorem on a global contraction metric for a periodic orbit
• Verification estimates for the construction of Lyapunov functions using meshfree collocation
• Transverse contraction criteria for existence, stability, and robustness of a limit cycle
• A Differential Lyapunov Framework for Contraction Analysis
• Kernel techniques: From machine learning to meshless methods
• Computation and Verification of Lyapunov Functions
• Meshless Collocation: Error Estimates with Application to Dynamical Systems
• On Global Asymptotic Stability of Solutions of Differential Equations
• Radial Basis Functions
• Kernel-Based Discretization for Solving Matrix-Valued PDEs
• Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting
• Dynamical Systems with a Certain Local Contraction Property.
• Scattered Data Approximation
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