We show that contraction metrics for continuous time dynamical systems can be computed numerically using numerical integration of certain initial value problems with a subsequent numerical quadrature. Further, we show that for any compact subset of an equilibrium’s basin of attraction and any ε > 0, the parameters for the numerical methods, i.e. the integration interval and the step-size, can be chosen such that the error in the contraction metric is less than ε at any point in the compact subset. These results will be used as a part of a numerical method to rigorously compute contraction metrics.
Giesl, P., Hafstein, S., Mehrabi Nezhad, I. (2023). Contraction Metrics by Numerical Integration and Quadrature: Uniform Error Estimate. In Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - (Volume 1) (pp.196-205). Science and Technology Publications, Lda [10.5220/0012183300003543].
Contraction Metrics by Numerical Integration and Quadrature: Uniform Error Estimate
Mehrabi Nezhad I.
2023
Abstract
We show that contraction metrics for continuous time dynamical systems can be computed numerically using numerical integration of certain initial value problems with a subsequent numerical quadrature. Further, we show that for any compact subset of an equilibrium’s basin of attraction and any ε > 0, the parameters for the numerical methods, i.e. the integration interval and the step-size, can be chosen such that the error in the contraction metric is less than ε at any point in the compact subset. These results will be used as a part of a numerical method to rigorously compute contraction metrics.
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