• Corpus ID: 231846762

Linear Matrix Inequality Approaches to Koopman Operator Approximation

@article{Dahdah2021LinearMI,
  title={Linear Matrix Inequality Approaches to Koopman Operator Approximation},
  author={Steven Dahdah and James Richard Forbes},
  journal={ArXiv},
  year={2021},
  volume={abs/2102.03613}
}
Koopman operator theory [1–4] provides a means to globally represent a nonlinear system as a linear system by transforming its states into an infinite-dimensional space of lifted states. The Koopman operator advances the current lifted state of the system to the next lifted state, much like the state transition matrix of a linear system. While originally proposed by B. O. Koopman in 1931 [1], modern computational resources, along with recent theoretical developments [2–4], have led to a… 
1 Citations
System Norm Regularization Methods for Koopman Operator Approximation
TLDR
DMD and DMD with control are reformulated as convex optimization problems with linear matrix inequality constraints and hard asymptotic stability constraints and system norm regularizers are considered as methods to improve the numerical conditioning of the approximate Koopman operator.

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