preprint · arXiv (Cornell University) · 2018
Sample Complexity for Nonlinear Dynamics
Cited by 2Open access
Abstract
We consider the identification problems for nonlinear dynamical systems. An explicit sample complexity bound in terms of the number of data points required to recover the models accurately is derived. Our results extend recent sample complexity results for linear dynamics. Our approach for obtaining sample complexity bounds for nonlinear dynamics relies on a linear, albeit infinite dimensional, representation of nonlinear dynamics provided by Koopman and Perron-Frobenius operator. We exploit the linear property of these operators to derive the sample complexity bounds. Such complexity bounds will play a significant role in data-driven learning and control of nonlinear dynamics. Several numerical examples are provided to highlight our theory.
Cite this paper
Chen, Y., & Vaidya, U. (2018). Sample Complexity for Nonlinear Dynamics. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1810.11747
Chen, Yongxin, and Umesh Vaidya. “Sample Complexity for Nonlinear Dynamics.” arXiv (Cornell University), 2018, https://doi.org/10.48550/arxiv.1810.11747.
Chen, Yongxin, and Umesh Vaidya. 2018. “Sample Complexity for Nonlinear Dynamics.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1810.11747.
Chen, Y. and Vaidya, U. (2018) ‘Sample Complexity for Nonlinear Dynamics’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1810.11747.
@misc{chen2018sample,
title = {{Sample Complexity for Nonlinear Dynamics}},
author = {Chen, Yongxin and Vaidya, Umesh},
journal = {arXiv (Cornell University)},
year = {2018},
doi = {10.48550/arxiv.1810.11747}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.