Learning deep Koopman operators with convex stability constraints
<|reference_start|>Learning deep Koopman operators with convex stability constraints: In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization problems. More specifically, we tackle the problem of imposing asymptotic stability to a Koopman matrix learned from data during iterative gradient descent optimization processes. We show that this sufficient condition can be decoupled by rows of the system matrix, and propose a control barrier function-based projected gradient descent to enforce gradual evolution towards the stability set by running an optimization-in-the-loop during the iterative learning process. We compare the performance of our algorithm with other two recent approaches in the literature, and show that we get close to state-of-the-art performance while providing the added flexibility of allowing the optimization problem to be further customized for specific applications.<|reference_end|>
@article{mitjans2024learning,
    title={Learning deep Koopman operators with convex stability constraints},
    author={Marc Mitjans, Liangting Wu, Roberto Tron},
    journal={arXiv preprint arXiv:2404.15978},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.15978},
    primaryClass={eess.SY cs.SY}
}