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arXiv · 2404.15978

Learning deep Koopman operators with convex stability constraints

Marc Mitjans·Liangting Wu·Roberto Tron
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Abstract

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.

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Marc Mitjans, Liangting Wu, Roberto Tron. 2024-04-24. Learning deep Koopman operators with convex stability constraints. https://arxiv.org/abs/2404.15978

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