Stability-Certified Learning of Control Systems with Quadratic Nonlinearities

• URL: http://arxiv.org/abs/2403.00646v1
• Date: Fri, 1 Mar 2024 16:26:47 GMT
• Title: Stability-Certified Learning of Control Systems with Quadratic Nonlinearities
• Authors: Igor Pontes Duff and Pawan Goyal and Peter Benner
• Abstract summary: This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models. Our main objective is to develop a method that facilitates the inference of quadratic control dynamical systems with inherent stability guarantees.
• Score: 9.599029891108229
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability is a fundamental attribute of dynamical systems, yet it is not always assured in models derived through inference. Our main objective is to develop a method that facilitates the inference of quadratic control dynamical systems with inherent stability guarantees. To this aim, we investigate the stability characteristics of control systems with energy-preserving nonlinearities, thereby identifying conditions under which such systems are bounded-input bounded-state stable. These insights are subsequently applied to the learning process, yielding inferred models that are inherently stable by design. The efficacy of our proposed framework is demonstrated through a couple of numerical examples.

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