Stability-Certified Learning of Control Systems with Quadratic Nonlinearities
This work addresses the challenge of ensuring stability in learned control models for applications in physics-informed machine learning and control engineering, representing an incremental improvement by integrating stability analysis into existing inference frameworks.
The researchers tackled the problem of learning stable low-dimensional dynamical models for control systems with quadratic nonlinearities, developing an operator inference method that incorporates stability guarantees by analyzing energy-preserving nonlinearities to ensure bounded-input bounded-state stability, with validation through numerical examples.
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.