Stability-Certified Learning of Control Systems with Quadratic
  Nonlinearities
Igor Pontes Duff Pawan Goyal Peter Benner
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.