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.

本研究主要集中于一种操作器推理方法，旨在基于先验假设构建基于低维度动力学模型，这些假设通常基于已建立的物理学或专家见解。我们的主要目标是开发一种能够推断具有固有稳定性保证的二次控制动力学系统的方法。我们研究具有能量保持非线性的控制系统的稳定性特征，从而识别出这些系统在什么条件下是有界输入有界状态稳定的。随后，这些见解被应用于学习过程，从而产生设计上固有稳定的推断模型。我们通过几个数值示例来验证我们提出的框架的有效性。