We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the time domain, we find a realization that approximates the data well while guaranteeing that the energy functional satisfies a dissipation inequality. To this end, we use the framework of port-Hamiltonian (pH) systems and modify the dynamic mode decomposition, respectively operator inference, to be feasible for continuous-time pH systems. We propose an iterative numerical method to solve the corresponding least-squares minimization problem. We construct an effective initialization of the algorithm by studying the least-squares problem in a weighted norm, for which we present the analytical minimum-norm solution. The efficiency of the proposed method is demonstrated with several numerical examples.

翻译：我们提出了一种新颖的物理信息系统辨识方法，用于构建无源线性时不变系统。具体而言，针对给定的二次能量泛函，利用系统在时域中的输入、状态和输出测量值，我们找到一种既能良好近似数据又能保证能量泛函满足耗散不等式的实现形式。为此，我们采用端口-哈密顿（pH）系统框架，对动态模态分解（即算子推断）进行改进，使其适用于连续时间pH系统。我们提出一种迭代数值方法来求解相应的最小二乘最小化问题。通过研究加权范数下的最小二乘问题，我们构建了该算法的有效初始化方案，并给出了该问题的解析最小范数解。多个数值算例验证了所提方法的有效性。