论文标题
哈米尔顿港动态模式分解
Port-Hamiltonian Dynamic Mode Decomposition
论文作者
论文摘要
我们提出了一种新颖的物理信息系统识别方法，用于构建一个被动的线性时间不变系统。更详细地说，对于给定的二次能量功能，在时域中系统的输入，状态和输出的测量值，我们找到了一个实现的实现，可以很好地近似数据，同时保证能量功能能够满足耗散不平等。为此，我们使用港口 - 哈米尔顿港（pH）系统的框架，并分别修改动态模式分解，分别对连续时间pH系统可行。我们提出了一种迭代数值方法，以解决相应的最小二乘最小化问题。我们通过研究加权规范中的最小二乘问题来构建算法的有效初始化，为此我们介绍了分析性最小值解决方案。通过几个数值示例证明了所提出的方法的效率。
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.
