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:我们提出了一个新的物理知情系统识别方法,用于构建一个被动线性时变系统。更详细地说,对于特定二次能量功能、对一个系统在时间领域的输入、状态和输出的测量,我们发现一个认识非常接近数据,同时保证能源功能能满足消散不平等。为此,我们使用港口-汉堡系统框架,并修改动态模式分解,分别由操作员推断,对连续时间pH系统是可行的。我们提出一个迭代数字方法,以解决相应的最小方位最小化问题。我们通过在加权规范中研究最小方位问题,从而构建一个有效的算法初始化过程,为此我们提出了分析最低规范解决方案。提议的方法的效率以几个数字例子来说明。