We consider the problem of identifying a dissipative linear model of an unknown nonlinear system that is known to be dissipative, from time-domain input–output data. We first learn an approximate linear model of the nonlinear system using standard system identification techniques and then perturb the system matrices of the linear model to enforce dissipativity, while closely approximating the dynamical behavior of the nonlinear system. Further, we provide an analytical relationship between the size of the perturbation and the radius in which the dissipativity of the linear model guarantees local dissipativity of the unknown nonlinear system. We demonstrate the application of this identification technique through two examples.

中文翻译：

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非线性系统耗散线性模型的数据驱动识别


我们考虑从时域输入输出数据识别已知耗散的未知非线性系统的耗散线性模型的问题。我们首先使用标准系统识别技术学习非线性系统的近似线性模型，然后扰动线性模型的系统矩阵以增强耗散性，同时紧密逼近非线性系统的动态行为。此外，我们提供了扰动大小与半径之间的解析关系，其中线性模型的耗散性保证了未知非线性系统的局部耗散性。我们通过两个例子演示了这种识别技术的应用。