论文标题
凸非参数公式用于鉴定梯度流
Convex Nonparametric Formulation for Identification of Gradient Flows
论文作者
论文摘要
在本文中，我们为非线性梯度流动动力学开发了一种非参数系统识别方法。在这些系统中，向量场是势能函数的梯度场。关于系统动力学的这个基本事实在提出的识别方法中扮演着结构性先验知识以及约束的作用。尽管识别问题的性质是功能空间中的估计，但我们得出了等效的有限尺寸公式，这是二次程序形式的凸优化。这提供了问题的可扩展性，并为利用最近开发的大规模优化求解器提供了机会。提出的方法中的核心思想是将能量函数表示为两个凸函数的差异，并共同估算了这些凸函数。基于功能凸度的必要条件和足够的条件，提出了识别问题，然后解决了解决方案的存在，唯一性和平滑度。我们还为一个例证示例以数值说明了该方法。
In this paper, we develop a nonparametric system identification method for the nonlinear gradient-flow dynamics. In these systems, the vector field is the gradient field of a potential energy function. This fundamental fact about the dynamics of system plays the role of a structural prior knowledge as well as a constraint in the proposed identification method. While the nature of the identification problem is an estimation in the space of functions, we derive an equivalent finite dimensional formulation, which is a convex optimization in form of a quadratic program. This gives scalability of the problem and provides the opportunity for utilizing recently developed large-scale optimization solvers. The central idea in the proposed method is representing the energy function as a difference of two convex functions and estimating these convex functions jointly. Based on necessary and sufficient conditions for function convexity, the identification problem is formulated, and then, the existence, uniqueness and smoothness of the solution is addressed. We also illustrate the method numerically for a demonstrative example.
