基于局部稳定性先验的动态系统学习
Learning Dynamical Systems using Local Stability Priors
摘要：
提出了一种耦合计算方法，从系统生成的轨迹中同时学习矢量场和平衡点的吸引区域。非线性识别利用局部稳定性信息作为系统的先验信息，有效地赋予估计这一重要的结构属性。此外，吸引区域的知识通过告知从其生成轨迹的初始条件的选择以及通过使得能够使用系统的李雅普诺夫函数作为正则化项来发挥实验设计的作用。数值结果表明，所提出的方法允许有效的采样，并提供了一个准确的估计的动力学在其吸引区域的内部近似。
英文摘要：
A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system is proposed. The nonlinear identification leverages the local stability information as a prior on the system, effectively endowing the estimate with this important structural property. In addition, the knowledge of the region of attraction plays an experiment design role by informing the selection of initial conditions from which trajectories are generated and by enabling the use of a Lyapunov function of the system as a regularization term. Numerical results show that the proposed method allows efficient sampling and provides an accurate estimate of the dynamics in an inner approximation of its region of attraction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
