Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems
Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems
复制标题
使用轨迹测量来估计非线性系统的吸引区域
DOI：
10.1109/cdc.2018.8618959
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
M. Peet
中科院分区：
文献类型：
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作者：
Brendon K. Colbert;M. Peet
我们提出了一种方法来估计区域的吸引力的非线性常微分方程的基础上，仅测量的轨迹-这意味着非线性向量场不需要已知的先验。该方法基于使用轨迹数据来确定状态空间中有限数量点处的匡威李雅普诺夫函数的形式的值。然后使用最小绝对偏差将此数据拟合到平方和多项式，其水平集然后成为吸引区域的估计。这个学习的李雅普诺夫函数可以用来预测新生成的初始条件是否位于吸引区域。大量的数值测试表明，该方法在超过95%的生成测试数据上正确预测新的初始条件是否在非线性常微分方程的吸引区域内。
We propose a method to estimate the region of attraction of a nonlinear ODE based only on measurements of the trajectory - implying that the nonlinear vector field need not be known a priori. This method is based on using trajectory data to determine values of a form of converse Lyapunov function at a finite number of points in the state-space. Least absolute deviations is then used to fit this data to a Sum-of-Squares polynomial whose level sets then become estimates for the region of attraction. This learned Lyapunov function can then be used to predict whether newly generated initial conditions lie in the region of attraction. Extensive numerical testing is used to show that the method correctly predicts whether a new initial condition is within the region of attraction of the nonlinear ODE on over 95% of a generated set of test data.