Properties of isostables and basins of attraction of monotone systems
Properties of isostables and basins of attraction of monotone systems
复制标题
单调系统的等稳态性质和吸引盆
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
A. Mauroy
中科院分区：
文献类型：
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作者：
Aivar Sootla;A. Mauroy
本文通过研究单调系统的平衡点和吸引域，研究单调系统的几何性质。等稳态是由所谓的Koopman算子定义的特定前向不变集的边界，它提供了非线性系统的线性无限维描述。首先，我们研究了单调系统中Koopman算子及其半群的谱性质。我们的结果推广了著名的Perron-Frobenius定理的非线性情况下，并允许我们导出的几何性质的均衡和盆地的吸引力。此外，我们表明，在一定的条件下，我们可以在参数不确定性的向量场的吸引盆上的边界的特征。我们讨论了计算方法来估计均衡和盆地的吸引力，并说明两个和四个状态单调系统的结果。
In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invariant sets defined by the so-called Koopman operator, which provides a linear infinite-dimensional description of a nonlinear system. First, we study the spectral properties of the Koopman operator and the associated semigroup in the context of monotone systems. Our results generalize the celebrated Perron-Frobenius theorem to the nonlinear case and allow us to derive geometric properties of isostables and basins of attraction. Additionally, we show that under certain conditions we can characterize the bounds on the basins of attraction under parametric uncertainty in the vector field. We discuss computational approaches to estimate isostables and basins of attraction and illustrate the results on two and four state monotone systems.