收缩分析与收缩度量计算综述
Review on contraction analysis and computation of contraction metrics
摘要：
收缩分析考虑两个相邻轨迹之间的距离。如果这个距离是收缩的，那么轨迹具有相同的长期行为。这种分析的主要优点是它独立于所考虑的解决方案。使用适当的度量，相对于距离收缩，可以显示收敛到唯一的平衡，或者如果吸引力只发生在某些方向上，则收敛到周期轨道。收缩分析最初被认为是常微分方程，但已扩展到离散时间系统，控制系统，延迟方程和许多其他类型的系统。此外，类似的技术可以应用于吸引子的维数的估计和用于熵的不同概念（包括拓扑熵）的估计。这篇综述试图将数学和工程文献中的参考文献联系起来，并进一步指出收缩度量计算中的最新进展和算法。
英文摘要：
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the solutions under consideration. Using an appropriate metric, with respect to which the distance is contracting, one can show convergence to a unique equilibrium or, if attraction only occurs in certain directions, to a periodic orbit. Contraction analysis was originally considered for ordinary differential equations, but has been extended to discrete-time systems, control systems, delay equations and many other types of systems. Moreover, similar techniques can be applied for the estimation of the dimension of attractors and for the estimation of different notions of entropy (including topological entropy). This review attempts to link the references in both the mathematical and the engineering literature and, furthermore, point out the recent developments and algorithms in the computation of contraction metrics.
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。
