论文标题
审查收缩分析和计算收缩指标
Review on contraction analysis and computation of contraction metrics
论文作者
论文摘要
收缩分析考虑了两个相邻轨迹之间的距离。如果此距离是收缩的，则轨迹具有相同的长期行为。该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，距离收缩，可以显示融合到独特的平衡，或者如果吸引仅在某些方向上发生到周期性轨道。最初考虑了普通微分方程的收缩分析，但已扩展到离散的时间系统，控制系统，延迟方程和许多其他类型的系统。此外，可以应用类似的技术，以估计吸引子的维度和估计不同熵概念（包括拓扑熵）。这篇综述试图将数学和工程文献中的参考文献链接起来，此外，还指出了收缩指标计算中的最新发展和算法。
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.
