Schwartz Ira B., Carr Thomas W., Triandaf Ioana
Special Project in Nonlinear Science, Code 6700.3, Plasma Physics Division, Naval Research Laboratory, Washington, D.C. 20375.
Chaos. 1997 Dec;7(4):664-679. doi: 10.1063/1.166285.
Tracking controlled states over a large range of accessible parameters is a process which allows for the experimental continuation of unstable states in both chaotic and non-chaotic parameter regions of interest. In algorithmic form, tracking allows experimentalists to examine many of the unstable states responsible for much of the observed nonlinear dynamic phenomena. Here we present a theoretical foundation for tracking controlled states from both dynamical systems as well as control theoretic viewpoints. The theory is constructive and shows explicitly how to track a curve of unstable states as a parameter is changed. Applications of the theory to various forms of control currently used in dynamical system experiments are discussed. Examples from both numerical and physical experiments are given to illustrate the wide range of tracking applications. (c) 1997 American Institute of Physics.
在大范围可及参数上追踪受控状态是一个过程，它能在感兴趣的混沌和非混沌参数区域对不稳定状态进行实验性延拓。以算法形式而言，追踪能让实验者研究许多对诸多观测到的非线性动力学现象负有责任的不稳定状态。在此，我们从动力学系统以及控制理论的视角为追踪受控状态给出一个理论基础。该理论具有建设性，并且明确展示了随着一个参数的改变如何追踪一条不稳定状态曲线。讨论了该理论在当前动力学系统实验中所使用的各种控制形式上的应用。给出了数值实验和物理实验的例子以说明追踪应用的广泛范围。（c）1997美国物理研究所。
