TRACKING CONTROLLED CHAOS - THEORETICAL FOUNDATIONS AND APPLICATIONS

Tracking controlled states over a large range of accessible parameters is a process which allows for the experimental continuation of unstab le states in both chaotic and non-chaotic parameter regions of interes t. In algorithmic form, tracking allows experimentalists to examine ma ny of the unstable states responsible for much of the observed nonline ar dynamic phenomena. Here: we present a theoretical foundation for tr acking cent-roiled states from both dynamical systems as well as contr ol theoretic viewpoints. The theory is constructive and shows explicit ly 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 nume rical and physical experiments are given to illustrate the wide range of tracking applications. (C) 1997 American Institute of Physics.