The subject of this paper is the development of a nonlinear parametric identification method using chaotic data. In former research, the main problem in using chaotic data in parameter estimation appeared to be the numerical computation of the chaotic trajectories. This computational problem is due to the highly unstable character of the chaotic orbits. The method proposed in this paper is based on assumed physical models and has two important components. First, the chaotic time series is characterized by a "skeleton" of unstable periodic orbits. Second, these unstable periodic orbits are used as the input information for a nonlinear parametric identification method using periodic data. As a consequence, problems concerning the numerical computation of chaotic trajectories are avoided. The identifiability of the system is optimized by using the structure of the phase space instead of a single physical trajectory in the estimation process. Furthermore, before starting the estimation process, a huge data reduction has been accomplished by extracting the unstable periodic orbits from the long chaotic time series. The method is validated by application to a parametrically excited pendulum, which is an experimental nonlinear dynamical system in which transient chaos occurs.
Control of Chaos in the Rössler System
