Dynamic algorithm for parameter estimation and its applications

We consider a dynamic method, based on synchronization and adaptive control , to estimate unknown parameters of a nonlinear dynamical system from a giv en scalar chaotic time series. We present an important extension of the met hod when the time series of a scalar function of the variables of the under lying dynamical system is given. We find that it is possible to obtain sync hronization as well as parameter estimation using such a time series. We th en consider a general quadratic flow in three dimensions and discuss the ap plicability of our method of parameter estimation in this case. In practica l situations one expects only a finite time series of a system variable to be known. We show that the finite time series can be repeatedly used to est imate unknown parameters with an accuracy that improves and then saturates to a constant Value with repeated use of the time series. Finally, we sugge st an important application of the parameter estimation method. We propose that the method can be used to confirm the correctness of a trial function modeling an external unknown perturbation to a known system. We show that o ur method produces exact synchronization with the given time series only wh en the trial function has a form identical to that of the perturbation.