Parameter Estimation for Chaotic Systems

This paper discusses the estimation of parameters in models of chaotic systems from measured time series. It is suggested that the classic output error method is unsuitable for time series much longer than the time scale given by a system´s maximum Lyapunov exponent. It is pointed out that an analogous situation arises with nonchaotic engineering systems which are open loop unstable, but stabilized by an exogenous feedback control The use of the prediction error method is proposed. Use of an ad hoc feedback version, proposed by Maine and Murray in the feedback control situation, is considered [12]. Estimation of parameters in a numerical simulation of a damped, sinusoidally driven pendulum is given as an example.