Parametric estimation of nonlinear dynamic systems with time delayed feedback

The experimental modeling of delayed dynamic systems is an open problem. This paper presents an approach based on the genetic algorithms to estimate the system parameters and time delays in the feedback simultaneously through the minimization of residual error of system equation. Several operations such as crossover and mutation are combined so as to improve the convergence rate in the process of parametric estimation. The approach is illustrated by two examples of numerical simulation. Due to the global optimum in a parallel, random and blind way, the approach works for both linear and nonlinear systems with delays. In the case of many system parameters to be estimated, it is suggested to estimate a part of system parameters through an open-loop experiment and then the time delays and the remaining parameters through a closed-loop experiment.