A New Method of Nonlinear System Identification using Interpolated Cell Mapping

The method presented in this paper is a two-stage procedure. At the first stage, a discrete-time map defined on a grid in the state space is processed using the method of Interpolated Cell Mapping (ICM) to obtain maps of geometrically decreasing time steps. In the limit as the time step approaches zero, the state derivatives are estimated by way of difference quotients. Then, during the second stage, a Least Squares function fit is performed on the derivatives, yielding the equations of motion. The method bridges the gap between discrete and continuous-time dynamics and is particularly attractive for nonlinear systems, for which traditional system identification schemes frequently fail. The formulation is developed for autonomous and nonautonomous systems, and some results of applying it to a sample nonlinear equation are shown.