On Decoupled Optimal Input Design for Nonlinear Systems with Infinite Memory

For linear dynamic systems the problem of optimal input design is well studied and well documented in the literature. However, for nonlinear systems the field is still in development. Recently new progress has been made for nonlinear systems with limited memory. However extension of these methods to systems with large or infinite memory does not seem possible. In this work a new method is proposed in order to find a "good" input for a system consisting of an IIR filter followed by a static nonlinearity. Instead of maximizing the determinant of Fisher information matrix of the whole system , which is hard because it is unclear on which properties of the input the matrix depends, an iterative method is proposed that alternately improves the determinants of the subsystems. During this optimization certain constraints are added in order to make the solution well defined. The influence of different constraints on the shape of the input is also investigated.