A preliminary study on Optimal Input Design for Nonlinear Systems

While optimal input design is successfully applied in the case of linear dynamic systems many question remains when it comes to nonlinear dynamic systems. In this text an indirect method based on the dispersion function will be introduced in order to come up with optimal input for FIR filters followed by a polynomial nonlinearity. The optimization will be done with respect to the tuple frequency vector instead of the time sequence. Without constraints a solution is found that does not correspond to a time sequence. By imposing that the solution should lie in the subspace described by a symmetric and non-overlapping base a feasible solution was found that is considered optimal in its subspace.