D-Optimal Input Design for FIR-type Nonlinear Systems: A Dispersion-based Approach

Optimal input design is an important step of the identification process in order to reduce the model variance. In this work a D-optimal input design method for FIR-type nonlinear systems is presented. The optimization of the determinant of the Fisher matrix is expressed as a convex optimization problem. The optimization is performed using an equivalent dispersionbased criterion. This method is easy to implement and converges monotonically to the optimal solution. Without constraints, the optimal design cannot be realized as a time sequence. By imposing that the design should lie in the subspace described by a symmetric and non-overlapping basis, a realizable design is found. A graph-based method is implemented in order to find a time sequence that realizes this optimal constrained design. These methods are illustrated on a numerical example of which the results are thoroughly discussed.