A preliminary study on D-Optimal Input Design for Nonlinear Systems

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 dispersion-based 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. Next, a graph-based method is implemented in order to find a time sequence that realizes this optimal constrained design.