D-Optimal Input Design for Nonlinear FIR-type Systems:A Dispersion-based Approach
For practitioners of nonlinear system identification, this provides a computationally efficient and implementable approach to optimal input design.
This work presents a D-optimal input design method for nonlinear FIR-type systems, formulated as a convex optimization problem solved via a dispersion-based scheme. The method yields a realizable time sequence by imposing symmetry and non-overlap constraints, with computational speed compared to cvx.
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 finite-impulse-response-type nonlinear systems is presented. The optimization of the determinant of the Fisher information matrix is expressed as a convex optimization problem. This problem is then solved using a dispersion-based optimization scheme, which 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 set, a realizable design is found. A graph-based method is used 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. Additionally the computational speed of the algorithm is compared with the general convex optimizer cvx.