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

## TL;DR

This paper introduces a convex optimization approach using dispersion-based methods to design D-optimal inputs for nonlinear FIR-type systems, ensuring realizability and efficient computation.

## Contribution

It presents a novel dispersion-based optimization scheme for D-optimal input design in nonlinear FIR systems, with a graph-based method for realizability.

## Key findings

- The proposed method converges monotonically to the optimal solution.
- The approach is computationally faster than general convex optimizers.
- Numerical examples demonstrate the effectiveness of the design.

## Abstract

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.