Coherence-Based Input Design for Nonlinear Systems

Many off-the-shelf generic non-linear model structures have inherent sparse parametrizations. Volterra series and non-linear Auto-Regressive with eXogeneous inputs (NARX) models are examples of this. It is well known that sparse estimation requires low mutual coherence, which translates into input sequences with certain low correlation properties. This letter highlights that standard optimal input design methods do not account for this requirement which may lead to designs unsuitable for this type of model structure. To tackle this problem, this letter proposes incorporating a coherence constraint to standard input design problems. The coherence constraint is defined as the ratio between the diagonal and non-diagonal entries of the Fisher information matrix (FIM) and can be easily added to any input design problem for nonlinear systems, while the resulting problem remains convex. This letter provides a theoretical analysis of how the range of the optimal objective function of the original problem is affected by the coherence constraint. Additionally, this letter presents numerical evaluations of the proposed approach's performance on a Volterra series model in comparison to state-of-the-art algorithms.