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This technical note considers the identification of nonlinear discrete-timesystems with additive process noise but without measurement noise. Inparticular, we propose a method and its associated algorithm to identify thesystem nonlinear functional forms and their associated parameters from alimited number of time-series data points. For this, we cast thisidentification problem as a sparse linear regression problem and take aBayesian viewpoint to solve it. As such, this approach typically leads tononconvex optimisations. We propose a convexification procedure relying on anefficient iterative re-weighted $\ell_1$-minimisation algorithm that usesgeneral sparsity inducing priors on the parameters of the system and marginallikelihood maximisation. Using this approach, we also show how convexconstraints on the parameters can be easily added to our proposed iterativere-weighted $\ell_1$-minimisation algorithm. In the supplementary material\cite{appendix}, we illustrate the effectiveness of the proposed identificationmethod on two classical systems in biology and physics, namely, a geneticrepressilator network and a large scale network of interconnected Kuramotooscillators.

A Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems