This technical note considers the identification of
nonlinear discrete-time systems with additive process noise but
without measurement noise. In particular, we propose a method
and its associated algorithm to identify the system nonlinear functional
forms and their associated parameters from a limited number
of time-series data points. For this, we cast this identification
problem as a sparse linear regression problem and take a Bayesian
viewpoint to solve it. As such, this approach typically leads to
nonconvex optimizations. We propose a convexification procedure
relying on an efficient iterative re-weighted 1-minimization algorithm
that uses general sparsity inducing priors on the parameters
of the system and marginal likelihood maximisation. Using this
approach, we also show how convex constraints on the parameters
can be easily added to the proposed iterative re-weighted
1-minimization algorithm. In the supplementary material available
online (arXiv:1408.3549), we illustrate the effectiveness of the
proposed identification method on two classical systems in biology
and physics, namely, a genetic repressilator network and a large
scale network of interconnected Kuramoto oscillators.