Control algorithms combined with microfluidic
devices and microscopy have enabled in vivo real-time control
of protein expression in synthetic gene networks. Most control
algorithms rely on the a priori availability of mathematical
models of the gene networks to be controlled. These models
are typically black/grey box models, which can be obtained
through the use of data-driven techniques developed in the
context of systems identification. Data-driven inference of both
model structure and parameters is the main focus of this
paper. There are two main challenges associated with the
inference of dynamical models for real-time control of gene
regulatory networks in living cells. Since biological systems
are typically evolving over time, the first challenge stems
from the fact that model selection needs to be done online,
which prevents the application of computationally expensive
identification algorithms iterating through large amounts of
streaming data. The second challenge consists in performing
nonlinear model selection, which is typically too burdensome
for Kalman filtering related techniques due the heterogeneity
and nonlinearity of the candidate models. In this paper,
we combine sparse Bayesian techniques with classic Kalman
filtering techniques to tackle these challenges