  Boolean network (BN) is a simple model widely used to study complex dynamic
behaviour of biological systems. Nonetheless, it might be difficult to gather
enough data to precisely capture the behavior of a biological system into a set
of Boolean functions. These issues can be dealt with to some extent using
parametrised Boolean networks (ParBNs), as it allows to leave some update
functions unspecified. In this paper, we attack the control problem for ParBNs
with asynchronous semantics. While there is an extensive work on controlling
BNs without parameters, the problem of control for ParBNs has not been in fact
addressed yet. The goal of control is to ensure the stabilisation of a system
in a given state using as few interventions as possible. There are many ways to
control BN dynamics. Here, we consider the one-step approach in which the
system is instantaneously perturbed out of its actual state. A naive approach
to handle control of ParBNs is using parameter scan and solve the control
problem for each parameter valuation separately using known techniques for
non-parametrised BNs. This approach is however highly inefficient as the
parameter space of ParBNs grows doubly-exponentially in the worst case. In this
paper, we propose a novel semi-symbolic algorithm for the one-step control
problem of ParBNs, that builds on a symbolic data structures to avoid scanning
individual parameters. We evaluate the performance of our approach on real
biological models.
