  It has been shown that self-triggered control has the ability to reduce
computational loads and deal with the cases with constrained resources by
properly setting up the rules for updating the system control when necessary.
In this paper, self-triggered stabilization of Boolean control networks (BCNs),
including deterministic BCNs, probabilistic BCNs and Markovian switching BCNs,
is first investigated via semi-tensor product of matrices and Lyapunov theory
of Boolean networks. The self-triggered mechanism with the aim to determine
when the controller should be updated is given based on the decrease of the
corresponding Lyapunov functions between two successive sampling times. We show
that the self-triggered controllers can be chosen as the conventional
controllers without sampling, and also can be optimally constructed based on
the triggering conditions.
