The ability to control the behavior of intracellular networks has relevant applications, ranging from an optimized synthesis of metabolites in bacteria to the cure of human diseases. To implement a controller in vivo, one may insert synthetic biomolecules into the cell being controlled. This paper develops a formal approach, based on Supervisory Control Theory (SCT), to guide the design of synthetic genes that control the dynamics of gene regulatory networks, major players in cell dynamics, so that a set of specifications is achieved. Such a systematic procedure is important to make the control of large networks by synthetic molecules feasible.

In our approach, we assume that the behavior of gene networks can be abstracted by finite state machines, where each state corresponds to a set of gene expression levels and the events are associated with the activation/repression of genes. We then extend the SCT framework to address the so-called state attraction problem, for the case where the controller is allowed to: a) enable/disable events, b) force events, and c) preempt the occurrence of some (possibly all) plant events.