Output controllability of impulsive Boolean control networks based on hybrid-index model

In biological systems, impulses are often used to model mutations in gene expression. In order to describe the instantaneity of the impulse, this paper employs a hybrid-index model of impulsive Boolean networks with state-triggered impulses. Based on this model, the time-domain output controllability is investigated. Using the quotient mapping method, the hybrid-domain solutions of this model are mapped to the time-domain solutions, mathematically. Then a necessary and sufficient condition for output controllability in the time domain is presented. Finally, an example is given to demonstrate the correctness and effectiveness of the obtained results. By resorting to the tool of semi-tensor product, this study investigates the output controllability of Boolean control networks with state-triggered impulses, which is an important model for describing gene regulatory networks. Compared with the time or event-based impulse triggering models, the hybrid-index model employed in this paper is more helpful in charactering the instantaneity of the impulsive processes. By using the quotient mapping method, the hybrid-domain solutions are mapped to the time-domain solutions. Combining with the analysis of the output-state transition matrix, the necessary and sufficient conditions for output controllability of impulsive Boolean control networks are derived.image