Self-Triggered Scheduling for Boolean Control Networks

It has been shown that self-triggered control has the ability to deal with cases with constrained resources by properly setting up the rules for updating the system control when necessary. In this article, self-triggered stabilization of the Boolean control networks (BCNs), including the deterministic BCNs, probabilistic BCNs, and Markovian switching BCNs, is first investigated via the semitensor product of matrices and the Lyapunov theory of the Boolean networks. The self-triggered mechanism with the aim to determine when the controller should be updated is provided by the decrease of the corresponding Lyapunov functions between two consecutive samplings. Rigorous theoretical analysis is presented to prove that the designed self-triggered control strategy for BCNs is well defined and can make the controlled BCNs be stabilized at the equilibrium point.