On the Logical Control of Markovian Jump Boolean Networks: A Generalization

Markovian jump Boolean network (MJBN) switches between finite subsystems and the switching signal is a Markov chain, which is an extension of classic Boolean networks by taking into account the nondeterminacy. In this article, a constructive method of control scheme is proposed such that any given MJBNS is controllable, which covers some existing results as special cases. The design of controllers here includes presenting the control sequence as well as the construction of the logical relationship between the control nodes and system nodes. In addition, the design of controllers is based on the local neighbors’ information at the initial time instant without calculating the original transition matrix, which will dramatically reduce the computational complexity when steering MJBNs from the given initial value to the given desired state. Compared with the existing results, the proposed control protocol has some advantages since we do not need to know which subsystem the MJBN switched to in the previous time step, which is necessary for some previous literature. Finally, a biological example is provided to verify the effectiveness of the obtained results.