Disturbance Decoupling of Singular Boolean Control Networks

Output Feedback Control for Set Stabilization of Boolean Control Networks

In this paper, the output feedback set stabilization problem for Boolean control networks (BCNs) is investigated with the help of the semi-tensor product (STP) tool. The concept of output feedback control invariant (OFCI) subset is introduced, and novel methods are developed to obtain the OFCI subsets. Based on the OFCI subsets, a technique, named spanning tree method, is further introduced to calculate all possible output feedback set stabilizers. An example concerning lac operon for the bacterium Escherichia coli is given to illustrate the effectiveness of the proposed method. This technique can also be used to solve the state feedback (set) stabilization problem for BCNs. Compared with the existing results, our method can dramatically reduce the computational cost when designing all possible state feedback stabilizers for BCNs.

Robust Reachability of Boolean Control Networks

Boolean networks serve a powerful tool in analysis of genetic regulatory networks since it emphasizes the fundamental principles and establishes a nature framework for capturing the dynamics of regulation of cellular states. In this paper, the robust reachability of Boolean control networks is investigated by means of semi-tensor product. Necessary and sufficient conditions for the robust reachability of Boolean control networks are provided, in which control inputs relying on disturbances or not are considered, respectively. Besides, the corresponding control algorithms are developed for these two cases. A reduced model of the lac operon in the Escherichia coli is presented to show the effectiveness of the presented results.

Sampled-Data State Feedback Stabilization of Boolean Control Networks

In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.