Finite horizon tracking control of Boolean control networks

In this paper, we propose an approach to design tracking controllers for Boolean control networks (BCNs) to track a time-varying reference output trajectory of finite length by applying the semi-tensor product method. First, we give the necessary and sufficient conditions for the reachability of the output trajectory. Secondly, in the case of a reachable output trajectory, one control sequence that realizes exact tracking can be found directly by means of backward selection. Otherwise, a method to find a control sequence is proposed to minimize the tracking error. An additional advantage of the proposed approach is that state and transition constraints can be easily taken into account during the design of the controllers. Finally, illustrative examples are given to show the proposed results.