Finite Horizon Tracking Control of Boolean Control Networks

In this paper, we propose an approach to design tracking controllers for Boolean control networks to track a time-varying reference output trajectory of finite length by applying the semitensor product method. First, we give necessary and sufficient conditions for the trackability of the reference output trajectory. Second, in the case of a trackable output trajectory, one control sequence that realizes exact tracking can be found directly by means of backward selection. Otherwise, ℓ 4 and ℓ ∞ optimization problems can be formulated to find the control sequence that minimizes the tracking error. These optimization problems can be extended to take changes in control inputs into account. An additional advantage of the proposed approaches is that state, transition, and input constraints can be easily taken into account during the design of the controllers. Finally, illustrative example is given to demonstrate the proposed approaches.