This article investigates the reference trajectory output tracking issue of Boolean control networks (BCNs) that have controls in the output. Firstly, to solve the problem, some necessary and sufficient conditions are obtained. The tracking problem is studied from the perspective of set and matrix calculation. Next, an algorithm for determining whether the output tracking issue is solvable is proposed. Furthermore, the controller design algorithm satisfying the solvability condition is given. Using our methods, we can track some trajectories that cannot be tracked in BCNs without controls in output. In addition, for better application in practice, the corresponding changes in the network transition matrix and output matrix under state, transition, and input constraints are considered. Finally, some examples are presented to illustrate the validity of our results.

This paper focuses on output controllability and observability of mix-valued logic control networks (MLCNs), of which the updating of outputs is determined by both inputs and states via logical rules. First, as for output controllability, the number of different control sequences are derived to steer a MLCN from a given initial state to a destination output in a given number of time steps via semi-tensor product method. By construsting the output controllability matrix, criteria for the output controllability are obtained. Second, to solve the problem of observability, we construct an augmented MLCN with the same transition matrix, and use the set controllability approach to determine the observability of MLCNs. Finally, a hydrogeological example is presented to verify the obtained results.