Optimal output tracking of Boolean control networks

Abstract

The traditional output tracking problem for a system is to design a controller such that the output of the system tracks a constant signal or a network after a finite time. However, when the output of the system can not completely track the reference signal, there is no result to show how to deal with this situation. To solve such problem, we investigate the optimal output tracking problem of Boolean control networks (BCNs) with a constant reference signal in this paper, that is, to design an appropriate control scheme such that each state will evolve to their optimal output tracking trajectory. Firstly, the optimal output tracking cycle (OTC) of each state is defined. Secondly, a method is presented to compute the cycle with certain length in the system, and the least upper bound of the length for the optimal OTC is derived. Finally, a constructive algorithm is presented to design the state feedback controllers that enable the system to realize optimal output tracking. Moreover, an illustrative example is given to show the obtained results.