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Asymptotic Output Tracking of Probabilistic Boolean Control Networks

In this paper, we investigate the asymptotic output tracking control problem of probabilistic Boolean control networks. Firstly, based on the largest control invariant subset and the limit theory of Markov chains, the conditions are proposed to judge whether the output trajectory of a probabilistic Boolean control network can asymptotically track a constant reference signal via the state feedback control and output feedback control, respectively. Next, based on an augmented system, similar criteria are obtained to judge whether the output of a reference Boolean network is asymptotically trackable by the output trajectory of a probabilistic Boolean control network under the state feedback control and output feedback control, respectively. The corresponding controller design methods are given. Two examples are shown to illustrate the effectiveness of the obtained results.