The framework demonstrates invariant set theory and a recursive algorithm to ensure output tracking in biological networks.
This paper investigates the asymptotic output tracking problem in probabilistic Boolean control networks by introducing the concept of the tracking region of attraction (TROA). For a constant reference signal, we provide a formal definition of the TROA, and establish the existence and uniqueness of the maximum TROA. The core contributions include a verifiable sufficient condition for TROA identification based on invariant set theory, a corresponding state feedback control design method, and a recursive algorithm for computing the maximum TROA. The proposed framework is validated through two simplified biological network case studies, including an apoptosis network and an Escherichia coli lactose operon network. Simulation results demonstrate that the designed controllers ensure asymptotic output tracking with probability one from any initial state within the maximum TROA.
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Chen et al. (2025) studied this question.
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