The Region of Attraction for Output Tracking in Probabilistic Boolean Control Networks

Bingquan Chen, Yuyi Xue (), Meiyu Li, Jin-Jin Mao and Aiju Shi
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Bingquan Chen: School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Yuyi Xue: School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Meiyu Li: School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Jin-Jin Mao: School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Aiju Shi: School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

Mathematics, 2025, vol. 13, issue 22, 1-17

Abstract: 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.

Keywords: Boolean control networks; probabilistic switching; output tracking control; tracking region of attraction; semi-tensor product (STP) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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