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Robust Invariant Set Analysis of Boolean Networks

Author

Listed:
  • Bowen Li
  • Jungang Lou
  • Yang Liu
  • Zhen Wang

Abstract

In this paper, the robust invariant set (RIS) of Boolean (control) networks with disturbances is investigated. First, for a given fixed point, consider a special set called immediate neighborhoods of the fixed point; then a discrete derivative of Boolean functions at the fixed point is used to analyze the robust invariance, based on which a sufficient condition is obtained. Second, for more general sets, the robust output control invariant set (ROCIS) of Boolean control networks (BCNs) is investigated by semitensor product (STP) of matrices. Then, under a given output feedback controller, we obtain a necessary and sufficient condition to check whether a given set is robust control invariant set (RCIS). Furthermore, output feedback controllers are designed to make a set to be a RCIS. Finally, the proposed methods are illustrated by a reduced model of the lac operon in E. coli .

Suggested Citation

  • Bowen Li & Jungang Lou & Yang Liu & Zhen Wang, 2019. "Robust Invariant Set Analysis of Boolean Networks," Complexity, Hindawi, vol. 2019, pages 1-8, February.
    • Handle: RePEc:hin:complx:2731395
    DOI: 10.1155/2019/2731395
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    References listed on IDEAS

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    1. Tong, Liyun & Liu, Yang & Lou, Jungang & Lu, Jianquan & Alsaadi, Fuad E., 2018. "Static output feedback set stabilization for context-sensitive probabilistic Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 263-275.
    2. Qiuli Liu & Qingguo Zeng & Jinghao Huang & Deliang Li, 2018. "Optimal Intervention in Semi-Markov-Based Asynchronous Probabilistic Boolean Networks," Complexity, Hindawi, vol. 2018, pages 1-12, September.
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    Cited by:

    1. Luis A. Escobar & Hyobin Kim & Carlos Gershenson, 2019. "Effects of Antimodularity and Multiscale Influence in Random Boolean Networks," Complexity, Hindawi, vol. 2019, pages 1-14, June.
    2. Wu, Shuchen & Sun, Xiaohui & Li, Xiaodi & Wang, Haipeng, 2020. "On controllability and observability of impulsive control systems with delayed impulses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 65-78.

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