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Survey on Mathematical Models and Methods of Complex Logical Dynamical Systems

Author

Listed:
  • Xiangshan Kong

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

  • Qilong Sun

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

  • Haitao Li

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

Abstract

Logical dynamical systems (LDSs) have wide applications in gene regulation, game theory, digital circuits, and so on. In LDSs, phenomena such as impulsive effect, time delays, and asynchronous behavior are not negligible, which generate complex LDSs. This paper presents a detailed survey on models and methods of investigating LDSs. Firstly, some preliminary results on LDSs and semi-tensor product (STP) method are presented. Secondly, some new developments on modeling complex LDSs are summarized, including switched LDSs, probabilistic LDSs, delayed LDSs, LDSs with impulsive effects, asynchronous LDSs, constrained LDSs, and implicit LDSs. Finally, the control design techniques of LDSs are reviewed, including reachable set approach, sampled-data control, event-triggered control, and control Lyapunov function method.

Suggested Citation

  • Xiangshan Kong & Qilong Sun & Haitao Li, 2022. "Survey on Mathematical Models and Methods of Complex Logical Dynamical Systems," Mathematics, MDPI, vol. 10(20), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3722-:d:938534
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    References listed on IDEAS

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    Cited by:

    1. Qilong Sun & Haitao Li, 2022. "Robust Stabilization of Impulsive Boolean Control Networks with Function Perturbation," Mathematics, MDPI, vol. 10(21), pages 1-12, October.

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