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Optimal state-flipped control and learning for synchronization of probabilistic Boolean networks.

Chenyang Bian1, Zhipeng Zhang2, Leihao Du3

  • 1School of Control Science and Engineering, Tiangong University, Tianjin, 300387, China.

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|June 5, 2025
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Summary

This study achieves guaranteed synchronization in Probabilistic Boolean Networks (PBNs) using optimal state-flipped control and Q-learning. These methods efficiently solve complex synchronization problems in large-scale PBNs.

Keywords:
Probabilistic Boolean networksQ-learning algorithmState flip controlSynchronization

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Area of Science:

  • Computational Biology
  • Control Theory
  • Artificial Intelligence

Background:

  • Probabilistic Boolean Networks (PBNs) are complex systems with applications in gene regulatory networks and artificial intelligence.
  • Achieving guaranteed synchronization in PBNs is a challenging problem due to their inherent probabilistic nature.
  • Existing methods often struggle with the computational complexity of large-scale PBNs.

Purpose of the Study:

  • To develop a robust method for achieving synchronization with probability 1 in PBNs.
  • To transform the synchronization problem into a more tractable set stabilization problem using the Semi-Tensor Product (STP) framework.
  • To enhance computational efficiency for both small and large-scale PBNs.

Main Methods:

  • The study employs the Semi-Tensor Product (STP) to convert the PBN synchronization problem into a set stabilization problem.
  • Optimal state-flipped control strategies are combined with Q-learning for efficient synchronization.
  • A reachable set criterion based on state-flipping is introduced to identify optimal flipping sequences.
  • A two-step Q-learning optimization strategy is proposed for large-scale PBNs, involving Q-table generation and optimal sequence enumeration.

Main Results:

  • The proposed methods successfully achieve synchronization with probability 1 in PBNs.
  • A novel reachable set criterion enhances computational efficiency by identifying optimal state-flipping sequences.
  • The Q-learning-based strategy significantly reduces the computational complexity for large-scale PBN synchronization.
  • Numerical simulations validate the effectiveness and practicality of the developed algorithms.

Conclusions:

  • The integration of optimal state-flipped control and Q-learning provides an effective solution for PBN synchronization.
  • The STP framework and reachable set criteria offer a computationally efficient approach to PBN analysis.
  • The proposed methods are practical and scalable, demonstrating significant potential for applications in complex biological and artificial systems.