Dynamic protection of human-cyber-physical systems based on CPN and multi-agent reinforcement learning: Evidence from smart coal mines

Abstract

Smart coal mines increasingly function as Human-Cyber-Physical Systems (HCPS), in which tightly coupled interactions generate dynamic risks that traditional static safeguards fail to address. This study develops a dynamic protection framework that integrates Colored Petri Nets (CPN) with Multi-Agent Reinforcement Learning (MARL) to model and mitigate cross-layer failures. A three-layer HCPS model is constructed to quantify interdependencies through a cross-layer propagation coefficient, and risk evolution is described using a simplified two-term time-evolution equation separating endogenous growth and external shocks. Gradual degradation and sudden disturbances are modeled via Gamma-Poisson hybrid processes, while CPN enables visualization of cascading faults across layers. MARL is used to optimize defense strategies under a joint-reward mechanism, facilitating coordinated interventions among human, cyber, and physical agents. Simulation results indicate that the cyber layer is particularly sensitive to external shocks, highlighting the necessity of enhanced real-time monitoring and cyber-attack resilience. MARL-enhanced strategies effectively slow risk accumulation and reduce cascading propagation. The contributions are refined into concise, parallel statements to improve clarity. The proposed framework provides a reproducible and adaptive approach for dynamic safety management in intelligent mining environments.