Resource allocation game for secure transmission scheduling in two‐hop CPSs subject to strategic DoS attacks

Abstract This paper investigates the secure transmission scheduling problem for remote state estimation in cyber‐physical systems (CPSs) with a two‐hop network architecture. We formulate a dynamic zero‐sum game to model the strategic interactions between a defensive team (comprising an energy‐harvesting sensor and a relay) and a strategic denial‐of‐service attacker. The defensive team collaborates to forward state estimates to a remote estimator, while the attacker aims to degrade the system performance by intelligently disrupting the wireless channels. A key aspect of our model is the attacker's strategy: it must simultaneously target both communication channels (sensor‐to‐relay or relay‐to‐estimator), but also determine the amount of energy to expend in each attack, all under a total energy budget. On the defensive side, the sensor and relay are powered by energy harvesting from a stochastic environment, which is modeled as a Markov chain to capture the temporal correlations in energy availability. The corresponding Nash Equilibrium (NE) strategies are derived and analyzed using a Markov decision process framework and verified via a multi‐agent reinforcement learning algorithm. Finally, simulation results are presented to validate the theoretical findings.