Secure Control of Networked Switched Systems Based on Two‐Level Stackelberg Game Approach Against Multiple Denial‐of‐Service Attackers

This article investigates the secure control strategy for networked switched systems against multiple denial‐of‐service (DoS) attackers by employing a two‐level Stackelberg game approach. Specifically, the sensor‐to‐controller (SC) DoS attacker group, the controller, and the controller‐to‐actuator (CA) DoS attacker group are modeled as three players in a game‐theoretic framework. Based on their respective positions in the network transmission process, a two‐level Stackelberg game is formulated. The sequence of actions is defined as follows: the SC DoS attacker group acts first, followed by the controller, and finally the CA DoS attacker group. The attack strength coefficient is introduced to quantify the contributions of individual attackers within a multiple‐attacker group. The packet loss rates and the controller gains are utilized to construct strategy sets for the attackers and the controller, respectively. Moreover, an algorithm is developed to compute the corresponding two‐level Stackelberg equilibrium based on the convex optimization approach. To handle the open‐loop and asynchronous switching scenarios caused by DoS attacks, sufficient conditions based on dwell‐time (DT) condition are derived to ensure the mean‐square stability. Moreover, considering the nonconvexity and strong nonlinearity of optimizing the switching signal, an improved particle swarm optimization (PSO) algorithm incorporating DT‐constrained decoding method is proposed to enhance the system performance. Finally, a practical example involving a continuous stirred tank reactor is presented to validate the effectiveness and superiority of the proposed methods.