Secure Control for VTOLH System Against Hybrid Attacks: A Hierarchical Zero‐Sum Game Approach

ABSTRACT This paper investigates secure control for vertical take‐off and landing helicopter (VTOLH) systems under hybrid cyber‐physical attacks, where denial‐of‐service (DoS) and false data injection (FDI) attacks coexist within the same communication channel. To address the interdependence and coordination between these attacks, a hierarchical zero‐sum game framework is established, capturing both the internal coordination among attackers and the external confrontation with the controller. A dual‐phase optimization algorithm is then developed to efficiently compute the equilibrium strategies of the system. In the first phase, the DoS and FDI attackers cooperatively determine their optimal attack probabilities by solving a constrained resource‐allocation optimization problem. In the second phase, the controller and the unified hybrid attacker engage in a zero‐sum game to derive the equilibrium strategies. Based on the obtained equilibrium strategies, the sufficient conditions for mean‐square exponential stability of the VTOLH system are derived. Finally, simulations demonstrate the method's effectiveness in maintaining stability with reduced computational complexity, validating the proposed approach.