Distributed Fault–Tolerant Attitude–Vibration Control of a Satellite with an Ultra–Large Flexible Antenna Via Stackelberg Games

Ultra–large space antennas (hundreds of meters) represent a key technology to advance Earth Observation and deep space exploration, pushing the limits of wide–range monitoring and high–resolution imaging. These structures exacerbate the coupling between attitude and vibrations and highly require fault–tolerant control over networks of distributed actuators. Thus, this paper proposes a hierarchical game–theoretic framework based on a Stackelberg formulation, where the leader ensures satellite attitude stabilization through optimized feedback, while the followers implement (i) saturated sliding–mode control for multi–modal vibration suppression and (ii) ADMM–based control allocation for fault tolerance without explicit fault diagnosis. The proposed approach is validated on a case study resembling NASA’s Innovative Space–Based Radar Antenna Technology (ISAT), modeled via rigid–flexible Lagrangian dynamics with distributed actuators. Compared with centralized and non–optimized distributed strategies, the proposed method achieves attitude error of 3.39×10–4 deg, stability accuracy of 1.24×10–4 deg/s, convergence within 117 s, first–mode displacement of 0.0414 with damping within 138 s, load balancing of 97.1%, and steady–state redundancy utilization of 1.41%. Results demonstrate effective attenuation of modal response, reduced torque demand under actuator failures, and scalability of the architecture to large actuator networks. This provides a viable pathway towards integrated fault–tolerant attitude–vibration control for ultra–flexible space structures in future missions.