Resilient Tracking of Bearing-Constrained Leader–Follower Formations Under Denial-of-Service Attacks

Rigidity-based formation control under cyber-attacks remains largely unexplored. This paper proposes a resilient bearing-based formation control framework for multi-agent systems subject to Denial-of-Service (DoS) attacks that disrupt inter-agent measurements. The framework accommodates both single-integrator and double-integrator agent dynamics and allows the desired formation to be time-varying, with constant or bounded velocity. Within this framework, DoS attacks are classified into two independent categories, namely rigidity-maintained and rigidity-broken attacks. The control parameters are systematically designed by explicitly incorporating both the formation topology and the characteristics of the attacks. Under some conditions on the communication graph and attack durations, the proposed control law, which relies solely on relative position measurements, guarantees asymptotic formation tracking for single-integrator agents when the leaders move with a common constant velocity. In the presence of bounded time-varying common leader velocities, finite-time recovery of the formation is ensured. For double-integrator agents, asymptotic formation tracking is achieved when both relative position and relative velocity measurements are available and the leaders move with a common constant velocity. Moreover, in the presence of bounded time-varying common leader velocities, the proposed control law guarantees uniformly ultimately bounded tracking errors under the additional assumption that each follower has access to its local velocity measurement. All theoretical results are rigorously proved and validated through simulations.