Adaptive Fault-Tolerant Boundary Control of UAV Formations with Reliable Interior Sensing via a PDE Continuum Model

An adaptive fault-tolerant boundary controller is developed for large UAV leader–follower formations affected by leader actuator faults. The formation-error dynamics are modeled by a one-dimensional parabolic PDE with reaction and convection terms, with the leader represented as the actuated boundary. The faulty boundary input contains an unknown loss of effectiveness and an unknown additive bias. The controller and estimator use a reliable interior UAV as the sensing node, avoiding leader-side measurements that may be compromised by faults on the leader platform. A filter-based input–output parameterization relates this interior measurement to the actuator efficiency, the bias fault, and an equivalent spatial residual kernel. Normalized projection-based adaptive laws estimate the unknown fault parameters and keep the efficiency estimate strictly positive. The stabilizing command is obtained from a PDE backstepping transformation, and estimation mismatch is treated as a boundary residual. The analysis proves closed-loop boundedness, ideal convergence under asymptotically exact fault compensation and boundary-relevant state reconstruction, and practical stability in the presence of residual modeling error, measurement noise, and input saturation. Simulations on a continuum PDE, finite-dimensional UAV chains, and a moving planar UAV formation confirm the recovery mechanism.