Observer-based ADP for secure resource allocation in high-order nonlinear multi-agent systems under FDI attacks.

This paper investigates the secure resource allocation problem (RAP) for high-order nonlinear multi-agent systems (MASs) under false data injection (FDI) attacks. Different from conventional RAPs, the considered problem involves both actuator-side and sensor-side attacks, which may simultaneously corrupt the closed-loop control input and the output information used for local gradient computation. As a result, the gradient-consensus mechanism and resource-balance condition may be disrupted, leading to incorrect resource allocation or even closed-loop instability. To address this problem, an observer-based adaptive dynamic programming (ADP) framework is proposed. First, an adaptive attack-estimation mechanism is designed to compensate for actuator-side attacks and recover trustworthy output information from corrupted measurements. Based on the corrected output, a deviation dynamic system is constructed by embedding gradient information and multiplier dynamics, such that the Karush-Kuhn-Tucker conditions of the RAP can be incorporated into the high-order closed-loop control design. Then, a single-critic neural network is employed to approximate the Hamilton-Jacobi-Bellman equation online, leading to a performance-oriented secure allocation controller that jointly accounts for allocation error, control energy, and attack-compensation effort. Theoretical analysis shows that the closed-loop error signals are practical fixed-time stable, and that the resulting allocation satisfies an approximate KKT condition within fixed time. Finally, numerical simulations are provided to verify the effectiveness of the proposed method.