Resilient algorithm for distributed resource allocation under false data injection attacks

For a first-order nonlinear multi-agent system who is subject to false data injection (FDI) attacks on agents' actuators and sensors, agents execute a distributed resource allocation algorithm according to the compromised control inputs and interactive information such that the multi-agent system is unstable and agents' decisions deviate from the optimal resource allocation. At first, we analyze the robustness of the distributed resource allocation algorithm under the FDI attacks. Then, a resilient distributed algorithm is proposed to solve the distributed resource allocation problem by resisting the adverse effect of the attacks. In detail, the unknown nonlinear term and the false data injected in agents are considered as extended states that can be estimated by extended state observers. The estimation is used in the feedback control to suppress the effect of the FDI attacks. As a result, the designed resilient algorithm ensures that agents' decisions converge to the optimal allocation without requiring any information about the nature of the attacks. An example is given to illustrate the results.