This work focuses on the finite-time synchronization (F-TS) for nonidentical delayed neural networks (DNNs) including Caputo fractional partial differential operator and reaction–diffusion terms. A novel F-TS lemma is proposed by constructing a new Caputo differential inequality. Applying the new lemma and designing two hybrid controllers with time delay and the sign function, the F-TS criteria on the introduced Caputo reaction–diffusion nonidentical DNNs under the Neumann boundary condition are derived by making use of the Filippov differential inclusion, Green's theorem, and fractional Razumikhin theorem. The conditions are expressed through the algebraic inequality which can greatly decrease the computation in checking the F-TS performance. Moreover, the validity and correctness of the F-TS results are illustrated by selecting various orders, spatial positions, and diffusion parameters.
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.