Finite-time formation control with prescribed performance for multi-agent systems against FDI attacks using neural network observers

The research developed a resilient time-varying formation control strategy with prescribed-time convergence to a bounded residual set for non-strict-feedback second-order MASs to maintain accurate tracking under these conditions. Neural networks function to predict unknown nonlinear dynamics, while a state observer based on neural networks uses partial leader information to reconstruct unmeasured states. The effects of FDI attacks and communication uncertainties were addressed through matrix equalities/inequalities that solve Laplacian asymmetry problems. The proposed method achieves semi-global practical finite-time stability because it maintains all closed-loop signals within their bounded limits while tracking errors stay within their defined performance limits. The simulation results showed that formation errors achieve the prescribed bounds in finite time while maintaining stability and reliable coordination under adversarial and uncertain conditions, which demonstrates the method's robustness and scalability.