This paper proposes an adaptive neural network-based backstepping controller that uses rigid graph theory to address the distance-based formation control problem and target tracking for nonlinear multi-agent systems with bounded time-delay and disturbance. The radial basis function neural network (RBFNN) is used to overcome and compensate for the unknown nonlinearity and disturbance in the system dynamics. The effect of the state time-delay of the agents is alleviated by using an appropriate control signal that is designed based on specific Lyapunov function and Young's inequality. The adaptive neural network (NN) weights tuning law is derived using this Lyapunov function. An upper bound for the singular value of the normalized rigidity matrix is introduced, and uniform ultimate boundedness (UUB) of the formation distance error is rigorously proven based on the Lyapunov stability theory. Finally, the performance and effectiveness of the proposed method are validated through the simulation results on nonlinear multi-agent systems. Comparisons between the proposed distance-based method and an existing, displacement-based method are provided to evaluate the performance of the suggested method.
