<p>This paper investigates distributed time-varying formation tracking for nonlinear multi-agent systems subject to input delay, external disturbances, and stochastic noise. A novel edge-based adaptive control protocol is developed that eliminates the need for Laplacian eigenvalue information and relies only on local relative state measurements among neighbors. To handle nonlinearity, a Lipschitz-based analysis is employed, while a formation compensation function is introduced to regulate time-varying formation dynamics. Furthermore, an adaptive update law is designed to mitigate the effects of stochastic noise and delayed inputs. Using Lyapunov stability theory, it is proven that the proposed strategy guarantees uniformly ultimately bounded formation tracking errors. Numerical simulations in both leaderless and leader–follower scenarios demonstrate the robustness and effectiveness of the proposed approach.</p>