Asymptotic target tracking for multi-agent systems under small communication delays in alignment interactions
Hyunjin Ahn, Seung‐Yeal Ha, Seungjun Lee · Journal of Mathematical Physics · 2026
We study asymptotic target tracking for multi-agent systems under communication time-delays. In the proposed models, the time-delay appears in the interaction term among tracking agents and represents the delay caused by information transmission through the communication network. The proposed systems consist of three main effects: delayed alignment among tracking agents, damping, and attraction toward prescribed targets. Here, asymptotic target tracking means that each tracking agent approaches its prescribed target as time tends to infinity. We consider two explicit tracking models with time-dependent communication delays, depending on the regularity and structure of the prescribed target trajectories. When the delays vanish, these models reduce to the non-delayed tracking models studied in our previous work. To handle the delayed communication terms, we introduce suitable delay-variation functionals and derive coupled energy–delay estimates. Under appropriate smallness conditions on the delay size, system parameters, interaction kernels, and initial data, we provide sufficient frameworks leading to asymptotic target tracking for the proposed models.