Finite-time trajectory tracking of multi-agent systems via higher-order dynamic networks with channel damage

For multi-agent trajectory tracking, strong communication channels between agents are crucial for group motion. In this paper, using undirected and directed higher-order complex networks described by second-order simplicial complexes, we investigated finite-time trajectory tracking of multi-agent systems when communication channels are damaged. By introducing the effective and damaged rates to the first-order and second-order channels of the multi-agent networks, and employing Lyapunov stability theory, and finite-time control techniques, we proposed several theoretical sufficient conditions that enable multiple agents in the response networks with damaged channels to track the trajectories of multiple agents in the drive networks within finite time. Extensive numerical simulations were conducted not only to verify the feasibility and effectiveness of the proposed theoretical results, but also to explore the effects of first-order channel, second-order channel, random damage, deliberate damage, one-time damage, and cascade damage on the finite-time tracking performance of multi-agent systems. We found that damage to first-order channels significantly impacts the tracking performance of multi-agent systems, while damage to second-order channels has a comparatively smaller impact. Deliberate damage is more detrimental to multi-agent systems than random damage. Random damage triggers significant phase fluctuations in tracking time. The directionality makes the network more vulnerable to channel damage.