Optimal Denial of Service attack on matrix-weighted multi-cluster consensus encircling a moving-target

Matrix-weighted graphs provide a powerful framework for modeling multidimensional interactions in multi-agent systems. This paper investigates multi-cluster consensus in matrix-weighted graphs under adversarial Denial-of-Service (DoS) attacks. We consider agents that coordinate around a moving leader while interacting over a matrix-weighted topology. An adversary seeks to disrupt this process by selectively disabling a limited set of communication links. The attack design is formulated as an optimal control problem, and necessary conditions for the optimal disruption strategy are derived using Pontryagin’s Maximum Principle. To enhance applicability, we further propose a weight-based heuristic that approximates the optimal attack policy. Numerical simulations demonstrate the effectiveness of the proposed strategies.