Hierarchical clustering and dimensional reduction for optimal control of large-scale agent-based models

Agent-based models (ABMs) capture complex systems of interacting entities that can exhibit emergent behaviours such as consensus formation and clustering. As the number of agents and the dimension of their internal state grow, optimal control synthesis becomes computationally prohibitively. We present a scalable control framework that combines two model-order reduction steps: agent clustering and projection via Proper Orthogonal Decomposition (POD). These are integrated into a feedback loop that designs and applies optimal control laws on a reduced representation of the system. Using a first-order opinion-dynamics model with state-dependent influence, we show that the method boosts control efficiency and succeeds in settings where direct control becomes intractable.