Boundary Control Strategies for Consensus of Fractional-Order Multi-Agent Systems Based on Coupling PDE-ODEs

This brief investigates the consensus problem in fractional-order multi-agent systems (MASs) modeling partial differential equations-ordinary differential equations (PDE-ODEs) by boundary control with directed topology. Boundary controllers reduce control costs, especially when deploying actuators in the entire spatial domain is impractical. As a result, actuators are positioned exclusively at spatial boundary locations in the boundary control method. Moreover, by applying the Mittage-Leffler function and some fractional-order inequalities, sufficient conditions for fractional-order MASs to reach consensus are obtained through LMI. Finally, a numerical simulation example illustrates the validity of the presented theory.