Observer-based quasi-consensus of fractional-order multi-agent systems via dynamic event-triggered boundary control

This paper addresses the quasi-consensus problem of fractional-order multi-agent systems (FOMASs) governed by partial differential equations under sensing and communication constraints. Two observer-based dynamic event-triggered boundary control strategies are proposed to estimate and regulate the system states in scenarios with partial spatial sensing and boundary sensing, respectively. Both a partial domain observer and a boundary observer of the Luenberger type are constructed to reconstruct the system dynamics under limited measurements. To reduce communication burden while maintaining control performance, dynamic event-triggered controllers with adaptive thresholds are developed. Rigorous Lyapunov-based analysis shows that the proposed strategies guarantee the achievement of quasi-consensus. Moreover, the existence of a strictly positive lower bound for the inter-event times is formally established, thereby excluding Zeno behavior. Numerical simulations are provided to verify the effectiveness of the proposed methods.