Two‐degree‐of‐freedom optimal consensus scheme of fractional‐order multi‐agent systems

Abstract

A two-degree-of-freedom consensus scheme is investigated for fractional-order multi-agent systems with time delay. The two-degree-of-freedom protocol including the individual controllers and the coupling controllers can realise the global tasks and improve consensus performance. Based on such a protocol, a closed-loop multi-input multi-output framework in frequency domain is established. Then the multi-agent system is decoupled into several subsystems with respect to the eigenvalues of the Laplacian matrix. For each subsystem, the robust stabilising region of the individual controller satisfying H ∞ index is obtained on the basis of the improved D-partition method. The controller parameters chosen in the region can provide robustness for the individual agent. The parameters of the coupling controller that ensure fast consensus are determined by first deriving the stabilising region and then searching for the fastest consensus speed in the obtained region. The two-degree-of-freedom structure can trade off the consensus performance and disturbance rejection and is applicable to arbitrary-order multi-agent systems with time delay including the fractional-order system and the integer-order system. The two-degree-of-freedom consensus controller satisfying other performance criteria can also be designed based on the resultant stabilising region. The simulation results verify the effectiveness of the proposed method.