Two-degree-of-freedom low-order control scheme for multi-agent systems

Two-degree-of-freedom distributed low-order control scheme which can both realize the global tasks and provide good performance for the multi-agent systems is proposed in this paper. The two-degree-of-freedom control protocol which contains the individual controllers and the coupling controllers is firstly presented. The individual and coupling controllers are both of the proportion-integration-differentiation (PID) type. The two-degree-of-freedom multi-agent system is established according to the proposed protocol. Such the system is decoupled to several single-input-single-output (SISO) subsystems based on matrix theory. For each SISO subsystems, the PID stable region of the individual controllers satisfying H ∞ index is obtained based on the extended Hermite-Biehler theorem so as to improve the performance of each agent. Then, the control parameters of the coupling controllers that ensure the fast consensus of the whole system is determined by first deriving the stable region and then searching for the minimum of the real part of the roots of the characteristic equation in the obtained stable region. The simulation result verifies the effectiveness of the proposed method. The proposed two-degree-of-freedom low-order control scheme is applicable to the systems with arbitrary-order stable or unstable agents.