Consensus of Fractional-Order Double-Integral Multi-Agent System in a Bounded Fluctuating Potential

At present, the consensus problem of fractional complex systems has received more attention. However, there is little literature on the consensus problem of fractional-order complex systems under noise disturbance. In this paper, we present a fractional-order double-integral multi-agent system affected by a common bounded fluctuating potential, where the protocol term consists of both the relative position and velocity information of neighboring agents. The consensus conditions of the presented system in the absence of noise are analytically given and verified by a numerical simulation algorithm. Then, the influences of the system order and other system parameters on the consensus of the presented system in the presence of bounded noise are also analyzed. It is found that when compared with the classical integer-order system, the presented fractional-order system has a larger range of consensus parameters and has more rich dynamic characteristics under the action of random noise. Especially, the bounded noise has a promoting effect on the consensus of the presented fractional-order system, while there is no similar phenomenon in the corresponding integer-order system.