Abstract
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.
Highlights
Complexity science [1–3] studies complex systems and complexity and reveals and explains the operating laws of complex systems, involving nature, engineering, biology, economics, management, politics, and society
Due to the more accurate description of the historical dependence on systems, various modeling methods and theories of fractional-order dynamic systems based on the definition of fractional calculus have gradually been successfully applied in many fields, such as high-energy physics, anomalous diffusion, complex viscoelastic material mechanics, system control, rheology, biomedical engineering, and economics [20–22]
Several consensus problems are studied for fractional-order multi-agent systems (FOMASs) [23–28]
Summary
Complexity science [1–3] studies complex systems and complexity and reveals and explains the operating laws of complex systems, involving nature, engineering, biology, economics, management, politics, and society. There is little reported on the positive effect of noise on the consensus of MASs. Motivated by the above discussion, in this paper, we present a double-integral FOMAS in a common bounded fluctuating potential where the protocol term consists of both the relative position and velocity information of neighboring agents. The presented FOMAS can be synchronized by changing the noise intensity This method provided a brand-new way to realize consensus of fractional-order systems with uncontrollable system parameters by controlling the output noise intensity.
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