Bipartite consensus tracking of second-order fractional-order multi-agent systems on directed signed graphs

Abstract

This paper studies the bipartite consensus tracking problems of fractional-order multi-agent systems on directed signed graphs. Each agent is modelled as a second-order fractional-order dynamics with the order belonging to $(0,1]$, and the cooperative and competitive interactions between the agents coexist in the systems. Two distributed bipartite consensus tracking protocols are proposed for the systems based on continuous information and sampled information, respectively. Under the assumption that the directed signed graph is structurally balanced, it is shown that the second-order fractional-order multi-agent systems can achieve the bipartite consensus tracking if the feedback coefficients are chosen appropriately. Finally, several simulations are provided to verify the effectiveness of the theoretical results.

Keywords:

• Bipartite consensus tracking control
• second-order multi-agent systems
• fractional-order derivatives
• directed signed graphs
• periodic sampling schemes

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The paper describes entirely theoretical research. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 61903067 and 61976048].