Prescribed-time bipartite consensus for signed directed networks on time scales

Abstract

This note deals with the prescribed-time consensus problem for multi-agent systems over directed networks with hybrid cooperative and antagonistic interactions on time scales. Different from the regular finite/fixed-time control where the settling time depends on the system initial conditions or the system parameters, the proposed prescribed-time control protocol can directly lead to a predetermined convergence time. Existing results on finite/fixed-time consensus all require the considered network topologies depicted by undirected graphs or strongly connected and detail-balanced directed graphs. In this note, by resorting to a prescribed-time function and the direct Lyapunov method, it is shown that the prescribed-time bipartite consensus can be realised, which only requires the directed network topology to be strongly connected. In addition, based on the theory of time scales, a unified prescribed-time protocol is firstly proposed to solve the consensus problem for both continuous-time and discrete-time multi-agent systems simultaneously.

Keywords:

• Prescribed-time convergence
• bipartite consensus
• multi-agent systems
• signed directed networks
• antagonistic interactions
• time scales

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the National Key Research and Development Program of China under Grant 2018YFB1003800, in part by the Surface Project of Natural Science Foundation of Chongqing under Grant cstc2021jcyj-msxmX1043, in part by the Talent Introduction Fund under Grant E012A2021238, in part by the Major Project of Science and Technology Research Program of Chongqing Education Commission of China under Grant KJZD-M202100602, in part by the National Natural Science Foundation of China under Grant 61876200, in part by the key Cooperation Project of Chongqing Municipal Education Commission under Grant HZ2021008, and in part by the Natural Science Foundation of Chongqing under Grant cstc2019jcyj-cxttX0002 and Grant cstc2021ycjh-bgzxm0013.