Prescribed-time cluster lag consensus control for second-order non-linear leader-following multiagent systems

Yuanhong Ren; Wuneng Zhou; Zhiwei Li; Ling Liu; Yuqing Sun

doi:10.1016/j.isatra.2020.09.012

Prescribed-time cluster lag consensus control for second-order non-linear leader-following multiagent systems

ISA Trans. 2021 Mar:109:49-60. doi: 10.1016/j.isatra.2020.09.012. Epub 2020 Oct 7.

Authors

Yuanhong Ren¹, Wuneng Zhou², Zhiwei Li³, Ling Liu⁴, Yuqing Sun⁵

Affiliations

¹ College of Information Science and Technology, Donghua University, Shanghai 201620, China. Electronic address: renyuanhong@sohu.com.
² College of Information Science and Technology, Donghua University, Shanghai 201620, China. Electronic address: wnzhou@dhu.edu.cn.
³ College of Information Science and Technology, Donghua University, Shanghai 201620, China; School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China. Electronic address: zhiwei.li@sues.edu.cn.
⁴ College of Information Science and Technology, Donghua University, Shanghai 201620, China.
⁵ School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China.

PMID: 33051052
DOI: 10.1016/j.isatra.2020.09.012

Abstract

Prescribed-time Lag consensus, as a special case of prescribed-time cluster lag consensus, is first investigated. The task is to design a control protocol for each follower so that the multiagent system (MAS) achieves lag consensus in any specified time. To achieve this goal, we propose a new distributed controller, in which the control gains are designed as time-varying functions related to the pre-specified time. In addition, a state transformation is introduced to tackle the technical difficulty caused by time-varying functions of different powers in the theoretical proof process. Then, a solution for the cluster lag consensus problem of the MAS is provided, so that under the proposed control protocol, each subsystem composed of followers from the same group and the leader achieves lag consensus with a different lag time in the specified time. By using a state transformation, Graph theory and generalized Lyapunov stability theory, the validity of the designed schemes is verified theoretically and sufficient conditions for the two conclusions are given respectively. Finally, we give two simulation examples to show performances of the proposed solutions.

Keywords: Cluster lag consensus; Leader-following multiagent systems; Non-linear dynamics; Prescribed-time consensus.