Bipartite consensus for multi-agent networks of fractional diffusion PDEs via aperiodically intermittent boundary control

Xinxin Zhang; Huaiqin Wu; Xinxin Zhang; Huaiqin Wu

doi:10.3934/mbe.2023563

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 12649-12665. doi: 10.3934/mbe.2023563

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Research article

Bipartite consensus for multi-agent networks of fractional diffusion PDEs via aperiodically intermittent boundary control

Xinxin Zhang ^{1
,
,},
Huaiqin Wu ²

1.
School of Information Engineering, Tianjin University of Commerce, Tianjin, China
2.
School of Science, Yanshan University, Qinhuangdao 066001, China

Academic Editor: Xiaodong Huang

Received: 05 April 2023 Revised: 09 May 2023 Accepted: 16 May 2023 Published: 26 May 2023

In this paper, the exponential bipartite consensus issue is investigated for multi-agent networks, whose dynamic is characterized by fractional diffusion partial differential equations (PDEs). The main contribution is that a novel exponential convergence principle is proposed for networks of fractional PDEs via aperiodically intermittent control scheme. First, under the aperiodically intermittent control strategy, an exponential convergence principle is developed for continuously differentiable function. Second, on the basis of the proposed convergence principle and the designed intermittent boundary control protocol, the exponential bipartite consensus condition is addressed in the form of linear matrix inequalities (LMIs). Compared with the existing works, the result of the exponential intermittent consensus presented in this paper is applied to the networks of PDEs. Finally, the high-speed aerospace vehicle model is applied to verify the effectiveness of the control protocol.
- multi-agent system,
- networks,
- fractional PDEs,
- bipartite consensus,
- intermittent boundary control
Citation: Xinxin Zhang, Huaiqin Wu. Bipartite consensus for multi-agent networks of fractional diffusion PDEs via aperiodically intermittent boundary control[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 12649-12665. doi: 10.3934/mbe.2023563

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Abstract

In this paper, the exponential bipartite consensus issue is investigated for multi-agent networks, whose dynamic is characterized by fractional diffusion partial differential equations (PDEs). The main contribution is that a novel exponential convergence principle is proposed for networks of fractional PDEs via aperiodically intermittent control scheme. First, under the aperiodically intermittent control strategy, an exponential convergence principle is developed for continuously differentiable function. Second, on the basis of the proposed convergence principle and the designed intermittent boundary control protocol, the exponential bipartite consensus condition is addressed in the form of linear matrix inequalities (LMIs). Compared with the existing works, the result of the exponential intermittent consensus presented in this paper is applied to the networks of PDEs. Finally, the high-speed aerospace vehicle model is applied to verify the effectiveness of the control protocol.

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