$ H_\infty $ deployment of nonlinear multi-agent systems with Markov switching topologies over a finite-time interval based on T–S fuzzy PDE control

Hongbo Wei; Xuerong Cui; Yucheng Zhang; Jingyao Zhang; Hongbo Wei; Xuerong Cui; Yucheng Zhang; Jingyao Zhang

doi:10.3934/math.2024199

AIMS Mathematics

2024, Volume 9, Issue 2: 4076-4097. doi: 10.3934/math.2024199

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$ H_\infty $ deployment of nonlinear multi-agent systems with Markov switching topologies over a finite-time interval based on T–S fuzzy PDE control

1.
College of Oceanography and Space Informatics, China University of Petroleum (East China), Qingdao 266000, China
2.
Center for Advanced Computing Research, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100080, China

Received: 24 September 2023 Revised: 28 December 2023 Accepted: 02 January 2024 Published: 12 January 2024
MSC : 35R13, 93A16, 93D40

The deployment of multi-agent systems (MASs) is widely used in the fields of unmanned agricultural machineries, unmanned aerial vehicles, intelligent transportation, etc. To make up for the defect that the existing PDE-based results are overly idealistic in terms of system models and control strategies, we study the PDE-based deployment of clustered nonlinear first-order and second-order MASs over a finite-time interval (FTI). By designing special communication protocols, the collective dynamics of numerous agents are modeled by simple fist-order and second-order PDEs. Two practical factors, external disturbance and Markov switching topology, are considered in this paper to better match actual situations. Besides, T–S fuzzy technology is used to approximate the unknown nonlinearity of MASs. Then, by using boundary control scheme with collocated measurements, two theorems are obtained to ensure the finite-time $ H_\infty $ deployment of first-order and second-order agents, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches.
- nonlinear MASs,
- $ H_\infty $ deployment,
- finite-time interval,
- fuzzy PDE-based control,
- Markov switching topologies
Citation: Hongbo Wei, Xuerong Cui, Yucheng Zhang, Jingyao Zhang. $ H_\infty $ deployment of nonlinear multi-agent systems with Markov switching topologies over a finite-time interval based on T–S fuzzy PDE control[J]. AIMS Mathematics, 2024, 9(2): 4076-4097. doi: 10.3934/math.2024199

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Abstract

The deployment of multi-agent systems (MASs) is widely used in the fields of unmanned agricultural machineries, unmanned aerial vehicles, intelligent transportation, etc. To make up for the defect that the existing PDE-based results are overly idealistic in terms of system models and control strategies, we study the PDE-based deployment of clustered nonlinear first-order and second-order MASs over a finite-time interval (FTI). By designing special communication protocols, the collective dynamics of numerous agents are modeled by simple fist-order and second-order PDEs. Two practical factors, external disturbance and Markov switching topology, are considered in this paper to better match actual situations. Besides, T–S fuzzy technology is used to approximate the unknown nonlinearity of MASs. Then, by using boundary control scheme with collocated measurements, two theorems are obtained to ensure the finite-time $ H_\infty $ deployment of first-order and second-order agents, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches.

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