Distributed optimization of nonlinear singularly perturbed multi-agent systems via a small-gain approach and sliding mode control

Qian Li; Zhenghong Jin; Linyan Qiao; Aichun Du; Gang Liu; Qian Li; Zhenghong Jin; Linyan Qiao; Aichun Du; Gang Liu

doi:10.3934/math.20241015

AIMS Mathematics

2024, Volume 9, Issue 8: 20865-20886. doi: 10.3934/math.20241015

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Research article

Distributed optimization of nonlinear singularly perturbed multi-agent systems via a small-gain approach and sliding mode control

1.
School of Vehicle and Transportation Engineering, Henan Institute of Technology, Xinxiang 453003, China
2.
School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore
3.
State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou 310027, China
4.
School of Mechanical and Electrical Department, Hami Vocational and Technical College, Hami 839000, China

Received: 24 April 2024 Revised: 11 June 2024 Accepted: 24 June 2024 Published: 27 June 2024
MSC : 93A16, 93C10, 93C70

This paper addressed the challenging problem of distributed optimization for nonlinear singular perturbation multi-agent systems. The main focus lies in steering the system outputs toward the optimal points of a globally objective function, which was formed by the combination of several local functions. To achieve this objective, the singular perturbation multi-agent system was initially decomposed into fast and slow subsystems. Compared to traditional methods, robustness in reference-tracking signals was ensured through the design of fast-slow sliding mode controllers. Additionally, our method ensured robustness against errors between reference signals and optimal values by employing a distributed optimizer to generate precise reference signals. Furthermore, the stability of the entire closed-loop system was rigorously guaranteed through the application of the small-gain theorem. To demonstrate the efficacy of the proposed approach, a numerical example was presented, providing empirical validation of its effectiveness in practical scenarios.
- distributed optimization,
- robust stability,
- singularly perturbed systems,
- small-gain theorem,
- sliding mode control
Citation: Qian Li, Zhenghong Jin, Linyan Qiao, Aichun Du, Gang Liu. Distributed optimization of nonlinear singularly perturbed multi-agent systems via a small-gain approach and sliding mode control[J]. AIMS Mathematics, 2024, 9(8): 20865-20886. doi: 10.3934/math.20241015

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Abstract

This paper addressed the challenging problem of distributed optimization for nonlinear singular perturbation multi-agent systems. The main focus lies in steering the system outputs toward the optimal points of a globally objective function, which was formed by the combination of several local functions. To achieve this objective, the singular perturbation multi-agent system was initially decomposed into fast and slow subsystems. Compared to traditional methods, robustness in reference-tracking signals was ensured through the design of fast-slow sliding mode controllers. Additionally, our method ensured robustness against errors between reference signals and optimal values by employing a distributed optimizer to generate precise reference signals. Furthermore, the stability of the entire closed-loop system was rigorously guaranteed through the application of the small-gain theorem. To demonstrate the efficacy of the proposed approach, a numerical example was presented, providing empirical validation of its effectiveness in practical scenarios.

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