@article{Li2024, 
author = {Qian Li and Zhenghong Jin and Linyan Qiao and Aichun Du and Gang Liu},
title = {Distributed optimization of nonlinear singularly perturbed multi-agent systems via a small-gain approach and sliding mode control},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {20865-20886},
keywords = {distributed optimization, robust stability, singularly perturbed systems, small-gain theorem, sliding mode control},
url = {https://www.sciopen.com/article/10.3934/math.20241015},
doi = {10.3934/math.20241015},
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.}
}