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

• Main Authors: Li, Qian, Jin, Zhenghong, Qiao, Linyan, Du, Aichun, Liu, Gang
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2024
• Subjects: Engineering; Mathematical Sciences; Distributed optimization; Robust stability
• Online Access: https://hdl.handle.net/10356/181837
• Institution: Nanyang Technological University

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.