Time-Varying Distributed Optimization for A Class of Stochastic Multi-Agent Systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917959086112768 |
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| author | Li, Wan-ying Huang, Nan-jing |
| author_facet | Li, Wan-ying Huang, Nan-jing |
| contents | Distributed optimization problems have received much attention due to their privacy preservation, parallel computation, less communication, and strong robustness. This paper presents and studies the time-varying distributed optimization problem for a class of stochastic multi-agent systems for the first time. For this, we initially propose a protocol in the centralized case that allows the tracking error of the agent with respect to the optimal trajectory to be exponentially ultimately bounded in a mean-square sense by stochastic Lyapunov theory. We then generalize this to the distributed case. Therein, the global variable can be accurately estimated in a fixed-time by our proposed estimator. Based on this estimator, we design a new distributed protocol, and the results demonstrate that the tracking error of all agents with respect to the optimal trajectory is exponentially ultimately bound in a mean-square sense by stochastic Lyapunov theory. Finally, simulation experiments are conducted to validate the findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12934 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-Varying Distributed Optimization for A Class of Stochastic Multi-Agent Systems Li, Wan-ying Huang, Nan-jing Optimization and Control Distributed optimization problems have received much attention due to their privacy preservation, parallel computation, less communication, and strong robustness. This paper presents and studies the time-varying distributed optimization problem for a class of stochastic multi-agent systems for the first time. For this, we initially propose a protocol in the centralized case that allows the tracking error of the agent with respect to the optimal trajectory to be exponentially ultimately bounded in a mean-square sense by stochastic Lyapunov theory. We then generalize this to the distributed case. Therein, the global variable can be accurately estimated in a fixed-time by our proposed estimator. Based on this estimator, we design a new distributed protocol, and the results demonstrate that the tracking error of all agents with respect to the optimal trajectory is exponentially ultimately bound in a mean-square sense by stochastic Lyapunov theory. Finally, simulation experiments are conducted to validate the findings. |
| title | Time-Varying Distributed Optimization for A Class of Stochastic Multi-Agent Systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.12934 |