Distributed Time-Varying Optimization via Unbiased Extremum Seeking
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912607813763072 |
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| author | Li, Xuebin Yang, Xuefei Fridman, Emilia Diagne, Mamadou Sun, Jiebao |
| author_facet | Li, Xuebin Yang, Xuefei Fridman, Emilia Diagne, Mamadou Sun, Jiebao |
| contents | This paper proposes a novel distributed optimization framework that addresses time-varying optimization problems without requiring explicit derivative information of the objective functions. Traditional distributed methods often rely on derivative computations, limiting their applicability when only real-time objective function measurements are available. Leveraging unbiased extremum seeking, we develop continuous-time algorithms that utilize local measurements and neighbor-shared data to collaboratively track time-varying optima. Key advancements include compatibility with directed communication graphs, customizable convergence rates (asymptotic, exponential, or prescribed-time), and the ability to handle dynamically evolving objectives. By integrating chirpy probing signals with time-varying frequencies, our unified framework achieves accelerated convergence while maintaining stability under mild assumptions. Theoretical guarantees are established through Lie bracket averaging and Lyapunov-based analysis, with linear matrix inequality conditions ensuring rigorous convergence. Numerical simulations validate the effectiveness of the algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21814 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributed Time-Varying Optimization via Unbiased Extremum Seeking Li, Xuebin Yang, Xuefei Fridman, Emilia Diagne, Mamadou Sun, Jiebao Optimization and Control Systems and Control This paper proposes a novel distributed optimization framework that addresses time-varying optimization problems without requiring explicit derivative information of the objective functions. Traditional distributed methods often rely on derivative computations, limiting their applicability when only real-time objective function measurements are available. Leveraging unbiased extremum seeking, we develop continuous-time algorithms that utilize local measurements and neighbor-shared data to collaboratively track time-varying optima. Key advancements include compatibility with directed communication graphs, customizable convergence rates (asymptotic, exponential, or prescribed-time), and the ability to handle dynamically evolving objectives. By integrating chirpy probing signals with time-varying frequencies, our unified framework achieves accelerated convergence while maintaining stability under mild assumptions. Theoretical guarantees are established through Lie bracket averaging and Lyapunov-based analysis, with linear matrix inequality conditions ensuring rigorous convergence. Numerical simulations validate the effectiveness of the algorithms. |
| title | Distributed Time-Varying Optimization via Unbiased Extremum Seeking |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2509.21814 |