Region of Synchronization Estimation for Complex Networks via SOS Programming
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909597039591424 |
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| author | Zhang, Shuyuan Jungers, Raphaël M. Wang, Lei |
| author_facet | Zhang, Shuyuan Jungers, Raphaël M. Wang, Lei |
| contents | In this article, we explore the problem of the region of synchronization (ROS) for complex networks with nonlinear dynamics. Given a pair of state- and target- sets, our goal is to estimate the ROS such that the trajectories originating within it reach the target set (i.e., synchronization manifold), without leaving the state set before the first hitting time. In order to do so, an exponential guidance-barrier function is proposed to construct the ROS along the synchronization manifold, and the corresponding sufficient conditions for estimating the ROS are developed. The resulting conditions lead to a sum-of-squares programming problem, thereby affording a polynomial-time solvability. Furthermore, when the synchronization manifold reduces to an equilibrium point, our method not only estimates a larger ROS compared to existing results but also allows the ROS to take more general shapes. Finally, we present two numerical examples to demonstrate the effectiveness of the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Region of Synchronization Estimation for Complex Networks via SOS Programming Zhang, Shuyuan Jungers, Raphaël M. Wang, Lei Optimization and Control In this article, we explore the problem of the region of synchronization (ROS) for complex networks with nonlinear dynamics. Given a pair of state- and target- sets, our goal is to estimate the ROS such that the trajectories originating within it reach the target set (i.e., synchronization manifold), without leaving the state set before the first hitting time. In order to do so, an exponential guidance-barrier function is proposed to construct the ROS along the synchronization manifold, and the corresponding sufficient conditions for estimating the ROS are developed. The resulting conditions lead to a sum-of-squares programming problem, thereby affording a polynomial-time solvability. Furthermore, when the synchronization manifold reduces to an equilibrium point, our method not only estimates a larger ROS compared to existing results but also allows the ROS to take more general shapes. Finally, we present two numerical examples to demonstrate the effectiveness of the theoretical results. |
| title | Region of Synchronization Estimation for Complex Networks via SOS Programming |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.20804 |