Virtual Contraction Approach to Decentralized Adaptive Stabilization of Nonlinear Time-Delayed Networks
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908550887899136 |
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| author | Kawano, Yu Sun, Zhiyong |
| author_facet | Kawano, Yu Sun, Zhiyong |
| contents | In this paper, we exploit a diagonally dominant structure for the decentralized stabilization of unknown nonlinear time-delayed networks. To this end, we first introduce a novel generalization of virtual contraction analysis to diagonally dominant time-delayed control systems. We then show that nonlinear time-delayed networks can be stabilized using diagonal high-gains, provided that the input matrices satisfy certain generalized (column/row) diagonally dominant conditions. To enable stabilization of unknown networks, we further propose a distributed adaptive tuning rule for each individual gain function, guaranteeing that all closed-loop trajectories converge to the origin while the gains converge to finite values. The effectiveness of the proposed decentralized adaptive control is illustrated through a case study on epidemic spreading control in SIS networks with transmission delays. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_10855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Virtual Contraction Approach to Decentralized Adaptive Stabilization of Nonlinear Time-Delayed Networks Kawano, Yu Sun, Zhiyong Systems and Control Optimization and Control In this paper, we exploit a diagonally dominant structure for the decentralized stabilization of unknown nonlinear time-delayed networks. To this end, we first introduce a novel generalization of virtual contraction analysis to diagonally dominant time-delayed control systems. We then show that nonlinear time-delayed networks can be stabilized using diagonal high-gains, provided that the input matrices satisfy certain generalized (column/row) diagonally dominant conditions. To enable stabilization of unknown networks, we further propose a distributed adaptive tuning rule for each individual gain function, guaranteeing that all closed-loop trajectories converge to the origin while the gains converge to finite values. The effectiveness of the proposed decentralized adaptive control is illustrated through a case study on epidemic spreading control in SIS networks with transmission delays. |
| title | Virtual Contraction Approach to Decentralized Adaptive Stabilization of Nonlinear Time-Delayed Networks |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2504.10855 |