Stabilization of solutions of the controlled non-local continuity equation
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916678964609024 |
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| author | Volkov, Aleksei |
| author_facet | Volkov, Aleksei |
| contents | Non-local continuity equation describes an infinite system of identical particles, which interact with each other through the common field. Solution of this equation is a probability measure that stands for spatial distribution of particles. The paper is concerned with stabilization of this solution in the case of controlled dynamic. By generalizing methods used control-Lyapunov function to the case of Wasserstein spaces, we construct a feedback strategy that provides local stabilization, i.e. leads the trajectory to a small neighbourhood of stabilization target. Based on this strategy, we construct a feedback that makes global stabilization, i.e. leads the trajectory infinitely close to stabilization target. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stabilization of solutions of the controlled non-local continuity equation Volkov, Aleksei Dynamical Systems Optimization and Control 93D15 (Primary) 35F20, 35Q70, 35R06, 82C22 (Secondary) Non-local continuity equation describes an infinite system of identical particles, which interact with each other through the common field. Solution of this equation is a probability measure that stands for spatial distribution of particles. The paper is concerned with stabilization of this solution in the case of controlled dynamic. By generalizing methods used control-Lyapunov function to the case of Wasserstein spaces, we construct a feedback strategy that provides local stabilization, i.e. leads the trajectory to a small neighbourhood of stabilization target. Based on this strategy, we construct a feedback that makes global stabilization, i.e. leads the trajectory infinitely close to stabilization target. |
| title | Stabilization of solutions of the controlled non-local continuity equation |
| topic | Dynamical Systems Optimization and Control 93D15 (Primary) 35F20, 35Q70, 35R06, 82C22 (Secondary) |
| url | https://arxiv.org/abs/2504.05935 |