Reachability for multiagent control systems via Lyapunov functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914225867194368 |
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| author | Cavagnari, Giulia Quincampoix, Marc |
| author_facet | Cavagnari, Giulia Quincampoix, Marc |
| contents | This paper concerns the problem of reachability of a given state for a multiagent control system in $\mathbb{R}^d$. In such a system, at every time each agent can choose his/her velocity which depends both on his/her position and on the position of the whole crowd of agents (modeled by a probability measure on $ \mathbb{R}^d$). The main contribution of the paper is to study the above reachability problem with a given rate of attainability through a Lyapunov method adapted to the Wasserstein space of probability measures. As a byproduct we obtain a new comparison result for viscosity solutions of Hamilton Jacobi equations in the Wasserstein space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_09179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reachability for multiagent control systems via Lyapunov functions Cavagnari, Giulia Quincampoix, Marc Optimization and Control 49L25, 49J52, 49K27, 49J15, 34A60, 93C15 This paper concerns the problem of reachability of a given state for a multiagent control system in $\mathbb{R}^d$. In such a system, at every time each agent can choose his/her velocity which depends both on his/her position and on the position of the whole crowd of agents (modeled by a probability measure on $ \mathbb{R}^d$). The main contribution of the paper is to study the above reachability problem with a given rate of attainability through a Lyapunov method adapted to the Wasserstein space of probability measures. As a byproduct we obtain a new comparison result for viscosity solutions of Hamilton Jacobi equations in the Wasserstein space. |
| title | Reachability for multiagent control systems via Lyapunov functions |
| topic | Optimization and Control 49L25, 49J52, 49K27, 49J15, 34A60, 93C15 |
| url | https://arxiv.org/abs/2503.09179 |