Properties of Measure Controls and Their Trajectories
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912866565619712 |
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| author | Garavello, Mauro Gong, Xiaoqian Piccoli, Benedetto |
| author_facet | Garavello, Mauro Gong, Xiaoqian Piccoli, Benedetto |
| contents | This paper deals with the concepts of measure controls and of measure vector fields, within the mathematical framework of measure differential equations (MDEs), recently proposed in~\cite{piccoli_measure_2019}. Measure controls can be seen as a generalization of relaxed control. Moreover, they are particularly suitable for studying dynamics with uncertainty.
The main results of this paper include establishing the existence and well-posedness of control systems with measure controls and proving the equivalence between measure controls and measure vector fields. The stability and closure properties of the trajectory set are also studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00752 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Properties of Measure Controls and Their Trajectories Garavello, Mauro Gong, Xiaoqian Piccoli, Benedetto Optimization and Control 34H05, 35Q93, 34A60, 35R06 This paper deals with the concepts of measure controls and of measure vector fields, within the mathematical framework of measure differential equations (MDEs), recently proposed in~\cite{piccoli_measure_2019}. Measure controls can be seen as a generalization of relaxed control. Moreover, they are particularly suitable for studying dynamics with uncertainty. The main results of this paper include establishing the existence and well-posedness of control systems with measure controls and proving the equivalence between measure controls and measure vector fields. The stability and closure properties of the trajectory set are also studied. |
| title | Properties of Measure Controls and Their Trajectories |
| topic | Optimization and Control 34H05, 35Q93, 34A60, 35R06 |
| url | https://arxiv.org/abs/2602.00752 |