Modelling car-following dynamics with stochastic input-state-output port-Hamiltonian systems
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909471966494720 |
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| author | Ackermann, Julia Ehrhardt, Matthias Kruse, Thomas Tordeux, Antoine |
| author_facet | Ackermann, Julia Ehrhardt, Matthias Kruse, Thomas Tordeux, Antoine |
| contents | In this contribution, we introduce a general class of car-following models with an input-state-output port-Hamiltonian structure. We derive stability conditions and long-term behavior of the finite system with periodic boundaries and quadratic interaction potential by spectral analysis and using asymptotic properties of multivariate Ornstein-Uhlenbeck processes. The uncontrolled dynamics exhibit instability and random collective behavior under stochastic perturbations. By implementing an open-loop speed control, the system stabilizes and weakly converges to Gaussian limit distributions. The convergence is unconditional for constant speed control. However, a stability condition arises for the closed-loop system where the speed control acts as a dynamic feedback depending on the distance ahead. The results are illustrated by numerical simulations. Interestingly, only the closed-loop system is able to reproduce, at least transiently, realistic stop-and-go behavior that can be resolved using the Hamiltonian component of the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modelling car-following dynamics with stochastic input-state-output port-Hamiltonian systems Ackermann, Julia Ehrhardt, Matthias Kruse, Thomas Tordeux, Antoine Dynamical Systems 76A30, 82C22, 60H10, 37H30 In this contribution, we introduce a general class of car-following models with an input-state-output port-Hamiltonian structure. We derive stability conditions and long-term behavior of the finite system with periodic boundaries and quadratic interaction potential by spectral analysis and using asymptotic properties of multivariate Ornstein-Uhlenbeck processes. The uncontrolled dynamics exhibit instability and random collective behavior under stochastic perturbations. By implementing an open-loop speed control, the system stabilizes and weakly converges to Gaussian limit distributions. The convergence is unconditional for constant speed control. However, a stability condition arises for the closed-loop system where the speed control acts as a dynamic feedback depending on the distance ahead. The results are illustrated by numerical simulations. Interestingly, only the closed-loop system is able to reproduce, at least transiently, realistic stop-and-go behavior that can be resolved using the Hamiltonian component of the model. |
| title | Modelling car-following dynamics with stochastic input-state-output port-Hamiltonian systems |
| topic | Dynamical Systems 76A30, 82C22, 60H10, 37H30 |
| url | https://arxiv.org/abs/2502.00370 |