Time-optimal synchronisation to self-sustained oscillations under bounded control
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912788817903616 |
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| author | Ríos-Monje, C. Plata, C. A. Guéry-Odelin, D. Prados, A. |
| author_facet | Ríos-Monje, C. Plata, C. A. Guéry-Odelin, D. Prados, A. |
| contents | Incorporating force bounds is crucial for realistic control implementations in physical systems. Here, we investigate the fastest possible synchronisation of a Liénard system to its limit cycle using a bounded external force. To tackle this challenging non-linear optimal control problem, our approach involves applying Pontryagin's Maximum Principle with a combination of analytical and numerical tools. We show that the optimal control develops a remarkably complex structure in phase space as the force bound is lowered. Trajectories rewound from the limit cycle's extreme points turn out to play a key role in determining the maximum number of control bangs for optimal connection. We illustrate these intricate features using the paradigmatic van der Pol oscillator model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-optimal synchronisation to self-sustained oscillations under bounded control Ríos-Monje, C. Plata, C. A. Guéry-Odelin, D. Prados, A. Optimization and Control Incorporating force bounds is crucial for realistic control implementations in physical systems. Here, we investigate the fastest possible synchronisation of a Liénard system to its limit cycle using a bounded external force. To tackle this challenging non-linear optimal control problem, our approach involves applying Pontryagin's Maximum Principle with a combination of analytical and numerical tools. We show that the optimal control develops a remarkably complex structure in phase space as the force bound is lowered. Trajectories rewound from the limit cycle's extreme points turn out to play a key role in determining the maximum number of control bangs for optimal connection. We illustrate these intricate features using the paradigmatic van der Pol oscillator model. |
| title | Time-optimal synchronisation to self-sustained oscillations under bounded control |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.19560 |