{"ID":2890416,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.19560","arxiv_id":"2507.19560","title":"Time-optimal synchronisation to self-sustained oscillations under bounded control","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2507.19560","url_pdf":"https://arxiv.org/pdf/2507.19560v2","authors":"[\"C. Ríos-Monje\",\"C. A. Plata\",\"D. Guéry-Odelin\",\"A. Prados\"]","published":"2025-07-25T09:37:44Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}