Time-optimal synchronisation to self-sustained oscillations under bounded control

2025/07/25 by Ríos-Monje, C., Plata, C. A., Guéry-Odelin, D. +1
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2507.19560

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.

Citations

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