发表机构
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过求解HJB方程发现，强耦合下最优控制会利用振幅坍缩实现低成本的相位重定位，超越了传统相位约化模型的预测，且该策略在等时及Van der Pol振子中同样适用。
AI 中文摘要
我们求解了两个扩散耦合的Stuart-Landau型振子的四维Hamilton-Jacobi-Bellman (HJB)方程，以获得全状态最优反馈控制。对耦合强度的扫描揭示了数值最优策略中的急剧变化：低于阈值耦合值时，控制器将相位差导向反相，同时使两个振子保持在极限环附近，这与约化模型所预示的一致。高于该阈值时，HJB解发生定性改变；控制器瞬态地将一个振子的振幅坍缩至接近零，从而在原点附近实现大幅相位重定位，之后再重建其振幅。直接的基于梯度和随机优化方法无法从所考虑的初始点恢复这条更低成本的坍缩轨迹，这表明该轨迹占据控制景观中难以通过直接搜索到达的区域。对非等时性和耦合的联合扫描表明，即使对于等时振子，坍缩也可能发生：在原点附近的相位重定位可能偏好偏离极限环的策略。非等时性通过小振幅下的相位速度盈余提供了额外的能量优势，定量地解释了所观察到的控制成本降低。与未耦合和耦合的相位约化基线的比较表明，在强耦合下，相位模型变得越来越不准确，且消耗显著更多的能量。对耦合Van der Pol振子的结果进一步表明，利用偏离极限环的动力学并非Stuart-Landau型振子所特有。
英文摘要
We solve the four-dimensional Hamilton-Jacobi-Bellman (HJB) equation for two diffusively coupled Stuart-Landau-like oscillators to obtain full-state optimal feedback control. A sweep over coupling strength reveals a sharp change in the numerically optimal strategy: below a threshold coupling value, the controller steers the phase difference toward anti-phase while keeping both oscillators near the limit cycle, as reduced-order models would suggest. Above this threshold, the HJB solution changes qualitatively; the controller transiently collapses one oscillator's amplitude to near zero, thereby enabling large phase repositioning near the origin before rebuilding its amplitude. Direct gradient-based and stochastic optimization do not recover this lower-cost collapse trajectory from the initializations considered, suggesting that it occupies a region of the control landscape that is difficult to access by direct search. A joint sweep over nonisochronicity and coupling shows that collapse can occur even for an isochronous oscillator: phase repositioning near the origin can favor an off-cycle strategy. Nonisochronicity provides an additional energetic benefit through a phase-velocity surplus at small amplitude, quantitatively accounting for the observed reduction in control cost. Comparisons with uncoupled and coupled phase-reduced baselines show that phase models become increasingly inaccurate and cost significantly more energy for strong coupling. Results for coupled Van der Pol oscillators further demonstrate that exploitation of off-cycle dynamics is not specific to the Stuart-Landau-like oscillators.
Comments8 pages, 5 figures. Accepted to the 65th IEEE Conference on Decision and Control (CDC 2026), Honolulu, HI, December 2026
