Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators
Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators
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DOI：
10.1007/s11071-021-06703-w
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发表时间：
2021-03
影响因子：
5.6
通讯作者：
Yuzuru Kato;Anatoly Zlotnik;Jr-Shin Li;H. Nakao
中科院分区：
文献类型：
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作者：
Yuzuru Kato;Anatoly Zlotnik;Jr-Shin Li;H. Nakao
提出了一种基于相位缩减和非线性规划的弱强迫极限环振子全局夹带周期输入波形优化的一般方法。我们从弱周期输入驱动的极限环振荡器的数学模型中推导出平均相位动力学，并优化输入波形的傅里叶系数以最大化规定的目标函数。与依赖于变分法的优化方法相反，所提出的方法可以应用于更广泛的优化问题，包括全局夹带目标。作为一个例子，我们考虑了两个优化问题，一个是实现振荡器到携带态的快速全局收敛，另一个是在一群相同的不耦合噪声振荡器中实现规定的全局相位分布。结果表明，所提出的方法在两种情况下都能成功地产生最优的输入波形来实现期望的状态。
We propose a general method for optimizing periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators based on phase reduction and nonlinear programming. We derive averaged phase dynamics from the mathematical model of a limit-cycle oscillator driven by a weak periodic input and optimize the Fourier coefficients of the input waveform to maximize prescribed objective functions. In contrast to the optimization methods that rely on the calculus of variations, the proposed method can be applied to a wider class of optimization problems including global entrainment objectives. As an illustration, we consider two optimization problems, one for achieving fast global convergence of the oscillator to the entrained state and the other for realizing prescribed global phase distributions in a population of identical uncoupled noisy oscillators. We show that the proposed method can successfully yield optimal input waveforms to realize the desired states in both cases.