Ensemble Controllability of Cellular Oscillators
Ensemble Controllability of Cellular Oscillators
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DOI：
10.1109/lcsys.2018.2870967
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发表时间：
2019-04
影响因子：
3
通讯作者：
Karsten Kuritz;Shen Zeng;F. Allgöwer
中科院分区：
文献类型：
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作者：
Karsten Kuritz;Shen Zeng;F. Allgöwer
许多疾病，包括癌症、帕金森氏病和心脏病，都是由振荡系统的调节机制丢失或故障引起的。这些疾病的成功治疗可能涉及恢复系统中振荡器的健康行为，即实现振荡器在其周期轨道上的同步或所需的分布。在这封信中，我们考虑了用相位模型描述的控制一群细胞振荡器的分布的问题。对蜂窝状态可观测性和可控性的不同实际限制自然导致了集合控制公式，在该公式中，寻求实现期望分布的种群水平反馈律。用系统论的方法解决这个问题，得到了Lyapunov和Lasalle类的论证，由此我们得到了我们的主要贡献，即利用相响应曲线的傅里叶系数控制相分布的新的充要条件。由于我们的处理是基于一个相当普遍的相位模型的公式，本文中提出的结果和方法很容易适用于控制广泛的其他类型的振荡种群，如昼夜节律时钟和尖峰神经元。
Many diseases including cancer, Parkinson’s disease and heart diseases are caused by loss or malfunction of regulatory mechanism of an oscillatory system. Successful treatment of these diseases might involve recovering the healthy behavior of the oscillators in the system, i.e., achieving synchrony or a desired distribution of the oscillators on their periodic orbit. In this letter, we consider the problem of controlling the distribution of a population of cellular oscillators described in terms of phase models. Different practical limitations on the observability and controllability of cellular states naturally lead to an ensemble control formulation in which a population-level feedback law for achieving a desired distribution is sought. A systems theoretic approach to this problem leads to Lyapunov- and LaSalle-like arguments, from which we develop our main contribution, novel necessary and sufficient conditions for the controllability of phase distributions in terms of the Fourier coefficients of the phase response curve. Since our treatment is based on a rather universal formulation of phase models, the results and methods proposed in this letter are readily applicable to the control of a wide range of other types of oscillating populations, such as circadian clocks, and spiking neurons.