控制网络集成
Controlling network ensembles
摘要：
最优控制领域通常需要假设人们期望控制的系统的完美知识，这对于通常受高水平不确定性影响的生物系统或网络是不现实的假设。在这里，我们调查的最小能量控制的网络集成，这可能需要一个有限数量的可能实现。我们确保所得到的控制器可以执行所需的控制与可调量的准确性，我们研究如何控制能量和整体控制成本规模与可能的实现的数量。我们在三个感兴趣的例子中验证了该理论：具有不确定边缘权重和自循环权重的单向链网络，每个边缘权重都来自给定分布的网络，以及在不确定参数存在下对应于自噬细胞信号网络的动态雅可比矩阵。我们的工作揭示了最优性和不确定性之间的关系的基本见解。我们的主要结果是，相应的最优控制问题的解决方案的最优成本仍然是有限的可能无限多的网络实现，只要不确定性是有界的。
英文摘要：
The field of optimal control typically requires the assumption of perfect knowledge of the system one desires to control, which is an unrealistic assumption for biological systems, or networks, typically affected by high levels of uncertainty. Here, we investigate the minimum energy control of network ensembles, which may take one of a finite number of possible realizations. We ensure the controller derived can perform the desired control with a tunable amount of accuracy and we study how the control energy and the overall control cost scale with the number of possible realizations. We verify the theory in three examples of interest: a unidirectional chain network with uncertain edge weights and self-loop weights, a network where each edge weight is drawn from a given distribution, and the Jacobian of the dynamics corresponding to the cell signaling network of autophagy in the presence of uncertain parameters. Our work sheds fundamental insight into the relationship between optimality and uncertainty. Our main result is that the optimal cost corresponding to the solution of the optimal control problem remains finite for possibly infinitely many network realizations as long as uncertainty is bounded.
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