具有最小新输入的线性网络控制
Controlling Linear Networks with Minimally Novel Inputs
摘要：
在本文中，我们提出了一个新颖的度量复杂网络的可控性的定量表征。这个固有的有界度量描述了输入相对于过去输入历史的平均角间隔。我们使用这个度量来找到最小的新颖输入，使用单位平均能量将线性网络驱动到期望的状态。具体地说，最小新颖输入被定义为一个连续时间，非凸最优控制问题的解决方案的基础上引入的度量。我们提供的存在性和唯一性的条件，以及一个明确的，封闭形式的解决方案的表达。我们支持我们的理论结果，通过表征最低限度的新颖输入的一个例子，经常性的神经网络。
英文摘要：
In this paper, we propose a novelty-based metric for quantitative characterization of the controllability of complex networks. This inherently bounded metric describes the average angular separation of an input with respect to the past input history. We use this metric to find the minimally novel input that drives a linear network to a desired state using unit average energy. Specifically, the minimally novel input is defined as the solution of a continuous time, non-convex optimal control problem based on the introduced metric. We provide conditions for existence and uniqueness, and an explicit, closed-form expression for the solution. We support our theoretical results by characterizing the minimally novel inputs for an example of a recurrent neuronal network.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
