非线性动态网络的控制节点选择算法
Control Node Selection Algorithm for Nonlinear Dynamic Networks
摘要：
非线性网络动力学的控制节点选择和控制行为设计耦合问题是一个应用广泛的基础科学问题。这些问题是深入研究的线性动力学，然而，尽管有一些开放的研究问题，非线性网络动力学的方法是欠发达。如各种研究所观察到的，用于选择控制节点的流行的基于图的可控性方法可能会导致非线性动态的显着次优控制性能。本文提出了一种新的、直观的、简单的方法来同时设计具有非线性动力学的复杂网络的控制节点和控制序列。该方法通过将控制节点选择问题纳入开环预测控制代价函数，并通过使用网格自适应直接搜索方法求解所得的混合整数优化问题来开发。所开发的框架是数值鲁棒的，可以处理刚性网络，网络与非光滑动态，以及控制和执行器的约束。通过在原型Duffing振子和联想记忆网络上的测试，证明了该方法具有良好的数值性能。开发的代码可以很容易地适应其他复杂系统的模型，可在线获得。
英文摘要：
The coupled problems of selecting control nodes and designing control actions for nonlinear network dynamics are fundamental scientific problems with applications in many diverse fields. These problems are thoroughly studied for linear dynamics; however, in spite of a number of open research questions, methods for nonlinear network dynamics are less developed. As observed by various studies, the prevailing graph-based controllability approaches for selecting control nodes might result in significantly suboptimal control performance for nonlinear dynamics. Herein we present a new, intuitive, and simple method for simultaneous control node selection and control sequence design for complex networks with nonlinear dynamics. The method is developed by incorporating the control node selection problem into an open-loop predictive control cost function and by solving the resulting mixed-integer optimization problem using a mesh adaptive direct search method. The developed framework is numerically robust and can deal with stiff networks, networks with non-smooth dynamics, as well as with control and actuator constraints. Good numerical performance of the method is demonstrated by testing it on prototypical Duffing oscillator and associative memory networks. The developed codes that can easily be adapted to models of other complex systems are available online.
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