Mwaffo Violet, DeLellis Pietro, Porfiri Maurizio
Department of Mechanical and Aerospace Engineering, Polytechnic School of Engineering, New York University, Brooklyn, New York 11201, USA.
Department of Electrical Engineering and Information Technology, University of Naples Federico II, Naples 80125, Italy.
Chaos. 2014 Mar;24(1):013101. doi: 10.1063/1.4861075.
This paper investigates the controllability of discrete-time networks of coupled chaotic maps through stochastic pinning. In this control scheme, the network dynamics are steered towards a desired trajectory through a feedback control input that is applied stochastically to the network nodes. The network controllability is studied by analyzing the local mean square stability of the error dynamics with respect to the desired trajectory. Through the analysis of the spectral properties of salient matrices, a toolbox of conditions for controllability are obtained, in terms of the dynamics of the individual maps, algebraic properties of the network, and the probability distribution of the pinning control. We demonstrate the use of these conditions in the design of a stochastic pinning control strategy for networks of Chirikov standard maps. To elucidate the applicability of the approach, we consider different network topologies and compare five different stochastic pinning strategies through extensive numerical simulations.
本文研究了通过随机牵制实现的离散时间耦合混沌映射网络的可控性。在这种控制方案中，网络动态通过随机应用于网络节点的反馈控制输入被引导至期望轨迹。通过分析误差动态相对于期望轨迹的局部均方稳定性来研究网络可控性。通过对显著矩阵的谱特性分析，根据单个映射的动态、网络的代数性质以及牵制控制的概率分布，得到了一组可控性条件工具箱。我们展示了这些条件在设计Chirikov标准映射网络的随机牵制控制策略中的应用。为了阐明该方法的适用性，我们考虑了不同的网络拓扑结构，并通过广泛的数值模拟比较了五种不同的随机牵制策略。
