复杂网络上多维系统的控制
Control of multidimensional systems on complex network
摘要：
通过复杂网络耦合的多维系统在自然界中广泛存在，因此经常被大量有趣的应用程序调用。从生态学到物理学，相互作用中的个体实体被分组为家族，种类相同。后者通过一系列自我调节的步骤有选择地相互作用，其根深蒂固的结构存储在指定的连接矩阵中。系统最终达到的渐近平衡及其相关的稳定性，可以通过采用标准的非线性动力学工具进行评估。然而，对于许多实际应用，重要的是从外部驱动系统朝向期望的平衡，该平衡对于外部扰动是弹性的，因此是稳定的。为此，我们在这里考虑一个系统组成的$N$相互作用的人口发展，根据一般的速率方程，轴承属性的普遍性。一个物种被添加到池中的相互作用的家庭，并作为一个动态控制器，以诱导新的稳定平衡。可以使用根轨迹法来根据固有反应性和所采用的注射方案形成所需的控制。所提出的方法进行测试的合成和真实数据，从而能够证明其鲁棒性和通用性。
英文摘要：
Multidimensional systems coupled via complex networks are widespread in nature and thus frequently invoked for a large plethora of interesting applications. From ecology to physics, individual entities in mutual interactions are grouped in families, homogeneous in kind. These latter interact selectively, through a sequence of self-consistently regulated steps, whose deeply rooted architecture is stored in the assigned matrix of connections. The asymptotic equilibrium eventually attained by the system, and its associated stability, can be assessed by employing standard nonlinear dynamics tools. For many practical applications, it is however important to externally drive the system towards a desired equilibrium, which is resilient, hence stable, to external perturbations. To this end we here consider a system made up of $N$ interacting populations which evolve according to general rate equations, bearing attributes of universality. One species is added to the pool of interacting families and used as a dynamical controller to induce novel stable equilibria. Use can be made of the root locus method to shape the needed control, in terms of intrinsic reactivity and adopted protocol of injection. The proposed method is tested on both synthetic and real data, thus enabling to demonstrate its robustness and versatility.
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