具有约束条件的复杂网络的建模、动力学行为和控制策略分析

In this project, we shall develop our research work in the following three aspects: At first, we shall construct complex network models with constraints based on the real background. Secondly, aggregated methods will be applied to aggregate general large-size networks to small-size ones but not affecting the dynamical behaviors. Here, we shall ensure that the aggregated models reserve the same consensus (or synchronization) status as the original models. Thirdly, we shall design simple and effective controllers (such as Fuzzy controllers, multi-channel sampled controllers and asynchronous controllers and so on) to discuss the synchronization (or consensus) of complex network models with constraints. The key research problem of this project is "Modeling, Dynamical Behavior and Control Strategy Analysis of Complex Networks with Constraints". The purpose of our project is to improve the integrity of modeling and the reliability of control behaviors by designing reasonable models for complex networks with constraints and simple controllers to achieve the synchronization (or consensus) of all nodes. The research results of this project is meaningful for the improvement of the whole complex networks theory. Furthermore, our research results can promote the modeling and optimization control of complex networks changed from potential to actual.

我们将开展以下三个方面的进一步研究：首先，立足于复杂网络的实际背景，建立具有约束条件的复杂网络模型；其次，在尽量不损害网络的动力学行为的基础上，将大规模的复杂网络模型转化为一个相对小规模的网络模型，然后以小规模网络的同步（一致性）代替大规模网络的同步（一致性）；再次，设计简单、实际且行之有效的控制器，如：模糊控制、多信道的采样控制、异步控制等，核心的科学问题是"具有约束条件的复杂网络的建模、动力学行为和控制策略分析"。通过对本项目构建的具有约束条件的复杂网络模型进行同步及一致性分析并设计行之有效的控制器的研究，达到提高复杂网络建模的完整性和确保控制行为可靠性及可行性的目的。同时，本项目的研究成果对于进一步发展和完善复杂网络理论也具有十分重要的科学意义，并且对推动网络建模与优化控制从实验室走向实际工程有潜在的应用价值。

本项目采取理论研究与实验验证相结合并交互进行的研究方法，建立具有多种约束条件的复杂网络模型，分析网络的聚合优化及同步行为，讨论网络的优化控制策略。首先，基于实际的物理背景，建立多种约束条件的复杂网络模型。其次，在不损害网络动力学行为的基础上，利用聚合优化算法，将大规模的复杂网络模型转化为一个小规模的网络模型。然后确保以小规模网络的同步（一致性）代替大规模网络的同步（一致性）。最后，基于已聚合的小规模复杂网络，设计了量化的迭代学习控制器、反推控制器、饱和的迭代学习控制器等行之有效的控制策略。