基于T-S模糊模型的复杂网络的控制及参数辨识研究

In view of the limitations that the traditional control methods require accurate mathematical models and are dependent on more information of the controlled objects, based on the T-S fuzzy theory, this project firstly constructs various fuzzy criteria and some corresponding fuzzy complex network models under the T-S fuzzy rules, and then analyzes the sufficient conditions on the stable control of general time_varying fuzzy complex networks(continuous and discrete included). Further, it discusses the synchronization of delayed complex networks with different delay distributions, and deeply analyzes how the different distributions of time delays affect on the network synchronization. Finally, for the uncertain complex networks with external disturbance or immeasurable states, it focuses on investigating the theoretical conditions on the synchronization of this kind of networks and derives a series of new criteria for parameter identification. This project invesgates the problem on the synchronization and control of complex networks based on the fuzzy control theory, which can overcome the drawback that existing results are too dependent on the accurate network models.Its control mechanism and strategies are easy to be accepted and understood, moreover, it need a small amount of calculation, and the controllers are simple and easy to be applied in practice. Simultaneously, the contents of this project will extend the research category of control and synchronization of complex networks, and promote the wide application and cross development of the fuzzy control theory in complex network field.

针对传统的控制方法要求受控对象有精确的数学模型和依赖较多的信息量这些局限性， 本项目拟基于T-S模糊理论，首先建立合理的模糊规则以及在相应模糊规则下的各类T-S模糊复杂网络模型；然后，分析一般时变的模糊复杂网络（连续和离散）达到稳定控制的充分性条件；进一步地探讨各种时滞分布情形下的模糊的延迟复杂网络的同步控制问题，并深入分析时滞分布的不同对实现网络同步的影响；最后，针对具有外部扰动或状态不完全可测的不确定复杂网络，重点研究这类网络达到同步的理论条件，并推导出一系列新的参数辨识准则。该项目基于T-S模糊控制理论研究复杂网络的同步控制问题，能克服众多已有结论分析过程中过多依赖准确的网络模型这一缺陷。其控制机理和策略易于接受与理解，控制计算量小、控制器设计简单，便于实际应用。同时，该项目的研究内容将推广目前复杂网络控制与同步的研究范畴，推动模糊控制理论在复杂网络领域中的广泛应用和交叉发展。

复杂网络的控制与同步一直是复杂网络中重要研究分支之一。 本项目利用非线性动力学理论、复杂网络理论、控制理论和计算机仿真的手段，在复杂动态网络和FitzHugh-Nagumo网络的控制和同步方面取得了一系列重要的创新性成果，先后分析了连续网络、离散网络，网络受外部扰动以及网络系统的参数受扰动等多种情形。另外，在多层复杂网络的结构演化及其优化设计方面也取得一些进展。这些成果分别发表在《Nonlinear Dynamics》、《IMA Journal of Mathematical Control and Information》、《Physics Letters A》等知名期刊和国际会议上，其中SCI收录期刊论文5篇，EI收录的国际会议论文2篇，北大中文核心期刊1篇。项目负责人张群娇获得2013 年湖北省自然科学奖一等奖，培养硕士研究生1 名。