具有消极关系的耦合非线性系统同步与控制研究

项目名称： 具有消极关系的耦合非线性系统同步与控制研究

项目编号： No.11502039

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 翟世东

作者单位： 重庆邮电大学

项目金额： 20万元

中文摘要： 具有消极关系的耦合非线性系统普遍存在于信息、生物和社会领域，研究这类复杂网络的同步与控制不仅具有重要的理论意义，而且可以为个性化推荐、种群多样性和舆论预测等实际问题提供一些建议。本项目以具有消极关系的耦合非线性系统为研究对象，将同步研究方法（如矩阵测度和压缩性理论、Lyapunov方法）与流形计算相结合，利用有限时间稳定性和有限时间半稳定性理论，研究系统的各种同步行为以及相应的控制策略。具体内容包括：分别研究双向同步及多同步与非线性系统、符号图和初始条件之间的关系，得到保证双向同步及多同步的若干充分条件；针对符号图上的耦合非线性系统，基于双向同步和多同步分析，分别设计满足约束条件的控制策略使得闭环系统达到双向同步和多同步；针对符号图上的耦合非线性系统，基于有限时间稳定性和有限时间半稳定性理论，分别设计满足约束条件的控制策略使得闭环系统有限时间达到双向同步和多同步。

中文关键词： 双向同步；多同步；符号图；非线性系统；流形计算

英文摘要： In social, biological and information fields, many complex networks can be presented as coupled nonlinear systems with negative relationships. Studying the synchronization behavior and control laws of this complex network not only has important theoretical significance, but also it can give some suggestions for practical problems, such as the personalized recommendation, diversity of population and prediction of opinions etc. This project investigates the synchronization and control problems for coupled nonlinear systems with negative relationships. By combining the methods of synchronization study (e.g. matrix measure and contraction theory, Lyapunov method) and computing manifold method, and using finite-time stability theory and finite-time semi-stable theory, we will study the two types of synchronization and corresponding control laws. The precise research topics include: study the relationship between bipartite synchronization (multi-synchronization) and nonlinear systems, the relationship between bipartite synchronization (multi-synchronization) and signed graphs, the relationship between bipartite synchronization (multi-synchronization) and initial conditions, and obtain some sufficient conditions such that the coupled system reaches bipartite synchronization and multi-synchronization, respectively; for a group of nonlinear systems, based on bipartite synchronization and multi-synchronization analysis, design control laws satisfying constraint conditions such that the closed-loop system reaches bipartite synchronization and multi-synchronization, respectively; for a group of nonlinear systems, based on finite-time stability theory and finite-time semi-stable theory, design control laws satisfying constraint conditions such that the closed-loop system reaches finite-time bipartite synchronization and multi-synchronization, respectively.

英文关键词： bipartite synchronization;multi-synchronization;signed graphs;nonlinear systems;manifold computation