非线性奇异系统解的性态分析及其应用

项目名称： 非线性奇异系统解的性态分析及其应用

项目编号： No.11271106

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 王培光

作者单位： 河北大学

项目金额： 60万元

中文摘要： 奇异系统是一类结构复杂的动力系统，在科学和工程技术领域有着广泛的应用。其解的性态分析与由微分方程描述的正常系统相比更为困难。本项目将借助非线性动力学和非线性分析的理论和研究方法，利用微分几何、矩阵论、拓扑度理论、比较原理、拟线性化方法及计算机模拟等工具，在现有研究工作的基础上，研究包括具有时滞影响和离散形式的非线性奇异系统解的存在性及相容性、各类稳定性及解的快速收敛性问题。在应用方面，通过对切换系统稳定性分析，选择适当的切换子系统及切换策略，研究增大视觉伺服切换系统稳定区域问题。揭示时滞对系统动力学行为的影响，完善和发展奇异系统的理论，给出适用性更广的研究结果，并在处理问题的方法上有新的进展和突破。本项目开展的工作既重视研究结果，也重视方法的改进、统一和扩展。

中文关键词： 奇异系统；稳定性；收敛性；拟线性化方法；比较原理

英文摘要： Singular system is a type of complicated dynamic system which is widely used in science and engineering.The behavior analysis of it is more difficult than that of the ordinary ones described by differential equations. On the basis of the existing researches, this project intends to focus on the following problems including singular system with delay and singular discrete form, the existence and compatibility of solutions, all sorts of stability and the fast convergence of the solutions. The theoretical bases are nonlinear dynamics and nonlinear analysis, Differential geometry, Matrix theory, Topological degree theory, Comparison principle, Quasilinearization method, Computer simulation and so on. In terms of application, it chooses suitable switching subsystems and switching strategies to make a research on the expanding of the stable zones of Visual Servoing system through the stability analysis of the generalized switching system. It is to demonstrate the influence of delay to the dynamical behaviors, improve the theories of singular system, propose more applicable results of the studies, and develop new breakthroughs on the approach to the problem. This project values not only the research result, but also the improvement, unity and expansion of the method.

英文关键词： Singular systems；Stability；Convergence；Quasilinearization method；Comparison principle