非线性控制系统输入-状态实用稳定性分析与设计

项目名称： 非线性控制系统输入-状态实用稳定性分析与设计

项目编号： No.61304011

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 杨晓霞

作者单位： 中南大学

项目金额： 26万元

中文摘要： 本项目通过将输入-状态稳定和实用稳定相结合，针对非线性控制系统提出输入-状态实用稳定性分析和控制器设计方法。首先，利用数学语言建立起输入-状态实用稳定的相关定义；然后，通过分析系统初始估计、系统运行轨迹估计和控制输入三者之间的关系，利用Lyapunov理论和非线性小增益定理，建立基于Lyapunov函数的输入-状态实用稳定性判别方法，并研究输入-状态实用稳定性与输入-状态稳定性和实用稳定性的本质联系，同时针对基于具有不定Lyapunov函数导数，通过建立新的比较原理，获得更低保守性的输入-状态实用稳定性判别方法；再者，建立输入-状态实用稳定控制器设计方法，获得范围更广状态吸引域；最后，建立三相电机实验系统相结合，验证项目所提方法的有效性和优越性。

中文关键词： 非线性控制系统；输入-状态稳定；实用稳定性；；

英文摘要： This project presents the analysis and design methods for input-state practical stability (ISPS) of nonlinear control systems by combining the concepts of the input-state stability (ISS) and the practical stability (PS). Firstly, the definitions of the ISPS will be established by using the strict mathematical language. Then, by analyzing the relationship among the systematic initial estimation, the systematic trajectory estimation and the control input and employing the Lyapunov theory and the nonlinear small gain theory, the criteria that verify the ISPS for the nonlinear control systems will be obtained, which are based on the Lyapunov function. Meanwhile, the Lyapunov function with the indefinite derivative will be introduced to derive the less conservative conditions of the ISPS by introducing a new comparison theory. Moreover, the relationship among the ISPS, the ISS and the PS will be investigated to show the importance of the ISPS. In addition, the controller designing method for ISPS will be established to derive the larger systematic trajectory estimation. Finally, the experiment system for three-phase electric machine will be built to verify the effectiveness and the merits of the proposed methods of the project.

英文关键词： Nonlinear control systems；Input-state stability；Practical stability；；