非线性ODE-PDE耦合系统的模糊建模与控制

项目名称： 非线性ODE-PDE耦合系统的模糊建模与控制

项目编号： No.61473011

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 吴淮宁

作者单位： 北京航空航天大学

项目金额： 85万元

中文摘要： 现代高新技术的迅速发展派生出许多复杂的非线性集中参数与分布参数相耦合的系统。本项目拟针对一类非线性ODE-PDE耦合系统，从其机理模型出发，来开展模糊ODE-PDE耦合系统的分析与控制设计理论研究。探讨建立模糊ODE-PDE耦合模型的方法，分析模糊ODE-PDE耦合系统的适定性、能控（稳）性与能观（检）性、稳定性及性能等，并建立相应的判据，在此基础上进一步研究模糊ODE-PDE耦合系统的模糊控制设计方法。而且，理论结果将被应用于高超声速飞行器的热防护控制中来检验其实用性。本项目的实施，不仅会为非线性ODE-PDE耦合系统提出一套全新的基于模糊ODE-PDE耦合模型的分析与控制设计理论，也会推动模糊控制技术与非线性分布参数控制理论向更高层次发展，具有重要的科学意义和实际应用价值。

中文关键词： 非线性耦合系统；T-S模糊模型；模糊控制；常微分方程；偏微分方程

英文摘要： The rapid development of mordern high-new technology yields a lot of complex nonlinear lumped parameter systems coupled with distributed parameter systems. This project is proposed for a class of nonlinear systems described by the ordinary differential equations (ODEs) coupled with partial differential equations (PDEs), which will start from their mechanism models to conduct the theoretical study of analysis and control design of fuzzy coupled ODE-PDE systems. First, the methods of establishing fuzzy coupled ODE-PDE model will be probed. Subsequently, the well-posedness, controllability(stabilizability) and observability (detectability), stability and performance of the fuzzy coupled ODE-PDE system will be analyzed, and the corresponding criteria will be set up. Then, based on the analysis results, the control design methods of the fuzzy coupled ODE-PDE system will be developed. Finally, the proposed theoretical results will be applied to the thermal protection control of hypersonic vehicles and the chaos control of semiconductor elements to verify their effectiveness.The implementation of the project will not only provide a new theory of analysis and control design based on fuzzy coupled ODE-PDE model for nonlinear coupled ODE-PDE systems, but also promote the developments of fuzzy control technique and nonlinear distributed parameter control theory to a higher level. It is of great scientific and practical importance.

英文关键词： Nonlinear coupled systems;T-S fuzzy model;Fuzzy control;Ordinary differential equations;Partial differential equations