基于Takagi-Sugeno模型的非线性系统数据驱动最优控制方法适定性的研究

项目名称： 基于Takagi-Sugeno模型的非线性系统数据驱动最优控制方法适定性的研究

项目编号： No.61273011

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 张大庆

作者单位： 辽宁科技大学

项目金额： 60万元

中文摘要： 拟研究基于Takagi-Sugeno(T-S)模糊模型的，以数据驱动为背景的，非线性系统最优控制问题的适定性与适定化的问题。首先，结合模糊逼近原理，研究基于正则化理论的T-S模糊系统辨识方法。其次，研究可用某种函数逼近器逼近的一类非线性系统最优控制问题的适定性。特别是深入研究相对逼近模型误差，某一特定最优控制问题解空间中函数序列的收敛特性。探讨这种收敛性与相关鲁棒控制器存在性之间的关系。研究正则化泛函的构造方法。建立收敛定理。构造有限差分法求解相应的Cauchy问题，得到具体算法。最后，研究基于T-S模糊模型的，从目标非线性系统的历史输入输出数据到模糊最优控制器这一整体过程的适定性，以及基于正则化理论的适定化方法。本项目研究有利于从问题的适定性角度丰富基于数据驱动的非线性系统最优控制方法的研究内容，并完善必要的理论基础。

中文关键词： 模糊控制；最优控制；数据驱动模型；适定性；正则化理论

英文摘要： We are concerned with the well-posedness of nonlinear systems optimal control, which is to be solved based on Takagi-Sugeno(T-S) fuzzy model and data-driven method. If the problem is ill-posed, we are interested in how to make it to be well-posed. Firstly, with the aid of fuzzy approximation principle, the fuzzy system structure identification problem will be taken into account based on regularization theory. Next, the well-posedness of a class of nonlinear systems, which can be approximated by some function approximators, are focused on. Especially, for a particular optimal control problem, the converging character of the sequences in the solution space against to approximate model errors will be studied intensively. Furthermore, the relationship between such converging character and the existence of the related robust controller will be considered as well. The methods of constructing regularization functional are to be explored, and the convergence theorem will be established. To get the specific algorithms, the Cauchy problems will be solved by using finite differential methods. Finally, the problems of well-posedness and how to make the process to be well-posed by using regularization theory will be discussed deeply for the process of designing optimal controller from the information in the given nonlinear s

英文关键词： fuzzy control；optimal control；data-driven model；well-posedness；regularization theory