基于符号表达与多元逼近的智能控制的稳定性分析与控制设计

In nonlinear control and intelligent control field, some dynamics analysis and control design methods are made on a series of small state areas that the state space of the systems is segmented into, but some problems on the stability analysis and the stable controller design problems in these methods doesn't be solved and the project proposed here will focused on that. Firstly, based on the multivariable approximation theory, the interpolation nodes and the compact-support radius base functions as the interpolation base functions are applied to describe the state space as the symbolic-element (SE) space and the approximating-element (AE) space, and then the models of the nonlinear dynamic systems are transformed as the SE and the AE dynamic systems. Therefore, the systems analysis, such as stability, controllability and performance analysis, and the stable control design problem will be study in among the continuous variable space, the AE space and the SE space. The new study will prompt the study on the analysis and control design of the nonlinear systems and intelligent control systems, especially the large-range state transfer control problem of the nonlinear systems with the local dynamics. Our team is with the good foundations on multivariable approximation, automata, nonlinear dynamics, and the rich research experiences on system modeling, identification, system analysis, control design, and will fulfill the project.

在非线性控制、智能控制领域,存在一类通过将状态(输出)空间划分为子区域来进行动力学分析和控制设计的方法,但其稳定性分析和稳定控制设计一直未有很好的解决。本申请项目拟基于多元函数逼近论通过构造插值节点,引入紧支径向基插值函数,对非线性系统建立连续变量空间的符号元和逼近元描述,以及相应的符号元和逼近元动力学模型,将控制系统的分析和设计演化为在连续变量、逼近元和符号元三个空间层面上展开,系统研究逼近元和符号元空间的建模、稳定性、能控性、稳定的并具有期望性能控制策略设计等问题,目标为建立针对非线性动力学特性的稳定性分析和控制设计方法,为解决非线性系统、智能控制系统的控制设计,尤其是状态大范围转移控制问题提供新思路。本项目涉及多元函数逼近、细胞自动机、非线性动力学等基础理论,需要有系统建模与辨识、动力学系统分析、控制器设计等领域良好的研究基础和能力,本课题组已基本具备承担该研究的条件。