基于有界信息的复杂互联系统的镇定设计

项目名称： 基于有界信息的复杂互联系统的镇定设计

项目编号： No.60874008

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 轻工业、手工业

项目作者： 叶华文

作者单位： 中南大学

项目金额： 26万元

中文摘要： 李雅普诺夫函数是镇定设计的主要依据，但没有普遍适用的构造规律。运用饱和和小增益原理能够缓解构造李雅普诺夫函数的困难，但有时仍然是一种复杂的处理方式。本项目从运用有界信息的角度出发考虑问题，不再倚重复杂李雅普诺夫函数和复杂小增益分析，为较难处理的前馈型系统和链式结构系统提供简单的构造性设计。综合运用鲁棒稳定刻画、迭代分析思想及互联系统观点，获取有限时间后的有界信息、极限形式的渐近增益和定性的有界信息等不同类型的有界信息,用于定量地估计系统方程中的复杂非线性项，估计信息反过来指导小控制的幅值调整，以保证非线性项成为影响稳定性的次要因素。相关理论与方法已用于大量典型机械模型如直升机、惯性轮倒立摆、小车上倒摆及球梁模型等的镇定设计。本项目形成了一种主要依靠有界估计信息的设计新思路，一定程度地促进了非线性系统的镇定研究。发表学术论文14篇，其中6篇发表在Automatica,IEEE Transactions on Control Systems Technology, International Journal of Robust and Nonlinear Control等重要国际期刊上。

中文关键词： 非线性系统的镇定；有界控制；互联系统；鲁棒稳定

英文摘要： Stabilization design is mainly based on Lyapunov functions, which cannot be constrcuted in a universal way.The use of saturation and small-gain theory can sometimes reduce the difficulty of constructing Lyapunov functions, but related analysis/synthesis remains to be intractable. From the viewpoint of using boundedness information, this program no longer heavily relies on complicated Lyapunov functions and complicated small-gain analysis, and can provide simple constructive designs for feedforward nonlinear systems and interlaced systems that are often difficult to deal with. By jointly using robust stability theory,recursive analysis approaches as well as cascade systems theory, different kinds of boundedness information including boundedness information in finite time, asymptotical gain and qualitative boundedness information are achieved to quantitatively compute complex nonlinear terms of system eauations, and corresponding estimates are in turn employed to regulate the control amplitude so that nonlinear terms have minor effects on the stability. The results established have been applied to the stabilization for a good number of classical mechanical models such as planar vertical take-off and landing aircraft (PVTOL), inertia wheel pendulum, cart pole system and ball-and-beam system. Via this program, a new method that mainly depends on boundedness information has come into being, which to some degree boosts the stabilization research of nonlinear systems.Fourteen academic papers have been published, among which six papers are published in important international journals such as Automatica, IEEE Transactions on Control Systems Technology, International Journal of Robust and Nonlinear Control.

英文关键词： stabilization of nonlinear systems; bounded control; cascade systems; robust stability