State Filtering and Parameter Identification for Nonlinear Polynomial Systems, based on Optimal H_2 and H_infinity Algorithms

基于最优 H_2 和 H_infinity 算法的非线性多项式系统的状态滤波和参数识别

基本信息

批准号：
EP/F029195/1
负责人：
Peng Shi
金额：
$ 4.1万
依托单位：
University of South Wales
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2008
资助国家：
英国
起止时间：
2008 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FF029195%2F1
关键词：
State Filtering Parameter Identification Nonlinear

项目摘要

Although the optimal control (regulator) problem for linear systems was solved, as well as the filtering one, in 1960s, the optimal control law for nonlinear systems has to be determined using the general principles of maximum or dynamic programming, which do not provide an explicit form for the optimal control in most cases. For nonlinear systems with unknown parameters, the situation seems to be far worse: even the optimal Linear-Quadratic-Gaussian controller problem for linear systems with unknown parameters has not been consistently studied. To create a tool for handling a controller problem for incompletely measured systems with unknown parameters, methods for optimal joint state filtering and parameter identification have to be developed for nonlinear polynomial (in particular, bilinear) systems. Indeed, namely bilinear systems are obtained upon extending the state vector by including unknown parameters as additional states.This project therefore deals with a particular type of nonlinear systems, polynomial systems, for which a closed form of the state filtering and parameter identification equations can be developed in view of specific properties of polynomial functions. Two kinds of exogenous disturbances will be considered: unbounded white noises and integral-quadratically bounded noises. For the first kind, the H_2 filtering problem is considered, whose solution results in minimizing a standard quadratic cost function; for the second kind, the H_infinity problem is appropriate, which maintains the transfer function norm from the noise input to the output estimation error less than a prescribed attenuation level.The general objective is to develop and verify the optimal H_2 state filtering and parameter identification algorithms for nonlinear polynomial systems, as well as the central suboptimal H_infinity state filtering and parameter identification algorithms for nonlinear polynomial systems, based on the obtained optimal H_2 algorithms for those classes of systems. Verification of the obtained algorithms through numerical simulations follows.The proposed design of the central suboptimal H_infinity filters for nonlinear polynomial systems with integral-quadratically bounded disturbances naturally carries over from the design of the optimal H_2 filters for nonlinear polynomial systems with unbounded disturbances (white noises). The entire design approach creates a complete state filtering and parameter identification algorithm of handling nonlinear polynomial systems with unbounded or integral-quadratically bounded disturbances optimally. for all attenuation levels uniformly or for any fixed attenuation level separately.

尽管线性系统的最优控制（调节器）问题以及滤波问题在 20 世纪 60 年代都得到了解决，但非线性系统的最优控制律必须使用最大或动态规划的一般原理来确定，而这并不能提供大多数情况下最优控制的显式形式。对于参数未知的非线性系统，情况似乎要糟糕得多：即使是参数未知的线性系统的最优线性二次高斯控制器问题也没有得到一致的研究。为了创建一个工具来处理具有未知参数的不完全测量系统的控制器问题，必须为非线性多项式（特别是双线性）系统开发最佳联合状态过滤和参数识别的方法。事实上，即双线性系统是通过将未知参数作为附加状态来扩展状态向量而获得的。因此，该项目处理特定类型的非线性系统，即多项式系统，对于该系统，可以将状态过滤和参数识别方程的闭合形式表示为是根据多项式函数的特定性质而开发的。将考虑两种外源干扰：无界白噪声和积分二次有界噪声。对于第一类，考虑H_2过滤问题，其解决方案导致标准二次成本函数最小化；对于第二类，H_无穷大问题是合适的，它保持从噪声输入到输出估计误差的传递函数范数小于规定的衰减水平。总体目标是开发和验证最优的H_2状态滤波和参数识别算法非线性多项式系统的最优 H_2 算法，以及非线性多项式系统的中心次优 H_infinity 状态滤波和参数识别算法，基于所获得的此类系统的最优 H_2 算法。下面通过数值模拟验证所获得的算法。对于具有积分二次有界扰动的非线性多项式系统，所提出的中心次优 H_infinity 滤波器的设计自然地继承了具有无界扰动的非线性多项式系统（白噪声）的最优 H_2 滤波器的设计）。整个设计方法创建了一个完整的状态滤波和参数识别算法，可以最佳地处理具有无界或积分二次有界扰动的非线性多项式系统。统一适用于所有衰减级别或单独适用于任何固定衰减级别。