基于时间加权H2指标的Markov跳变系统的模型降阶问题研究

项目名称： 基于时间加权H2指标的Markov跳变系统的模型降阶问题研究

项目编号： No.61203101

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 自动化学科

项目作者： 孙敏慧

作者单位： 中国海洋大学

项目金额： 24万元

中文摘要： 实际物理系统进行数学建模后往往具有较高的阶次，这给系统的分析、仿真和设计带来了很大的困难。模型降阶以简化模型为目的，在某种误差指标下寻求高阶系统的近似低阶模型。本项目拟在H2范数的基础上定义时间加权H2范数作为误差指标，并基于该指标研究Markov跳变系统的模型降阶问题。引入新型指标的目的是保证误差系统H2性能的同时，使得在相同输入下,降阶系统的输出更快地逼近原系统的输出。主要研究内容包括：1）定义并计算离散Markov跳变系统的时间加权H2范数，建立该降阶问题的可解条件；2）在连续及离散两种情况下，分别给出高效的Markov跳变系统的时间加权H2模型降阶算法；3）改进时间加权H2指标并设计相应的模型降阶方法，同时满足误差系统响应速度和超调量要求。本项目旨在建立Markov跳变系统时间加权H2模型降阶的基本概念和方法，不但有利于工程实践，对模型降阶理论的进一步完善和发展也将起到促进作用。

中文关键词： Markov 跳变系统；时间加权H2范数；模型降阶；；

英文摘要： It is well known that mathematical modelling of physical systems often involves high-order models, which bring difficulties in simulation, analysis, design of the systems concerned. This has motivated the investigation on a variety of model reduction problems. The prime purpose of model reduction is to find a lower-order model to approximate the original model, often subject to a given performance index. In this project, a new error measure named time-weighted H2 norm is defined based on the classical H2 norm for model reduction purpose. In this new error measure a heavy penalty is placed as time increases, hence the steady-state behavior of the error system will be greatly emphasized and the convergence rate of the error output is expected to be larger. In this project, we are concerned with the time-weighted H2 model reduction problem of Markov jump linear systems. First, the time-weighted H2 norm of discrete Markov jump system is defined and a computational method is constructed. One-order conditions are also given such that the corresponding time-weighted H2 model reduction problem can be solved.Second, efficient reduction approaches are proposed for Markov jump systems in both continuous and discrete time case. Finally, the definition of time-weighted H2 norm is improved by taking the amplitude of error out

英文关键词： Markov jump systems；time-weighted H2 norm；model reduction；；