带有随机干扰的非齐次马尔科夫跳变系统的鲁棒滤波研究

项目名称： 带有随机干扰的非齐次马尔科夫跳变系统的鲁棒滤波研究

项目编号： No.61503121

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 自动化技术、计算机技术

项目作者： 华民刚

作者单位： 河海大学

项目金额： 20万元

中文摘要： 马尔科夫（Markov）跳变系统因能有效描述许多实际对象，所以具有广泛的应用价值，而该类系统的鲁棒滤波问题正是其中的研究热点之一。本项目研究的Markov跳变系统的转移概率矩阵是时变（非齐次）的，同时考虑实际中普遍存在的随机干扰现象，因此拟对带有随机干扰的非齐次Markov跳变系统的滤波问题进行研究。首先，研究带有随机干扰的非齐次Markov跳变系统的H∞滤波和混合H2/H∞滤波问题；其次，研究带有随机干扰的非齐次Markov跳变系统的L2-L∞滤波问题；再次，研究带有随机干扰的非齐次Markov跳变系统的非脆弱滤波和保成本滤波问题。在此基础上，还研究存在不确定性和时滞等现象时系统的鲁棒滤波问题。最后进行数值算例仿真，并把研究成果应用在带有随机干扰的非齐次Markov跳变复杂网络中。本项目的成功实施将进一步丰富Markov跳变系统的控制理论，对其发展具有重要的理论意义和应用价值。

中文关键词： 滤波；H∞滤波

英文摘要： Markov jump system can be used efficiently to describe many practical plants, so it has widely application value. And the robust filtering problem of this kind of system is a hot research topic. The transition probability matrix of Markov jump system in this project is assumed to be time-varying (nonhomogeneous). At the same time the stochastic perturbation exists generally in practice, so the robust filtering problem for nonhomogeneous Markov jump systems with stochastic perturbation will be studied in this project. Firstly, the H∞ filtering and mixed H2/H∞ filtering problem for nonhomogeneous Markov jump systems with stochastic perturbation will be investigated. Secondly, the L2-L∞ filtering problem for nonhomogeneous Markov jump systems with stochastic perturbation will be investigated. Thirdly, the non-fragile and guaranteed cost filtering problem for nonhomogeneous Markov jump systems with stochastic perturbation will be investigated. Based on this, the robust filtering problem for systems with uncertainties and time delay are also studied. At last, numerical examples are given to show the effectiveness of the obtained results and the research results will be applied in nonhomogeneous Markov jump complex networks with stochastic perturbation. The successful implementation of this project will further enrich the control theory of Markov jump systems and play important roles in the developments of theory and applications.

英文关键词： filtering;H∞ filtering