基于模态错序的随机马氏跳变系统的建模、控制及应用研究

项目名称： 基于模态错序的随机马氏跳变系统的建模、控制及应用研究

项目编号： No.61473140

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 王国良

作者单位： 辽宁石油化工大学

项目金额： 80万元

中文摘要： 马氏跳变系统控制理论与方法广泛应用于电力系统、航天工程、经济系统等领域。目前，关于马氏系统的模态依赖控制都假设控制器的模态顺序可得。本项目研究随机马氏系统在控制器模态存在错序时的控制问题。针对系统原模态与控制器模态不同步问题，运用增广模态向量建立体现控制器模态有错序的系统模型。基于随机稳定理论，运用非脆弱思想提出一种新的仅依赖于系统原模态的随机控制器设计方法，大大减少了模态发生错序时所需控制器的数量；阐明转移速率含有不确定性和部分未知时对随机镇定带来的影响；建立新的自适应策略研究系统在转移速率不确定性上界未知时的随机控制问题；应用所提方法探讨复杂网络在仅利用噪声实现牵制控制的可能性及方法。本项目的实施将为研究随机马氏系统在控制器模态错序条件下的随机控制问题开辟新途径，首次建立原模态依赖和新模态依赖控制器存在条件之间的联系，给出复杂网络牵制控制的新方法，对其发展具有重要的理论意义和应用价值。

中文关键词： 马尔可夫跳变系统；模态错序；随机控制；复杂网络

英文摘要： The control theory of Markovian jump systems (MJSs) has been applied to many engineering fields, such as power systems, aerospace engineering, economic systems, etc. . However, the existing results on MJSs have an ideal assumption on mode-dependent controller (MDC) that the operation mode is assumed to be available in sequence. This project considers the stabilization of stochastic MJSs via disordered controllers. An augmented vector of mode is introduced to describe the disagreement between system and controller modes. Based on the stochastic stability theory, a new design method for stochastic stabilizing controller depending on the original mode is developed via using the non-fragile method, which could decrease the number of controllers largely. Moreover, some extensions to stochastic MJSs with general transition rate matrix (TRM) are obtained, in which the effects of TRM with element-wise uncertainties and being partially unknown are studied. When the bound of uncertainties of TRM is unknown, a new adaptation law is proposed such that not only the estimated errors are bounded almost surely but also, the states of the closed-loop system are asymptotically stable almost surely. Finally, applications of the proposed methods are applied to stochastic complex networks with switching property, whose pining control problem will be restudied by using a novel controller only in the diffusion part. New results on pinning control problem of such complex networks via a disordered controller without in the drift part are firstly established. The implementation of this project will present a new approach to study the stochastic stabilization of stochastic MJSs by a disordered controller, which firstly establishes the correlations between the original and new mode-dependent controllers and gives a unified algorithm to design such controllers. Based on the proposed methods, a novel pining control strategy of complex networks by exploiting a kind of controller existing only in the diffusion section is developed. This research will play important roles in the developments of theory and applications.

英文关键词： Markovian jump systems;disordering operation modes;stochastic stabilization;complex networks