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

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.

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。

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方法大都假设其模态顺序可得。本项目研究了随机马氏系统在模态存在错序时的控制问题。针对随机马氏系统的控制器模态与系统原模态不同步的实际情况，建立了体现控制器模态存在错序的数学模型，提出了一种系统原模态依赖随机控制器设计方法，给出了相应控制器的LMI存在条件，大大减少了模态发生错序时所需控制器的数量，实现了系统原模态依赖控制器与系统新模态依赖控制器存在条件的合理统一；在所得模型基础上，建立了直接求解系统原模态依赖参数的方法，分析了转移速率含有不确定性以及部分未知等一般条件带来的影响；针对在转移概率上界未知的一般情况，建立了新的自适应控制策略。跟传统方法相比，该方法具有更好的收敛效果，即不仅保证相应系统的参数估计误差几乎处处有界，可以使得原系统系统状态1概率渐近稳定；针对时滞随机马氏系统，建立了部分时滞依赖的分析设计方法。研究结果表明，所提方法可以较好的阐述时滞项与非时滞项对时滞系统镇定的重要程度，并可以降低传统分析设计方法的保守性，是现有时滞系统理论与方法的重要补充与拓展；针对随机马氏系统的故障检测与容错控制问题，提出一种基于多包不确定性的分析与设计方法。研究成果表明，该设计方法更具一般性，且参数求解方便，具有较广的应用范围，为研究系统模态一般条件下随机马氏系统的相关问题提供了新思路；基于所得研究成果建立了利用噪声实现复杂网络牵制控制新方法，系统阐述了转移概率含有不确定性，转移概率部分未知以及控制器模态错序对随机牵制控制带来的影响。本项目的实施将为研究随机马氏系统在系统模态错序条件下的相关问题开辟了新途径，首次建立了原模态依赖和新模态依赖控制器存在条件之间的联系，给出了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。