脉冲随机系统的有限时间稳定性分析与控制研究

发布时间：2018-05-29 12:14

  本文选题：脉冲随机系统 + 有限时间稳定　； 参考：《安徽工业大学》2017年硕士论文

【摘要】：近年来,混杂系统受到越来越多学者的关注,原因在于它不仅能代表现实中很多复杂的系统,而且有着重要的理论研究价值与工程实践背景;脉冲随机系统作为一类重要的混杂系统,为系统工程和控制领域提供了许多丰富的研究课题,引起了国内外众多学者的研究兴趣。此外,在工程应用中,例如导弹系统、机器人操控系统、通信网络系统等一些工作时间短、反应快的系统中,有限时间稳定性就显得比渐近稳定性更为重要。本文主要研究了脉冲随机系统的有限时间稳定性与控制设计问题,具体内容如下:1.研究了一类线性脉冲随机定常时滞系统的有限时间稳定与控制问题。首先,基于有限时间稳定性的概念,利用Lyapunov-Krasovskii泛函法和Lyapunov函数法,结合时滞微分不等式技巧以及相关引理,获得了两个基于平均脉冲区间约束下的系统有限时间均方稳定充分条件。然后对两种方法得到的稳定充分条件进行了分析比较,并在有限时间稳定充分条件的基础上,以线性矩阵不等式(LMIs)形式给出了状态反馈控制器的设计方案。最后,由数值例子和图像仿真说明了结果的正确性。2.进一步讨论了带时变时滞的非线性脉冲随机系统的有限时间稳定与控制问题。首先,通过建立合适的时滞相关Lyapunov-Krasovskii泛函以及适当的不等式放缩技巧,结合相关引理和平均脉冲区间的概念,并以LMIs形式给出系统有限时间均方稳定的充分条件。然后基于所提出的稳定条件,为系统设计了状态反馈控制器,以保证相应的闭环系统是有限时间均方稳定的。最后,以数值例子和图像仿真验证了该部分结论的可行性。3.考虑到H∞控制理论在扰动抑制方面的重要作用,针对一类脉冲随机系统的有限时间H∞控制问题进行了研究。首先,基于H∞控制理论以及Lyapunov函数法等,结合相关引理、矩阵分析以及平均脉冲区间的约束条件,以LMIs形式给出了系统有限时间均方稳定以及均方有界的充分条件。然后分析了系统的有限时间H∞性能,并设计了有限时间H∞控制器保证闭环系统是有限时间均方有界的且满足一定H∞性能指标。最后,通过数值例子和图像仿真验证了所设计控制器的有效性。
[Abstract]:In recent years, hybrid systems have attracted more and more attention of scholars, because they not only represent many complex systems in reality, but also have important theoretical research value and engineering practice background. As an important class of hybrid systems, impulsive stochastic systems provide a lot of research topics for the system engineering and control fields, and have aroused the interest of many scholars at home and abroad. In addition, finite time stability is more important than asymptotic stability in engineering applications, such as missile system, robot control system, communication network system and so on. In this paper, the finite time stability and control design of impulsive stochastic systems are studied. The main contents are as follows: 1. In this paper, the finite time stability and control problems of a class of linear impulsive stochastic time-delay systems are studied. First of all, based on the concept of finite time stability, using Lyapunov-Krasovskii functional method and Lyapunov function method, combined with delay differential inequality techniques and related Lemma, Two sufficient conditions for the finite time mean square stability of the system based on the mean impulsive interval constraint are obtained. Then, the stability sufficient conditions obtained by the two methods are analyzed and compared. On the basis of the sufficient stability conditions in finite time, the design scheme of the state feedback controller is given in the form of linear matrix inequality (LMI). Finally, numerical examples and image simulations show the correctness of the results. The finite time stability and control of nonlinear impulsive stochastic systems with time-varying delays are discussed. Firstly, by establishing appropriate delay-dependent Lyapunov-Krasovskii Functionals and appropriate inequality scaling techniques, combining the concepts of correlation Lemma and mean impulsive interval, a sufficient condition for the finite time mean square stability of the system is given in the form of LMIs. Then a state feedback controller is designed for the system based on the proposed stability conditions to ensure that the closed-loop system is finite-time mean-square stable. Finally, the feasibility of the conclusion is verified by numerical examples and image simulations. Considering the important role of H 鈭，

本文编号：1950842