Markov切换系统的有限时间约束控制与滤波

发布时间：2018-04-14 21:53

本文选题：Markov切换系统 + 约束控制与滤波　；参考：《安徽工业大学》2017年硕士论文

【摘要】：作为混杂系统的一种重要分支,Markov切换系统由于其数学表达方式简便,又在电力系统、电路网络系统、航空航天、机器人机械系统、经济学系统、制造业等领域有着广泛的应用,从而吸引了国内外许多学者的关注。本文在已有的研究结果基础上,针对Markov切换系统模态获取受到约束和网络传输受到约束情况下的控制和滤波问题进行相关研究,主要内容集中在有限时间l_2-l_∞跟踪控制器设计、有限时间异步H_∞滤波器设计、有限时间异步l_2-l_∞滤波器设计等方面。具体内容为:1.针对一类具有Markov切换的重复标量非线性系统,研究其有限时间l_2-l_∞跟踪控制问题。所考虑系统的模态信息获取是不完整的,且服从一个确定的伯努利分布的白噪声序列。主要目的是设计一个状态反馈控制器使得所考虑的系统在模态部分可获取时仍然在有限时间内跟踪给定的信号且满足一定的l_2-l_∞性能指标。通过利用模态依赖的对角占优Lyapunov泛函方法,得到了可行的状态反馈控制器存在的一些充分条件。在此基础上,通过改进的矩阵解耦方法可以求得可行的控制器参数。最后,通过一个数值例子和一个经济模型验证了所提方法的有效性。2.研究了一类不确定通信连接的网络化离散Markov切换系统有限时间异步H_∞滤波器设计问题。其中,网络传输约束问题被充分考虑到系统的输出端,其会导致数据包丢失、时延等现象。此外,传感器非线性以及系统模态切换和滤波器模态切换存在异步现象在设计过程中也给予了考虑,两个随机变量用来描述其随机发生现象。这使得我们的系统模型比其他文献更具有通用性。基于有限时间随机分析理论,得到了使得滤波误差系统是有限时间均方随机有界且满足期望的H_∞性能指标的异步滤波器存在的相应判据。借助于该判据并且将第三章中改进的求解控制器的矩阵解耦方法运用到滤波器求解问题中,使得所提出的相应异步滤波器设计方法具有更低的保守性。最后,所给的数值例子和PWM驱动的升压转换器模型说明了所提出方法的优越性和可行性。3.基于2中的结果,进一步将其推广到网络化的非线性Markov切换系统,探讨了其有限时间异步l_2-l_∞滤波器设计问题。在进行异步l_2-l_∞滤波器设计时,也同时考虑了网络的传输约束问题、传感器非线性以及系统模态与滤波器模态之间的异步现象。在有限时间稳定理论框架下,结合Takagi-Sugeno模糊模型,深入剖析了该类非线性系统的特点,并分析了滤波误差系统有限时间有界性以及l_2-l_∞性能,给出了所考虑系统的异步l_2-l_∞滤波器设计方法。最后通过数值例子和一个倒立摆模型说明了所提出设计方法是可用的。
[Abstract]:As an important branch of hybrid system, Markov switching system because of its mathematical expression is simple, and in the electric power system, electric network system, aerospace, robot system, economics, manufacturing and other fields have a wide range of applications, which has attracted the attention of many scholars at home and abroad. Based on the existing research results on the mode of Markov switching system for access is restricted and controlled by the network transmission and filtering problem constraints were studied, the main contents focus tracking controller design in finite time robust l_2-l_ design, asynchronous H_ filter limited time, limited time asynchronous l_2-l_ filter design. The specific contents are as follows: repeated scalar 1. for a class of nonlinear systems with Markov switching, study the finite time robust l_2-l_ tracking control problem. The modal information system under consideration Access is not complete, and subject to a determination of the distribution of Bernoulli white noise sequence. The main purpose is to design a state feedback controller can be obtained in the modal part still in finite time tracking of the given signal and satisfy the l_2-l_ for certain performance index makes the system. By using the Lyapunov functional method diagonally dominant the mode dependent, we get some sufficient conditions for the existence of the state feedback controller is feasible. On this basis, the controller parameters can be obtained by decoupling matrix method and feasible improvement. Finally, the validity of.2. through a number of examples and an economic model show that the proposed method is studied for a class of uncertain network communication the connection of Markov discrete finite time switching system of asynchronous H_ filter design problem. The network transmission constraints by considering output system , which will lead to packet loss, delay and so on. In addition, the sensor nonlinearity and system mode switching and mode switching filter exist asynchronous phenomenon in the design process is considered, two random variables are used to describe the random phenomena. This system makes our model is more general than other finite time literature. Based on the stochastic analysis theory, has been such that the filtering error system is mean square random finite time bounded and satisfy the corresponding criterion of existence of asynchronous H_ filter 2 performance of the expected. With the help of the criterion and the decoupling method of matrix controller is improved in Chapter third to solve the problem of using the filter, the corresponding asynchronous filter design the proposed method is less conservative. Finally, a numerical example and the PWM boost converter to drive the model to illustrate the proposed method The superiority and feasibility of.3. 2 based on the results, further extended to nonlinear Markov switching network system, discusses the finite time asynchronous l_2-l_ filter design. In the design of asynchronous l_2-l_ filter, also considering transmission constraints of the network, as well as between modal and sensor nonlinear modal filter the asynchronous phenomenon. In the framework of finite time stability, combined with the Takagi-Sugeno fuzzy model, in-depth analysis of the characteristics of the nonlinear system, and analyzes the filtering error system finite time boundedness and robust l_2-l_ filter performance, design method of asynchronous l_2-l_ systems are considered. Finally through the model to illustrate the proposed design the method is available for a numerical example and an inverted pendulum.

【学位授予单位】：安徽工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN713;TP273

【参考文献】