布尔网络的反馈控制与镇定问题研究

发布时间：2018-01-10 23:03

本文关键词：布尔网络的反馈控制与镇定问题研究　出处：《东南大学》2017年硕士论文　论文类型：学位论文

【摘要】：由于布尔模型在系统生物学中能够很好的模拟基因之间的相互作用关系,因此越来越多的人被吸引到布尔网络的研究当中,其中包括生物学家,物理学家和系统控制等方面的专家等.其中布尔网络的可控性问题又是控制理论中一个重要的研究方向.对于布尔网络控制性问题方面的研究一直受到各方面的广泛关注.本文利用矩阵半张量积方法,讨论时滞布尔网络的镇定控制问题,布尔网络的输出追踪控制问题以及基于牵引控制策略的布尔网络集镇定问题.本文的主要结构安排如下:第一章主要介绍布尔网络的研究现状及国内外主要结果.第二章主要介绍了矩阵半张量积的相关知识点,包括定义,定理,性质,以及如何用矩阵的半张量积去构建布尔网络的代数模型等.第三章研究基于状态反馈的时滞布尔控制网络的镇定问题.在本章中,通过利用矩阵的半张量积,得到了使得系统镇定的充要条件.给出了具体的步骤去设计控制器,它使得系统在控制器控制下能够实现镇定.基于本章这个设计方法,控制器矩阵的数量可被明确的计算出来.与现有结果相比,本章的方法既减少了计算量又易获得控制器的数量.最后通过一个生物例子来说明设计方法的可行性.第四章研究布尔控制网络的输出追踪控制问题.本章给出一个使得系统实现输出追踪的充要条件.先找到最大不变集,然后基于这个最大不变集去设计控制器.这些被设计出来的控制器能够保证系统实现最优输出追踪控制.与现有结果相比较,本章的设计方法极大的减少计算量,同时还能够保证系统在最短的时间内实现输出追踪.最后通过一个生物例子说明本章设计方法的可行性.第五章研究基于牵引控制策略的布尔网络的集镇定问题.通过运用矩阵的半张量积首先得到了系统的代数表达式-代数矩阵.基于这个代数矩阵,本章给出了一个挑选牵引控制节点的方法.通过对这些牵引点施加控制来实现系统的集镇定.本章预先定义了一个矩阵集.基于这个预先定义的矩阵集去设计控制器,既能够降低计算的复杂度又能保证解的可行性.最后通过一个例子来演示本章的设计方法.第六章对本文进行总结,并对未来的研究工作进行展望.
[Abstract]:Because Boolean models can well simulate the interaction between genes in systems biology, more and more people are attracted to the study of Boolean networks, including biologists. Among them, the controllability of Boolean network is an important research direction in control theory. In this paper, the matrix semi-tensor product method is used. The stabilization control problem of Boolean networks with time delay is discussed. The output tracking control problem of Boolean network and the stabilization problem of Boolean network set based on traction control strategy. The main structure of this paper is as follows:. The first chapter mainly introduces the research status of Boolean network and the main results at home and abroad. The second chapter mainly introduces the related knowledge of matrix semi-tensor product. It includes definitions, theorems, properties, and how to construct algebraic models of Boolean networks by using the semi-tensor product of matrices. Chapter 3 studies the stabilization of time-delay Boolean control networks based on state feedback. By using the semi-tensor product of the matrix, the necessary and sufficient conditions for the stabilization of the system are obtained, and the concrete steps to design the controller are given. It can stabilize the system under the control of the controller. Based on the design method of this chapter, the number of controller matrix can be calculated clearly, compared with the existing results. The method in this chapter not only reduces the amount of computation but also easily obtains the number of controllers. Finally, a biological example is given to illustrate the feasibility of the design method. Chapter 4th studies the output tracking control problem of Boolean control networks. A necessary and sufficient condition for the system to realize output tracing. First, find the maximum invariant set. Then the controller is designed based on the maximum invariant set. These controllers can guarantee the optimal output tracking control. The design method of this chapter greatly reduces the calculation cost. Finally, a biological example is given to illustrate the feasibility of the design method. Chapter 5th studies the set stabilization problem of Boolean network based on traction control strategy. By using the semi-tensor product of the matrix, we first obtain the algebraic expression of the system-algebraic matrix based on this algebraic matrix. In this chapter, a method of selecting traction control nodes is given. By applying control to these traction points, the system is stabilized. In this chapter, a matrix set is predefined. Based on this predefined matrix set, the controller is designed. The machine. It can reduce the computational complexity and guarantee the feasibility of the solution. Finally, an example is given to demonstrate the design method of this chapter. Chapter 6th summarizes this paper and looks forward to the future research work.
【学位授予单位】：东南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5;O231

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