【作者】 张乐群；

【导师】 程代展； 冯俊娥；

【作者基本信息】 山东大学 ， 运筹学与控制论， 2014， 博士

【摘要】 利用矩阵半张量积,论文将逻辑动态系统表示为代数状态空间动力系统.并在这个框架下,讨论并解决或部分解决了切换布尔网络的能控能观性,混合值逻辑系统的干扰解耦,以及基于混合值逻辑的队列控制问题.论文第一章,作为预备知识介绍了布尔网络,队列控制,半张量积的背景知识和研究现状.第二章介绍了布尔网络的模型,半张量积定义和性质以及将逻辑运算形式的布尔网络动态方程代数化的方法.第三章研究了切换布尔网络的能控性和能观性.利用矩阵的半张量积,切换布尔控制网络的动态方程可转换为代数形式.随后提出了MIS (model-input-state)矩阵并研究了其相关性质.MIS矩阵包含了模型、输入、状态映射的完整信息.然后是切换布尔网络能控性的充要条件.能控条件下,我们给出了点到点之间的控制和切换律设计算法.关于切换系统的能观性,我们先给出了一个充分条件.然后,在能控性假设下,我们也给出了能观性的充要条件.在此章最后一节我们研究了高阶切换布尔网络的能控性.我们给出了它的两种代数形式.基于第二种代数形式得到了能控性的充要条件.第四章,我们研究混合值逻辑网络的干扰解耦问题.利用质因子分解定理,我们得到唯一的混合值逻辑网络的Y_友好子空间.对于干扰解耦问题的可解性我们得到了充要条件,并且找到了一个新的算法,可以得到一个系统所有存在的干扰解耦控制器.这个方法比现存的其它算法有更好的操作性,我们用一个算例验证了这一点.第五章中,我们用混合值逻辑的方法研究了队列控制问题.首先,给出一个改进的寻找混合值逻辑网络轨迹的算法.然后首次为队列控制问题建立基于混合值逻辑的离散时间模型,并给出状态反馈控制器.我们还提出了部分队列控制的概念,并给出数学描述.最后,本文详细讨论了一个十分有趣的例子,来进一步解释部分队列问题的应用.更多还原

【Abstract】 In Chapter1of this dissertation, Boolean network and semi-tensor product are introduced for preliminary. The controllability and observability are investigated for a class of switched Boolean control networks (SBCNs) in Chapter2. Using semi-tensor product of matrices, the dynamics of an SBC-N can be transformed into an algebraic form. The model-input-state matrix of an SBCN is introduced and studied for the first time. This matrix contain-s complete information of the model-input-state mapping. A necessary and sufficient condition for the controllability of SBCN is obtained. The corre-sponding control and switching law which drive a point to a given reachable point are designed. A sufficient condition for the observability of an SBCN is also given. Moreover, under the assumption of controllability, one neces-sary and sufficient condition is derived for the observability. Controllability of higher order SBCNs is investigated in this chapter. Two algebraic forms of higher order SBCNs are derived. A necessary and sufficient condition of controllability for higher order SBCNs is obtained. Finally, two illustrative examples are given to show the validity of the main results. In Chapter3, we investigate the disturbance decoupling problems (DDPs) of mix-valued logical control networks (MLCNs) via semi-tensor product method. By us-ing prime factor decomposition, a unique Y-friendly subspace of mix-valued logical networks (MLNs) is derived. A necessary and sufficient condition is obtained for the solvability of DDPs. An algorithm is proposed to find all disturbance decoupling controllers. This approach is more operational than the existing results in which the Y-friendly subspace is not unique. Finally an illustrative numerical example is given to show the effectiveness of the proposed method. In Chapter4, the formation control (FC) problem is investigated via mix-valued logic approach. First, a trajectory tracking algo-rithm of MLCN is proposed. A new formulation of FC problems is established and a feedback controller is designed to solve FC problems. The mathemati-cal description of partial-formation control (PFC) problems is then designed as a structure of logical networks. An interesting practical example of PFC is also presented and discussed in detail.更多还原