基于事件触发和状态翻转的布尔控制网络输出跟踪

利用矩阵半张量积研究事件触发和翻转控制共同作用下布尔控制网络的输出跟踪问题.首先,基于布尔控制网络代数状态空间表示,构造增广系统将输出跟踪问题转化为状态集镇定问题;其次,得到布尔控制网络在两种控制下输出跟踪问题有解的充要条件,并在满足该条件时提出一种基于最小翻转节点集时间最优控制设计方法,进一步给出有限时间内寻找翻转节点集的计算过程;最后,给出一个算例说明结果的可行性.     

概率布尔控制网络的弱能控性

本文研究了概率布尔控制网络的弱能控性,系统的弱能控性是概率布尔网络精确能控的一个推广.首先利用矩阵的半张量积和逻辑变量的向量表示,概率布尔控制网络被表示为离散时间动态系统.接着给出概率布尔控制网络弱能控的定义,从离散时间系统的结构矩阵出发,构造了最大概率转移矩阵,矩阵中的元素表示相应状态之间可能发生转移的最大概率,在此基础上研究了概率布尔控制网络的弱能控的条件,同时给出了两个状态弱能达时控制序列的设计算法.最后通过例子进一步解释了弱能控的概念和控制序列设计算法的有效性.     

块序列布尔网络的拓扑结构

利用矩阵的半张量积,通过建立逻辑变量与向量的对应,块序列布尔网络被表示为离散时间系统,将对序列布尔网络的研究转化为对结构矩阵的研究.块序列布尔网络的结构矩阵是一个逻辑矩阵,利用逻辑矩阵的1特征值与和1特征向量的特殊性质,从矩阵特征值和特征向量的角度研究了块序列布尔网络的拓扑结构,显式表示出了不同长度极限环的个数,并指出网络的极限环总数等于(2n-结构矩阵的秩).     

基于牵制控制的切换布尔网络的分布式集合镇定

切换布尔网络是一种典型的网络化控制系统, 在基因调控、信息安全、人工智能、电路设计等领域具有重 要应用. 本文基于牵制控制方法, 研究切换布尔网络在任意切换下的分布式集合镇定问题. 首先, 利用矩阵半张量积 方法,得到切换布尔网络的代数形式. 其次, 基于代数形式, 提出构造性的算法来实现切换布尔网络在牵制控制的 作用下任意切换集合镇定, 并设计出状态反馈牵制控制器. 再次, 利用逻辑矩阵分解技术和分布式控制方法, 设计任 意切换下切换布尔网络的分布式集合镇定控制器, 并提出分布式控制器存在的充分条件. 文中给出3个例子来说明 所获得结果的有效性.     

具有切换概率分布的概率布尔网络的依分布稳定和镇定

布尔网络作为研究基因调控网络的一种重要模型,近年来引起了国内外很多学者的广泛关注.本文利用代数状态空间表示方法,研究具有切换概率分布的概率布尔网络的依分布稳定和镇定问题.首先,回顾针对切换布尔网络稳定性分析的现有的研究结果.其次,给出具有切换概率分布的概率布尔网络依分布稳定的定义,并利用矩阵的半张量积建立具有切换概率分布的概率布尔网络的代数表示.再次,基于该代数表示,建立具有切换概率分布的概率布尔网络的依分布稳定的充分必要条件.最后,给出具有切换概率分布的概率布尔控制网络镇定问题可解的充要条件,并给出相应的控制设计方法.     

状态翻转控制下布尔控制网络的可镇定性和Q学习算法

在给定一个子集的条件下, 本文研究了在状态翻转控制下布尔控制网络的全局镇定问题. 对于节点集的给定子 集, 状态翻转控制可以将某些节点的值从1 (或0)变成0 (或1). 将翻转控制作为控制之一, 本文研究了状态翻转控制下的 布尔控制网络. 将控制输入和状态翻转控制结合, 提出了联合控制对和状态翻转转移矩阵的概念. 接着给出了状态翻转 控制下布尔控制网络全局稳定的充要条件. 镇定核是最小基数的翻转集合, 本文提出了一种寻找镇定核的算法. 利用可 达集的概念, 给出了一种判断全局镇定和寻找联合控制对序列的方法. 此外, 如果系统是一个大型网络, 则可以利用一 种名为Q学习算法的无模型强化学习方法寻找联合控制对序列. 最后给出了一个数值例子来说明本文的理论结果.     

概率级联布尔网络的集镇定及其应用

随着系统生物学和医学的迅速发展,基因调控网络已经成为一个热点研究领域.布尔网络作为研究生物系统和基因调控网络的一种重要模型,近年来引起了包括生物学家和系统科学家在内的很多学者的广泛关注.本文利用代数状态空间方法,研究了概率级联布尔网络的集镇定问题.首先给出概率级联布尔网络集镇定的定义,并利用矩阵的半张量积给出了概率级联布尔网络的代数表示.其次基于该代数表示,定义了一组合适的概率能达集,并给出了概率级联布尔网络集镇定问题可解的充要条件.最后将所得的理论结果应用于概率级联布尔网络的同步分析及n人随机级联演化布尔博弈的策略一致演化行为分析.     

布尔网络的分析与控制——矩阵半张量积方法

布尔网络是描述基因调控网络的一个有力工具. 由于系统生物学的发展, 布尔网络的分析与控制成为生物学与系统控制学科的交叉热点. 本文综述作者用其原创的矩阵半张量积方法在布尔网络的分析与控制中得到的一系列结果. 内容包括: 布尔网络的拓扑结构, 布尔控制网络的能控、能观性与实现, 布尔网络的稳定性和布尔控制网络的镇定, 布尔控制网络的干扰解耦, 布尔 (控制) 网络的辨识,以及布尔网络的最优控制等.     

状态和输入受限的切换奇异布尔控制网络的最优控制

本文研究了状态和输入均受限的切换奇异布尔控制网络的最优控制问题.利用矩阵半张量积方法获得受限切换奇异布尔控制网络的等价代数形式.然后通过类似针变化得到了存在最优控制的必要条件,并且提出了一个算法设计切换序列和控制策略使收益函数最大化.最后给出例子验证所得结果的有效性.     

状态和输入受限的切换奇异布尔控制网络的最优控制（英文）

本文研究了状态和输入均受限的切换奇异布尔控制网络的最优控制问题.利用矩阵半张量积方法获得受限切换奇异布尔控制网络的等价代数形式.然后通过类似针变化得到了存在最优控制的必要条件,并且提出了一个算法设计切换序列和控制策略使收益函数最大化.最后给出例子验证所得结果的有效性.     

Stability and stabilization of Boolean networks with impulsive effects

This paper investigates the stability and stabilization of Boolean networks with impulsive effects. After giving a survey on semi-tensor product of matrices, we convert a Boolean network with impulsive effects into impulsive discrete-time dynamics. Then, some necessary and sufficient conditions are given for the stability and stabilization of Boolean networks with impulsive effects. Finally, examples are provided to illustrate the efficiency of the obtained results.     

Stability and stabilization of Boolean networks

The stability of Boolean networks and the stabilization of Boolean control networks are investigated. Using semi‐tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean (control) network can be converted to a discrete time linear (bilinear) dynamics, called the algebraic form of the Boolean (control) network. Then the stability can be revealed by analyzing the transition matrix of the corresponding discrete time system. Main results consist of two parts: (i) Using logic coordinate transformation, the known sufficient condition based on incidence matrix has been improved. It can also be used in stabilizer design. (ii) Based on algebraic form, necessary and sufficient conditions for stability and stabilization, respectively, are obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Analysis and control of general logical networks – An algebraic approach

Since Boolean network is a powerful tool in describing the genetic regulatory networks, accompanying the development of systems biology, the analysis and control of Boolean networks have attracted much attention from biologists, physicists, and systems scientists. From mathematical point of view, the dynamics of a Boolean (control) network is a discrete-time logical dynamic process. This paper surveys a recently developed technique, called the algebraic approach, based on semi-tensor product. The new technique can deal with not only Boolean networks, which allow each node to take two values, but also k-valued networks, which allow each node to take k different values, and mix-valued networks, which allow nodes to take different numbers of values.The paper provides a comprehensive introduction to the new technique, including (1) mathematical background of this new technique – semi-tensor product of matrices and the matrix expression of logic; (2) dynamic models of Boolean networks, and general (multi- or mix-valued) logical networks; (3) the topological structure of Boolean networks and general networks; (4) the basic control problems of Boolean/general control networks, which include the controllability, observability, realization, stability and stabilization, disturbance decoupling, identification and optimization, etc.; (5) some other related applications.     

Testing protocols in Internet of Things by a formal passive technique

In recent years, Extensible Messaging and Presence Protocol （XMPP） is gaining momentum in Internet of Things （IoT）. It has been widely used in chatting, message exchanging and unique addressing. As a matter of course, it raises an interesting issue： how to formally test the conformance and performance of XMPP in IoT environment. While conformance testing of communicating protocols is a functional test that verifies whether the behaviors of the protocol satisfy defined requirements, performance testing is a qualitative and quantitative test that aims at checking whether the performance requirements of the protocol are satisfied under certain conditions. In this paper, we present a logic-based passive testing approach that can test both the conformance and the performance of XMPP protocol through real execution traces and formally specified properties. To evaluate and assess our methodology, we present a developed prototype and the experiments with a set of XMPP properties. Finally, the relevant verdicts and conclusions are provided.     

Controllability of Boolean control networks avoiding states set

In this paper, using semi-tensor product and the vector form of Boolean logical variables, the Boolean control network （BCN） is expressed as a bilinear discrete time system about state and control variables. Based on the algebraic form, the reachability and controllability avoiding undesirable states set are discussed. The reachability and controllability discussed here are under certain constraint and tile definitions of reachability and controllability avoiding undesirable states set have practical meaning. Also, the necessary and sufficient conditions for reachability and controllability are given. At last, the control sequence that steers one state to another is constructed.     

Partial stability and stabilisation of Boolean networks

In this paper, we investigate the stability of Boolean networks and the stabilisation of Boolean control networks with respect to part of the system's states. First, an algebraic expression of the Boolean (control) network is derived by the semi-tensor product of matrices. Then, some necessary and sufficient conditions for partial stability of Boolean networks are given. Finally, the stabilisation of Boolean control networks by a free control sequence and a state-feedback control is investigated and the respective necessary and sufficient conditions are obtained. Examples are provided to illustrate the efficiency of the obtained results.