布尔控制网络的输出稳定与镇定

矩阵的半张量积是将逻辑变量转化为向量研究的主要工具.本文利用半张量积把逻辑控制系统表示为离散时间仿射线性系统,在逻辑系统的状态空间框架下研究了以布尔控制网络为代表的逻辑动态系统的输出稳定与镇定.首先给出布尔网络输出稳定的定义,研究了布尔网络输出稳定的充要条件;其次讨论了布尔控制网络的输出镇定,分别得到了布尔控制网络由常值输入变量、自由控制序列、状态反馈控制序列输出镇定的条件.本文讨论的系统输出稳定与镇定是(部分)变量稳定与镇定的推广.     

公理化的矩阵半张量积

本文给出矩阵半张量积的一个公理化框架, 它包括矩阵–矩阵半张量积、矩阵–向量半张量积和向量–向量半张量积. 首先, 对目前通用的各类矩阵半张量积的基本性质与应用做一个综述性的回顾. 然后, 介绍一种新近出现的矩阵半张量积, 即保维数矩阵半张量积. 跟普通矩阵乘法一样, 它是多功能的, 即它可同时实现矩阵–矩阵乘积、矩阵–向量乘积和向量–向量乘积这3种功能. 最后, 本文介绍保维数矩阵半张量积的一些代数性质, 包括非方矩阵的Cayley-Hamilton定理, 非方矩阵的特征值、特征向量等.     

概率布尔控制网络的集可控

本文研究概率布尔控制网络的集可控性问题.首先,利用矩阵半张量积方法,得到概率布尔控制网络的代数表示.其次,借助一个新的算子构造不同的可控矩阵,进而通过可控矩阵考虑自由控制序列和网络输入控制下概率布尔控制网络的集可控性问题,得到了概率布尔控制网络集可控性的充要条件.最后,给出数值例子说明本文结果的有效性.     

布尔控制网络的能控性与能观性

利用矩阵的半张量积,布尔控制网络被转化为离散时间系统.本文从离散时间系统的结构矩阵出发,讨论了逻辑控制系统的能控能观性条件,得到了一个新的能控性条件.新的条件简化了原有能控性矩阵的计算复杂性,矩阵的最高阶数由原来的2m+n降到了2n.另外,还得到了检验布尔控制网络能观性的条件.与原有条件相比,新的条件更容易计算检验.最后,给出一个实例,检验给出的能控能观性判断条件的正确性.     

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.     

切换奇异布尔网络的稳定性分析

基因调控网络的稳定性分析是系统生物学的研究热点问题之一.本文利用矩阵半张量积方法研究了切换奇异布尔网络的稳定性问题.首先给出了切换奇异布尔网络的代数表示,基于该代数表示,建立了系统解存在唯一的充要条件.然后通过将切换奇异布尔网络转化为等价的切换布尔网络,分别得到了系统在任意切换下稳定以及切换可稳的充要条件.最后给出例子验证所得结果的有效性.     

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).     

有限博弈的矩阵半张量积方法

矩阵半张量积被广泛地应用在有限博弈的研究中,例如:1)演化博弈; 2)势博弈; 3)有限博弈的向量空间分解; 4)基于势博弈的优化与控制; 5)合作博弈等.本文的目的,就是对上述各种应用做一个全面的介绍,包括其原理、主要成果、以及尚待解决的问题.     

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.     

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.     

受扰布尔控制网络全局可重构分析与状态估计

受扰布尔控制网络的状态转移,因受未知干扰影响而具有不确定性,这对状态观测器设计带来了困难.本文主要研究了受扰布尔控制网络全局可重构性问题,并在此基础上设计状态观测器.首先,将受扰布尔控制模型转化为多个子系统的切换未知布尔控制网络模型,在此基础上,提出了受扰布尔控制网络的4种不同状态集.其次,基于状态集估计方法,对受扰布尔控制网络状态估计问题进行分析.再次,提出有限时间可重构与全局可重构性概念;同时,根据状态集估计与状态转移分析,分别给出有限时间可重构判定算法与全局可重构性证明的充要条件.最后,给出观测器设计方法,并通过例子证明了本文提出方法的可行性.     

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.     

Simultaneous stabilization for a set of Boolean control networks

This paper investigates simultaneous stabilization of a collection of Boolean control networks (BCNs) by using the semi-tensor product method, and presents a number of new results. First, an algebraic expression of the BCNs is obtained by the semi-tensor product, based on which some necessary and sufficient conditions are presented to solve the simultaneous stabilization problem by a free control sequence, a state-feedback control, and an output-feedback control, respectively. Second, using the column stacking form of matrices, a new procedure is established to design both state-feedback and output-feedback controllers for the simultaneous stabilization problem. The study of two illustrative examples shows that the new results obtained in this paper are very effective in solving simultaneous stabilization of a collection of BCNs.     

Disturbance decoupling control design for switched Boolean control networks

This paper investigates a kind of disturbance decoupling problems (DDPs) for switched Boolean control networks (BCNs), that is, the disturbance-independent output decoupling problem, via the semi-tensor product of matrices. By converting the dynamics of switched BCNs into an algebraic form and using the redundant variable separation technique, all possible state feedback controllers are designed for the disturbance-independent output decoupling problem. Then, based on the obtained state feedback disturbance decoupling controllers and the system’s output equation, a constructive procedure is proposed to design all possible output feedback disturbance decoupling controllers. The study of two illustrative examples shows that the new results obtained in this paper are effective in designing disturbance decoupling controllers for switched BCNs.     

Morgan's problem of Boolean control networks

This paper investigates the Morgan''s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is converted into an output-decomposed form by constructing a set of consistent output-friendly subspaces, and a necessary and sufficient condition for the existence of the consistent output-friendly subspaces is obtained. Secondly, a type of state feedback controllers are designed to solve the Morgan''s problem if it is solvable. By solving a set of matrix equations, a necessary and sufficient condition for converting an output-decomposed form to an input-output decomposed form is given, and by verifying the output controllability matrix, the solvability of Morgan''s problem is obtained.     

Minimum‐Time State Feedback Stabilization of Constrained Boolean Control Networks

Ministry in 2005, and the National Prize of Natural Science of China in 2008. Currently, he is Associate Editor IMA Journal of Math Control and Inform., and a Technical Committee member of IFAC (TC2.3). This paper investigates the state feedback stabilization of Boolean control networks (BCNs) with state and input constraints by using the semi‐tensor product of matrices. Firstly, a kind of constrained input‐state incidence matrix is proposed for constrained BCNs, which contains all the reachability information of the constrained systems. Secondly, based on the constrained input‐state incidence matrix, a necessary and sufficient condition is presented for the stabilization of constrained BCNs via state feedback. Thirdly, a general procedure is proposed to design all possible minimum‐time state feedback stabilizers. The study of an illustrative example shows that the new results obtained are effective in analyzing the stabilization of constrained BCNs.     

A Semi‐Tensor Product Approach to Pseudo‐Boolean Functions with Application to Boolean Control Networks

Using the semi‐tensor product method, this paper investigates several fundamental problems of general pseudo‐Boolean functions with application to the optimal control of Boolean control networks, and establishes a new framework to deal with pseudo‐Boolean inequalities, the optimization problem and the best linear approximation of pseudo‐Boolean functions. First, the pseudo‐Boolean function is expressed in the algebraic form via constructing its unique structural matrix. Second, based on the matrix expression, solving pseudo‐Boolean inequalities is converted into finding solutions to algebraic inequalities, and a set of new formulas are presented. Third, the optimization problem and the linear approximation of the pseudo‐Boolean function are considered and several new results are established. Finally, as an application, we investigate the optimal control of Boolean control networks, and present a new optimal control design procedure. It is shown through the study of illustrative examples that the new results proposed in this paper work very well.     

Reconstructibility analysis and set-observer design for Boolean control networks

This paper deals with the issues of reconstructibility analysis and set-observer design for Boolean control networks (BCNs). A state estimation set is considered to find the state estimation of BCNs, and a reconstructibility judgment matrix (RJM) is obtained by compact vector of state estimation set. Then, a kind of state-reconstructible tree is constructed, and algorithms are also provided to construct it. The state-reconstructible tree can categorize BCNs to be globally reconstructible, locally reconstructible, and unreconstructible. The sufficient and necessary conditions for the reconstructibility of BCNs are given. Meanwhile, the relationship between input–output trajectory and estimated state is derived. Next, with the knowledge of input–output sequence, a set-observer is designed such that the state of BCNs for any global reconstructible BCNs is uniquely determined in a finite time. Some examples are also given to illustrate the effectiveness of the proposed methods.     

Output controllability and optimal output control of state-dependent switched Boolean control networks

In the present paper, we investigate the output-controllability and optimal output control problems of a state-dependent switched Boolean control network. By using the semi-tensor product, the algebraic form of the system is obtained. Then, output-controllability problems of the system are discussed and some necessary and sufficient conditions are given. Next, the Mayer-type optimal output control issue is considered and an algorithm is provided to find out the control sequence. At last, an example is given to show the effectiveness of the main results.