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.     

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.     

多值逻辑网络的输出跟踪牵制控制

本文利用代数状态空间方法,研究了多值逻辑控制网络的输出跟踪牵制控制.首先利用矩阵的半张量积给出了带牵制控制的多值逻辑控制网络的代数表示.其次基于该代数表示,定义了一组合适的能达集,并建立了多值逻辑控制网络输出跟踪牵制控制器的设计方法.再次,利用多值逻辑哑算子的性质,给出了多值逻辑控制网络分布式输出跟踪控制问题可解的充要条件.最后将所得的理论结果应用于网络演化博弈的演化行为分析.     

基于矩阵半张量积的有限值动态系统的最新进展

布尔网络可以简洁有效地描述作用在有限集上的动态离散模型.然而,随着研究的深入以及一些实际问题的需要,传统的布尔网络已经不能满足建模的需求,由此衍生出多值逻辑网络以及混合值逻辑网络,统称为有限值动态系统.通过矩阵半张量积,有限值动态系统可以转化为便于处理的等价代数形式.鉴于此,对矩阵半张量积以及有限值动态系统的最新发展进...     

基于双分支特征融合的场景文本检测方法

研究一类布尔控制网络的集成集可控性和集成集镇定性问题.首先,利用矩阵的半张量积理论,给出布尔控制网络等价的代数表示;其次,通过自由控制序列研究布尔控制网络的集成集可控性,并给出相应的充分必要条件,对于布尔控制网络的集成集镇定性问题,使其转换为集成集可控性问题,并给出相应的判定定理;最后,给出数值例子说明所提出方法的有效性.     

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.     

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.     

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.     

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).     

Semi-tensor product-based algebra-logic mixed representation and fault diagnosis for a class of gate networks

This article studies an algebra-logic mixed representation of gate networks and its application to stuck-at fault diagnosis. First, the gate network is characterized through a logic expression of disjoint sum-of-products, and the system structure of the gate network is described based on 2-to-1 multiplexers. Then, by resorting to the semi-tensor product of matrices, a novel algebra-logic mixed representation is proposed for the gate network through its logic expression and system structure. Furthermore, a novel stuck-at fault diagnosis algorithm for the gate network is presented, where the stuck-at fault testability of the gate network is equivalent to the solution existence of the system of linear equations. Finally, the fault diagnosis of the 4-bit carry look-ahead adder is carried out to demonstrate the effectiveness and feasibility of the proposed theoretical approach and algorithms.     

基于矩阵方法的Banzhaf值的计算及应用

在合作博弈中,Banzhaf值提供了每个参与者形成大联盟的预期边际贡献,因此Banzhaf值的求解是一个重要的研究内容.本文首先回顾合作博弈及Banzhaf值的定义,并且运用矩阵半张量积,给出合作博弈特征函数的代数表示.然后给出了Banzhaf值的等价的代数形式和简捷的计算方法.最后将所得结果应用于生物网络中,用Banzhaf值度量遗传疾病基因相关性的可能性,确定与遗传疾病发病高度相关的基因.     

Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks

This paper addresses two kinds of optimal control problems of probabilistic mix-valued logical control networks by using the semi-tensor product of matrices, and presents a number of new results on the optimal finite-horizon control and the first-passage model based control problems, respectively. Firstly, the probabilistic mix-valued logical control network is expressed in an algebraic form by the semi-tensor product method, based on which the optimal finite-horizon control problem is studied and a new algorithm for choosing a sequence of control actions is established to minimize a given cost functional over finite steps. Secondly, the first-passage model of probabilistic mix-valued logical networks is given and a new algorithm for designing the optimal control scheme is proposed to maximize the corresponding probability criterion. FinMly, an illustrative example is studied to support our new results/algorithms.     

Full-parameter vision navigation based on scene matching for aircrafts

Vision navigation based on scene matching between real-time images and a reference image has many advantages over the commonly used inertial navigation system （INS）, such as no cumulative measurement errors for long-endurance flight. Recent developments in vision navigation are mainly used for partial navigation parameters measurements, such as the position and the relative velocity, which cannot meet the requirements of completely autonomous navigation. We present the concept, principle and method of full-parameter vision navigation （FPVN） based on scene matching. The proposed method can obtain the three-dimensional （3D） position and attitude angles of an aircraft by the scene matching for multiple feature points instead of a single point in existing vision navigations. Thus, FPVN can achieve the geodetic position coordinates and attitude angles of the aircraft and then the velocity vector, attitude angular velocity and acceleration can be derived by the time differentials, which provide a full set of navigation parameters for aircrafts and unmanned aerial vehicles （UAVs）. The method can be combined with the INS and the cumulative errors of the INS can be corrected using the measurements of FPVN rather than satellite navigation systems. The approach provides a completely autonomous and accurate navigation method for long-endurance flight without the help of satellites.     

Controller design for disturbance decoupling of Boolean control networks

We investigate a type of disturbance decoupling problem (DDP) of Boolean control networks. Using the semi-tensor product of matrices, the dynamics of a Boolean control network is expressed in its algebraic form. Under the framework of output-friendly subspace, we give a necessary and sufficient condition for the solvability of DDP by analyzing the redundant variables, and we present a computationally feasible method to construct all the valid feedback control matrices. The logical functions of each controller can be recovered from the obtained feedback control matrix. Finally, an example is provided to show the effectiveness of the proposed method.     

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.     

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.     

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.