受限布尔网络发展现状

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,由此衍生出受限布尔网络,通过矩阵半张量积,该类型的网络可以转化为便于处理的等价代数表示.鉴于此,对受限布尔(控制)网络的来源、受限形式和相关问题,作了概括与总结.对于受限布尔网络中出现的典型问题、规范化与可解性,理清了其发展脉络与研究现状;对受限布尔网络的拓扑结构整理了相关结果.另一方面,在受限布尔控制网络部分,着重总结其能控性的发展现状,将现有的能控性分析方法归为Dimitriy-Michael方法和预反馈方法两大类,并分别介绍其分析过程.总结受限布尔控制网络在设计能控、镇定、最优控制信号等问题中的一些常用方法(输入-状态关联矩阵方法和Floyd算法),以及牵引控制和干扰解耦等其他研究方向.     

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.     

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.     

关于布尔控制网络的能观性和能检性的研究现状

布尔(控制)网络是模拟基因调控网络有效的数学模型.该模型将细胞内(或特定一个基因组内)基因与基因之间的相互作用关系量化,系统的状态和函数直接反应基因表达、复制、转录等生命活动,在新的数学工具矩阵半张量积的帮助下,取得了许多优秀成果.近些年,国内外病毒疫情频发,对全球各个方面造成巨大的冲击和损失,病毒检测技术是战“疫”中非常重要的一个环节.鉴于此,总结近年来矩阵半张量积在布尔(控制)网络的能观性和能检性方面取得的一些成果,以便更多学者关注这类问题和方法.首先回顾能观性和能检性的发展历程;然后,从理论角度分析并用网络图呈现4种能观性与3种能检性之间的关系,整理在布尔网络和布尔控制网络中相关的一些重要成果,包括状态反馈、输出反馈、含干扰、含切换等多种情形;最后通过简述能观性和能检性的应用现状展望其未来发展.     

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.     

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.     

非线性布尔网络系统模糊建模与动态性能分析

针对非线性系统难以精确建模与动态性能分析的基本控制问题,基于模糊动态模型把布尔网络系统理论推广到非线性布尔网络系统,建立了模糊动态布尔网络控制系统的模型。引入模糊动态模型,对非线性布尔网络进行模糊建模,分别建立了非线性布尔网络系统的局部模型和全局模型。从系统的局部意义和全局意义上,对系统进行了能控性、能观性、稳定性等动态性能分析。最后,以多输入多输出的非线性布尔网络系统实例为具体研究对象,建立了系统的局部模型和全局模型,并对动态性能进行了仿真分析,得到了实验结果。实验结果表明,模糊动态布尔网络控制系统对非线性布尔网络系统的建模是有效的,动态性能分析是合理的,对模糊动态布尔网络控制系统的进一步分析有重要意义。     

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.     

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.     

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.     

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.     

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.     

Realization of Boolean control networks

Based on the linear expression of the dynamics of Boolean networks, the coordinate transformation of Boolean variables is defined. It follows that the state space coordinate transformation for the dynamics of Boolean networks is revealed. Using it, the invariant subspace for a Boolean control network is defined. Then the structure of a Boolean control network is analyzed, and the controllable and observable normal forms and the Kalman decomposition form are presented. Finally the realization problem, including minimum realization, of Boolean control networks is investigated.     

Feedback control and output feedback control for the stabilisation of switched Boolean networks

This paper presents the feedback control and output feedback control for the stabilisation of switched Boolean network. A necessary condition for the existence of a state feedback controller for the stabilisation of switched Boolean networks under arbitrary switching signal is derived first, and constructive procedures for feedback control and output feedback control design are provided. An example is introduced to show the effectiveness of this paper.     

Robust stability and stabilisation of Boolean networks with disturbance inputs

This paper deals with the problems of robust stability analysis and robust stabilisation control design for Boolean networks with disturbance inputs. The main tool used in this paper is the semi-tensor product of matrices. First, a necessary and sufficient condition is presented for the robust stability of Boolean networks based on the algebraic representation of Boolean networks with disturbance inputs. Second, the concept of one-step robust reachability is defined for Boolean control networks (BCNs) with disturbance inputs, based on which a constructive procedure is proposed for the robust stabilisation control design of BCNs. The study of an illustrative example demonstrates the effectiveness of the obtained new results.     

Identification of Boolean control networks

In this paper the identification of Boolean control networks is addressed. First, necessary and sufficient conditions are obtained for the identification of state equation from input-state data. Then a necessary and sufficient condition for a controllable Boolean network to be observable is presented. Based on these two results, a necessary and sufficient condition for the identification from input–output data is achieved. To practically identify the model, a numerical algorithm is proposed. Two particular cases: (i) identification of systems with a known network graph; (ii) identification of a higher order Boolean network, are also investigated. Finally, the approximate identification for large size networks is explored.     

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.     

Feedback control design for the complete synchronisation of two coupled Boolean networks

In the literatures, to design state feedback controllers to make the response Boolean network synchronise with the drive Boolean network is rarely considered. Motivated by this, feedback control design for the complete synchronisation of two coupled Boolean networks is investigated in this paper. A necessary condition for the existence of a state feedback controller achieving the complete synchronisation is established first. Then, based on the necessary condition, the feedback control law is proposed. Finally, an example is worked out to illustrate the proposed design procedure.     

Minimum time control of large‐scale boolean control networks with constraints

The minimum time control that steers a large‐scale Boolean control network with constraints from an initial state to a given state is investigated. This problem is studied under the partition of the large‐scale Boolean control networks. Based on that, the problem is converted to finding the minimum time control for each subnetwork. Hence, the minimum time control for small size Boolean control networks with constraints is considered firstly. Then, a method to solve the problem for large‐scale Boolean control networks with constraints is presented. Finally, a numerical example on T‐cell receptor kinetics is given to show the effectiveness of the main results.