Controllability of time-variant Boolean control networks and its application to Boolean control networks with finite memories

This paper investigates the controllability of time-variant Boolean control networks(BCNs).For the time-variant BCNs,a necessary and sufcient condition for the controllability is given,and a control design algorithm is presented.For a BCN with fnite memories,an equivalent transformation to a time-variant BCN is constructed.Then a necessary and sufcient condition for the controllability and a control design algorithm are obtained.     

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.     

Subspace controllability of Boolean networks

Many Boolean control networks contain independent uncontrollable subnetworks, which may affect other nodes; and the rest of the system is called subspace of sub‐controllable states. This paper investigates the problem of subspace controllability under free input sequences, while the presumption that the initial states of those independent subnetworks are designable is canceled. An algorithm based on the common asymptotic periodic properties of the states is developed to find the reachable sets. Accordingly, the existing controllability criteria for subspaces when initial states of subnetworks are designable is improved, and a necessary and sufficient condition of subspace controllability via subnetworks and free inputs is derived. A design technique involving a kind of newly defined addition is presented to construct desired controls.     

Controllability of probabilistic Boolean control networks

This paper deals with the controllability of probabilistic Boolean control networks. First, a survey on the semi-tensor product approach to probabilistic Boolean networks is given. Second, the controllability of probabilistic Boolean control networks via two kinds inputs is studied. Finally, examples are given to show the efficiency of the obtained results.     

Controllability and observability of Boolean control networks

The controllability and observability of Boolean control networks are investigated. After a brief review on converting a logic dynamics to a discrete-time linear dynamics with a transition matrix, some formulas are obtained for retrieving network and its logical dynamic equations from this network transition matrix. Based on the discrete-time dynamics, the controllability via two kinds of inputs is revealed by providing the corresponding reachable sets precisely. Then the problem of observability is also solved by giving necessary and sufficient conditions.     

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.     

Controllability of Boolean control networks with time delays in states

This paper investigates the controllability of Boolean networks with time-invariant delays in states. After a brief introduction on converting the logic dynamics to discrete time delay systems, the controllability via two kinds of controls is studied. One kind of control is generated by Boolean control networks, another kind of control is free Boolean sequences. In both cases, necessary and sufficient conditions of the controllability of Boolean control networks are proved. Finally, examples are given to illustrate the efficiency of the obtained results.     

Controllability and stabilization of Boolean control networks by the auxiliary function of flipping

In this article, a hybrid method combining flip matrix approach and an open (or closed) loop control is proposed to study global controllability and stabilization of Boolean control networks (BCNs). First, the necessary and sufficient condition for global controllability of BCNs, by flipping some members of a perturbation set and under free control sequences, is proposed. After that, using a search algorithm, the minimal perturbation sets for global controllability (MS‐GCs) of the BCN are obtained. Next, we propose a necessary and sufficient criterion for global stabilization of BCNs by flipping some members of a perturbation set and under a state feedback control. Similarly, an algorithm is given to search for the minimal perturbation sets for global stabilization (MS‐GSs) of the BCN. Moreover, the time‐optimal MS‐GSs of the BCN are also obtained by an algorithm. Some examples are given to illustrate the effectiveness of the results.     

On controllability and stabilizability of probabilistic Boolean control networks

The controllability of probabilistic Boolean control networks(PBCNs)is first considered.Using the input-state incidence matrices of all models,we propose a reachability matrix to characterize the joint reachability.Then we prove that the joint reachability and the controllability of PBCNs are equivalent,which leads to a necessary and sufcient condition of the controllability.Then,the result of controllability is used to investigate the stability of probabilistic Boolean networks(PBNs)and the stabilization of PBCNs.A necessary and sufcient condition for the stability of PBNs is obtained first.By introducing the control-fixed point of Boolean control networks(BCNs),the stability condition has finally been developed into a necessary and sufcient condition of the stabilization of PBCNs.Both necessary and sufcient conditions for controllability and stabilizability are based on reachability matrix,which are easily computable.Hence the two necessary and sufcient conditions are straightforward verifiable.Numerical examples are provided from case to case to demonstrate the corresponding theoretical results.     

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.     

Finite-time observability of probabilistic Boolean control networks

In this paper, the finite-time observability (FO ) of probabilistic Boolean control networks (PBCNs ) based on set reachability and parallel extension is investigated. Under algebraic state space representation of PBCNs , finite-time set reachability (FSR ), finite-time single input sequence set reachability (FSSSR ), finite-time arbitrary input sequence set reachability (FASSR ), as well as finite-time output feedback set reachability (FOSR ) are addressed, where some efficient criteria are proposed. In the second part of this paper, several types of FO are provided, which can be converted to the corresponding FSR based on the parallel extension technique. Consequently, the obtained results for FSR are utilized to deal with FO . Finally, two examples including a biological network are given to demonstrate the theoretical results.     

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.     

Controllability and observability of state‐dependent switched Boolean control networks with input constraints

This paper investigates the controllability and observability of state‐dependent switched Boolean control networks (SDSBCNs) with input constraints. First, the algebraic form of SDSBCNs is derived via the semi‐tensor product of matrices. Then constrained model‐input‐state (CMIS) matrices are introduced for SDSBCNs with input constraints. On the basis of CMIS matrices, two necessary and sufficient conditions are provided for the controllability and observability. Finally, two examples are given to show the effectiveness of the main results.     

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.     

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.     

Set reachability and set stability of Boolean networks with state-dependent asynchronous updating rule

Asynchronous behavior is significant for real biological systems. This paper explores the impact of state-dependent asynchronous updating rule (SDAUR) on the set reachability and set stability of Boolean networks (BNs). First, a set of state-dependent control variables is introduced to describe the SDAUR. Second, a new asynchronous set reachablity matrix is constructed based on an auxiliary input and semi-tensor product. Third, using the asynchronous set reachablity matrix, several necessary and sufficient conditions are obtained for the set reachablity and set stability of BNs with SDAUR. Finally, the new results proposed in this paper are verified through the immunomic network.     

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.     

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.