Controllability and Synchronization Analysis of Identical-Hierarchy Mixed-Valued Logical Control Networks

Safe control of logical control networks with random impulses

Under the framework of a hybrid-index model, this paper investigates safe control problems of state-dependent random impulsive logical control networks (RILCNs) on both finite and infinite horizons, respectively. By using the ξ-domain method and the constructed transition probability matrix, the necessary and sufficient conditions for the solvability of safe control problems have been established. Further, based on the technique of state-space partition, two algorithms are proposed to design feedback controllers such that RILCNs can achieve the goal of safe control. Finally, two examples are shared to demonstrate the main results.

A State Space Approach to Decentralized Fault SE-Coprognosability of Partially Observed Discrete Event Systems

The problem of fault prognosis in the context of discrete event systems (DESs) is a crucial subject to study the security and maintenance of cyber-physical systems. In this article, the decentralized fault prognosis of partially observed DESs is analyzed with a universal state-estimate-based protocol. It follows (M,K) as the performance bound of any expected decentralized prognosers, where any fault can be predicted K steps before its occurrence and the fault is guaranteed to occur within M steps once a corresponding fault alarm is issued. To determine whether expected decentralized prognosers exist, the notion of state-estimate-coprognosability (SE-coprognosability) under the case of one fault type is proposed. Compared with existing other kinds of coprognosability, SE-coprognosability is a more generalized concept. Meanwhile, combining the formal method and algebraic state space approach, a novel state estimation algorithm is presented and based on which, the verification of SE-coprognosability is also solved.

Transient Bipartite Synchronization for Cooperative-Antagonistic Multiagent Systems With Switching Topologies

This article aims at addressing the transient bipartite synchronization problem for cooperative-antagonistic multiagent systems with switching topologies. A distributed iterative learning control protocol is presented for agents by resorting to the local information from their neighbor agents. Through learning from other agents, the control input of each agent is updated iteratively such that the transient bipartite synchronization can be achieved over the targeted finite horizon under the simultaneously structurally balanced signed digraph. To be specific, all agents finally have the same output moduli at each time instant over the desired finite-time interval, which overcomes the influences caused by the antagonisms among agents and topology nonrepetitiveness along the iteration axis. As a counterpart, it is revealed that the stability can be achieved over the targeted finite horizon in the presence of a constantly structurally unbalanced signed digraph. Simulation examples are carried out to demonstrate the effectiveness of the distributed learning results developed among multiple agents.

Finite-Time Set Reachability of Probabilistic Boolean Multiplex Control Networks

This study focuses on the finite-time set reachability of probabilistic Boolean multiplex control networks (PBMCNs). Firstly, based on the state transfer graph (STG) reconstruction technique, the PBMCNs are extended to random logic dynamical systems. Then, a necessary and sufficient condition for the finite-time set reachability of PBMCNs is obtained. Finally, the obtained results are effectively illustrated by an example.

Distributed Control of Time-Varying Signed Networks: Theories and Applications

Signed networks admitting antagonistic interactions among agents may polarize, cluster, or fluctuate in the presence of time-varying communication topologies. Whether and how signed networks can be stabilized regardless of their sign patterns is one of the fundamental problems in the network system control areas. To address this problem, this paper targets at presenting a self-appraisal mechanism in the protocol of each agent, for which a notion of diagonal dominance degree is proposed to represent the dominant role of agent's self-appraisal over external impacts from all other agents. Selection conditions on diagonal dominance degrees are explored such that signed networks in the presence of directed time-varying topologies can be ensured to achieve the uniform asymptotic stability despite any sign patterns. Further, the established stability results can be applied to achieve bipartite consensus tracking of time-varying signed networks and realize state-feedback stabilization of time-varying systems. Simulations are implemented to verify our uniform asymptotic stability results for directed time-varying signed networks.

Pinning Controllability for a Boolean Network With Arbitrary Disturbance Inputs

In this paper, pinning controllability for a Boolean network (BN) under arbitrary disturbance inputs is considered. By selecting a fraction of nodes as the pinning nodes and injecting controllers that depend on the values of the disturbance inputs of the previous time instant, the controllability can be guaranteed for any BNs under arbitrary disturbance inputs. First, based on the necessary and sufficient conditions for the controllability of a BN with arbitrary disturbance inputs obtained in this paper, a constructive method for designing the transition matrix of the BN is presented, which further provides a method for selecting the pinning nodes. Second, a logical relationship between the control input nodes and system nodes is provided through solving logical matrix equations. Third, the control input sequence algorithm is also given. Finally, an example is presented to show the effectiveness of the proposed results.

Target Controllability of Two-Layer Multiplex Networks Based on Network Flow Theory

In this paper, we consider the target controllability of two-layer multiplex networks, which is an outstanding challenge faced in various real-world applications. We focus on a fundamental issue regarding how to allocate a minimum number of control sources to guarantee the controllability of each given target subset in each layer, where the external control sources are limited to interact with only one layer. It is shown that this issue is essentially a path cover problem, which is to locate a set of directed paths denoted as P and cycles denoted as C to cover the target sets under the constraint that the nodes in the second layer cannot be the starting node of any element in P , and the number of elements in P attains its minimum. In addition, the formulated path cover problem can be further converted into a maximum network flow problem, which can be efficiently solved by an algorithm called maximum flow-based target path-cover (MFTP). We rigorously prove that MFTP provides the minimum number of control sources for guaranteeing the target controllability of two-layer multiplex networks. It is anticipated that this paper would serve wide applications in target control of real-life networks.

Event-Triggered Sampled Feedback Synchronization in an Array of Output-Coupled Boolean Control Networks

In this article, synchronization problem in an array of output-coupled Boolean control networks (BCNs) is studied by using event-triggered sampled feedback control. Algebraic forms of an array of output-coupled BCNs are presented via the semitensor product (STP) of matrices. Based on the algebraic forms, a necessary and sufficient condition is obtained for the synchronization of an array of output-coupled BCNs. Furthermore, an algorithm is proposed to design event-triggered sampled feedback controllers. Finally, the obtained results are well illustrated by numerical examples.

Stability and Stabilization in Probability of Probabilistic Boolean Networks

This article studies the stability in probability of probabilistic Boolean networks and stabilization in the probability of probabilistic Boolean control networks. To simulate more realistic cellular systems, the probability of stability/stabilization is not required to be a strict one. In this situation, the target state is indefinite to have a probability of transferring to itself. Thus, it is a challenging extension of the traditional probability-one problem, in which the self-transfer probability of the target state must be one. Some necessary and sufficient conditions are proposed via the semitensor product of matrices. Illustrative examples are also given to show the effectiveness of the derived results.

Necessary and Sufficient Conditions on Pinning Stabilization for Stochastic Boolean Networks

In this paper, the stabilization problem of the Boolean network (BN) with stochastic disturbances via pinning control has been investigated. The necessary and sufficient conditions are given for robust stabilization of a BN with stochastic disturbances. Then, pinning control is considered to stabilize a BN with stochastic disturbances. An algorithm is given to obtain a new stable system and the pinning control, including the pinned nodes, control design, and control adding, is also solved. Finding the minimal number of pinned nodes is further analyzed. The necessary and sufficient conditions are obtained for the solvability of pinning control, based on which some matrices sets are constructed which leads to the necessary and sufficient conditions of pinning t nodes. Furthermore, an algorithm is introduced to search the minimal number of pinned nodes and what exactly they are, which will reduce the computational burden. Examples are given to illustrate the efficiency of the obtained results.

Sampled-Data State-Feedback Stabilization of Probabilistic Boolean Control Networks: A Control Lyapunov Function Approach

This article investigates the partial stabilization problem of probabilistic Boolean control networks (PBCNs) under sample-data state-feedback control (SDSFC) with a control Lyapunov function (CLF) approach. First, the probability structure matrix of the considered PBCN is represented by a Boolean matrix, based on which, a new algebraic form of the system is obtained. Second, we convert the partial stabilization problem of PBCNs into the global set stabilization one. Third, we define CLF and its structural matrix under SDSFC. It is found that the existence of a CLF is equivalent to that of SDSFC. Then, a necessary and sufficient condition is obtained for the existence of CLF under SDSFC, based on which, all possible sample-data state-feedback controllers and corresponding structural matrices of CLF are designed by two different methods. Finally, examples are given to illustrate the efficiency of the obtained results.

Double-Integrator Dynamics for Multiagent Systems With Antagonistic Reciprocity

This article is dedicated to the consensus problem for interacting agents of the double-integrator dynamics subject to antagonistic reciprocity, described by negative scalar parameters. To this end, we first show the existence of the weighted gains which play an essential role for solving the consensus problem. Then, we establish the relationship between the weighted gains and scalar parameters to guarantee that the underlying "Laplacian" matrix contains a simple zero eigenvalue and the remaining eigenvalues enjoy positive real parts. Based on the above analysis, we further proceed to solve the considered problem. A major difficulty is that the Laplacian matrices, associated with the position and velocity information, are entirely distinct from each other, leading to the failure of the conventional consensus method for the second-order dynamics. We derive some criteria involving the weighted gains, the scaling parameters, and the real/image parts of the Laplacian matrix of the interaction graph. Moreover, some special frameworks, which have been extensively studied in the literature, are also elaborated on. Compared with the Altafini's model, we do not need to redefine a new Laplacian matrix, and more important, the restriction on the digon sign-symmetry property is removed. It is worth mentioning that the proposed consensus algorithm cannot be deduced by the Altafini's model or its variants. Finally, a wheeled multirobot system is formulated to validate the efficiency of the theoretical results.

The Robustness of Outputs With Respect to Disturbances for Boolean Control Networks

In this brief, we investigate the robustness of outputs with respect to disturbances for Boolean control networks (BCNs) by semi-tensor product (STP) of matrices. First, BCNs are converted into the corresponding algebraic forms by STP, then two sufficient conditions for the robustness are derived. Moreover, the corresponding permutation system and permutation graph are constructed. It is proven that if there exist controllers such that the outputs of permutation systems are robust with respect to disturbances, then there must also exist controllers such that the outputs of the corresponding original systems achieve robustness with respect to disturbances. One effective method is proposed to construct controllers to achieve robustness. Examples are also provided to illustrate the correctness of the obtained results.

Local Synchronization of Interconnected Boolean Networks With Stochastic Disturbances

This paper is concerned with the local synchronization problem for the interconnected Boolean networks (BNs) without and with stochastic disturbances. For the case without stochastic disturbances, first, the limit set and the transient period of the interconnected BNs are discussed by resorting to the properties of the reachable set for the global initial states set. Second, in terms of logical submatrices of a certain Boolean vector, a compact algebraic expression is presented for the limit set of the given initial states set. Based on it, several necessary and sufficient conditions are derived assuring the local synchronization of the interconnected BNs. Subsequently, an efficient algorithm is developed to calculate the largest domain of attraction. As for the interconnected BNs with stochastic disturbances, first, mutually independent two-valued random logical variables are introduced to describe the stochastic disturbances. Then, the corresponding local synchronization criteria are also established, and the algorithm to calculate the largest domain of attraction is designed. Finally, numerical examples are employed to illustrate the effectiveness of the obtained results/ algorithms.

Pinning Controllers for Activation Output Tracking of Boolean Network Under One-Bit Perturbation

This paper studies pinning controllers for activation output tracking (AOT) of Boolean network under one-bit perturbation, based on the semitensor product of matrices. First, the definition of AOT with respect to an activation number is presented, where the activation number means the number of active outputs whose logical variables are 1 s. Then, several criteria are established for AOT issue. Further, the impact of one-bit perturbation on AOT is studied, where one-bit perturbation means that only one logical function has one-bit change of its truth table by flipping the value from 1 to 0 or 0 to 1. In addition, if a one-bit perturbation is a valid perturbation on AOT, an output feedback pinning control is designed to recover AOT. The obtained results are effectively illustrated by a D. melanogaster segmentation polarity gene network and a reduced signal transduction network.

Tractable Learning and Inference for Large-Scale Probabilistic Boolean Networks

Probabilistic Boolean networks (PBNs) have previously been proposed so as to gain insights into complex dynamical systems. However, identification of large networks and their underlying discrete Markov chain which describes their temporal evolution still remains a challenge. In this paper, we introduce an equivalent representation for PBNs, the stochastic conjunctive normal form network (SCNFN), which enables a scalable learning algorithm and helps predict long-run dynamic behavior of large-scale systems. State-of-the-art methods turn out to be 400 times slower for middle-sized networks (i.e., containing 100 nodes) and incapable of terminating for large networks (i.e., containing 1000 nodes) compared to the SCNFN-based learning, when attempting to achieve comparable accuracy. In addition, in contrast to the currently used methods which introduce strict restrictions on the structure of the learned PBNs, the hypothesis space of our training paradigm is the set of all possible PBNs. Moreover, SCNFNs enable efficient sampling so as to statistically infer multistep transition probabilities which can provide information on the activity levels of individual nodes in the long run. Extensive experimental results showcase the scalability of the proposed approach both in terms of sample and runtime complexity. In addition, we provide examples to study large and complex cell signaling networks to show the potential of our model. Finally, we suggest several directions for future research on model variations, theoretical analysis, and potential applications of SCNFNs.

Fast-Time Stability of Temporal Boolean Networks

In real systems, most of the biological functionalities come from the fact that the connections are not active all the time. Based on the fact, temporal Boolean networks (TBNs) are proposed in this paper, and the fast-time stability is analyzed via semi-tensor product (STP) of matrices and incidence matrices. First, the algebraic form of a TBN is obtained based on the STP method, and one necessary and sufficient condition for global fast-time stability is presented. Moreover, incidence matrices are used to obtain several sufficient conditions, which reduce the computational complexity from O(n2ⁿ) (exponential type) to O(n⁴) (polynomial type) compared with the STP method. In addition, the global fast-time stabilization of TBNs is considered, and pinning controllers are designed based on the neighbors of controlled nodes rather than all the nodes. Finally, the local fast-time stability of TBNs is considered based on the incidence matrices as well. Several examples are provided to illustrate the effectiveness of the obtained results.

Sampled-Data Control for the Synchronization of Boolean Control Networks

In this paper, we investigate the sampled-data state feedback control (SDSFC) for the synchronization of Boolean control networks (BCNs) under the configuration of drive-response coupling. Necessary and sufficient conditions for the complete synchronization of BCNs are obtained by the algebraic representations of logical dynamics. Based on the analysis of the sampling periods, we establish an algorithm to guarantee the synchronization of drive-response coupled BCNs by SDSFC. An example is given to illustrate the significance of the obtained results.

Event-Triggered Control for the Disturbance Decoupling Problem of Boolean Control Networks

This paper investigates the disturbance decoupling problem (DDP) of Boolean control networks (BCNs) by event-triggered control. Using the semi-tensor product of matrices, algebraic forms of BCNs can be achieved, based on which, event-triggered controllers are designed to solve the DDP of BCNs. In addition, the DDP of Boolean partial control networks is also derived by event-triggered control. Finally, two illustrative examples demonstrate the effectiveness of proposed methods.

Single-Input Pinning Controller Design for Reachability of Boolean Networks

This brief is concerned with the problem of a single-input pinning control design for reachability of Boolean networks (BNs). Specifically, the transition matrix of a BN is designed to steer the BN from an initial state to a desirable one. In addition, some nodes are selected as the pinning nodes by solving some logical matrix equations. Furthermore, a single-input pinning control algorithm is given. Eventually, a genetic regulatory network is provided to demonstrate the effectiveness and feasibility of the developed method.

Variable structure controller design for Boolean networks

The paper investigates the variable structure control for stabilization of Boolean networks (BNs). The design of variable structure control consists of two steps: determine a switching condition and determine a control law. We first provide a method to choose states from the reaching mode. Using this method, we can guarantee that the number of nodes which should be controlled is minimized. According to the selected states, we determine the switching condition to guarantee that the time of global stabilization in the BN is the shortest. A control law is then determined to ensure that all selected states can enter into the sliding mode, such that any initial state can arrive in the steady-state mode. Some examples are provided to illustrate the theoretical results.

Observability of Boolean multiplex control networks

Boolean multiplex (multilevel) networks (BMNs) are currently receiving considerable attention as theoretical arguments for modeling of biological systems and system level analysis. Studying control-related problems in BMNs may not only provide new views into the intrinsic control in complex biological systems, but also enable us to develop a method for manipulating biological systems using exogenous inputs. In this article, the observability of the Boolean multiplex control networks (BMCNs) are studied. First, the dynamical model and structure of BMCNs with control inputs and outputs are constructed. By using of Semi-Tensor Product (STP) approach, the logical dynamics of BMCNs is converted into an equivalent algebraic representation. Then, the observability of the BMCNs with two different kinds of control inputs is investigated by giving necessary and sufficient conditions. Finally, examples are given to illustrate the efficiency of the obtained theoretical results.