Stabilization Of Boolean Control Networks Research Articles

Time-optimal open-loop set stabilization of Boolean control networks

We show that for stabilization of Boolean control networks (BCNs) with unobservable initial states, open-loop control and close-loop control are not equivalent. An example is given to illustrate the nonequivalence. Enlightened by the nonequivalence, we explore open-loop set stabilization of BCNs with unobservable initial states. More specifically, this issue is to investigate that for a given BCN, whether there exists a unified free control sequence that is effective for all initial states of the system to stabilize the system states to a given set. The criteria for open-loop set stabilization is derived and for any open-loop set stabilizable BCN, every time-optimal open-loop set stabilizer is proposed. Besides, we obtain the least upper bounds of two integers, which are respectively related to the global stabilization and partial stabilization of BCNs in the results of two literature articles. Using the methods in the two literature articles, the least upper bounds of the two integers cannot be obtained.

Self-Triggered Set Stabilization of Boolean Control Networks and Its Applications

Self-Triggered Set Stabilization of Boolean Control Networks and Its Applications

Set Stabilization of Boolean Control Networks With Missing Data and the Application in Finite-Field Networks

Set Stabilization of Boolean Control Networks With Missing Data and the Application in Finite-Field Networks

State-Feedback Set Stabilization of Boolean Networks With State-Dependent Random Impulses.

In this article, we are devoted to addressing the state-feedback set stabilization of Boolean control networks with state-dependent random impulses by utilizing a hybrid index model. By comparison with the previous impulsive Boolean networks, this model can be used to describe the instantaneousness of various impulsive behaviors more clearly. In order to avoid the occurrence of Zeno phenomenon, we first introduce the basic concept of forward completeness and further establish the judging criterion. After that, an algorithm is presented to derive the largest control invariant subset of a given subset. Based on this, we derive a necessary and sufficient criterion for finite-time feedback set stabilizability. Similarly, the result is also obtained for the asymptotic case, and the asymptotic set stabilizers are designed by dividing the whole state space into several layers. Moreover, we also investigate the relationships between different stabilizabilities. Last, two illustrative examples are presented to demonstrate the efficiency of the theoretical results.

Feedback Stabilization of Boolean Control Networks With Missing Data.

Data loss is often random and unavoidable in realistic networks due to transmission failure or node faults. When it comes to Boolean control networks (BCNs), the model actually becomes a delayed system with unbounded time delays. It is difficult to find a suitable way to model it and transform it into a familiar form, so there have been no available results so far. In this article, the stabilization of BCNs is studied with Bernoulli-distributed missing data. First, an augmented probabilistic BCN (PBCN) is constructed to estimate the appearance of data loss items in the model form. Based on this model, some necessary and sufficient conditions are proposed based on the construction of reachable matrices and one-step state transition probability matrices. Moreover, algorithms are proposed to complete the state feedback stabilizability analysis. In addition, a constructive method is developed to design all feasible state feedback controllers. Finally, illustrative examples are given to show the effectiveness of the proposed results.

Reachability, Controllability, and Stabilization of Boolean Control Networks With Stochastic Function Perturbations

Robust controllability and stabilization are two fundamental issues in modern control theory. This article investigates the robust controllability and stabilization of Boolean control networks (BCNs) subject to stochastic function perturbations (SFPs). First, by defining the concept of the weighted path and constructing the perturbed position index matrix, the robustness analysis of reachability is divided into two cases. According to these two cases, several criteria are proposed for the robust reachability of BCNs with SFPs. Second, based on the robust reachability, the robust controllability and state-feedback stabilization of BCNs with SFPs are further studied. Finally, the validity of the obtained results is supported by examples.

Lebesgue sampling approach to robust stabilization of boolean control networks with external disturbances

This paper introduces the Lebesgue sampling approach to the robust stabilization of Boolean control networks (BCNs) with external disturbances. Given a Lebesgue sampling region and a feedback control, a time aggregated system is obtained via the semi-tensor product method. Then, a new criterion is presented for the robust stabilization of time aggregated system. Furthermore, given a signal of Lebesgue sampling, a sequence of the Lebesgue type robust reachable sets is constructed. Based on these reachable sets, several algorithms are presented to design both Lebesgue sampling region and sampled-data state feedback control for the robust stabilization of BCNs.

Survey of semi-tensor product method in robustness analysis on finite systems.

Recently, the theory of semi-tensor product (STP) method of matrices has received much attention from variety communities covering engineering, economics and industries, etc. This paper describes a detailed survey on some recent applications of the STP method in finite systems. First, some useful mathematical tools on the STP method are provided. Second, many recent developments about robustness analysis on the given finite systems are delineated, such as robust stable analysis of switched logical networks with time-delayed, robust set stabilization of Boolean control networks, event-triggered controller design for robust set stabilization of logical networks, stability analysis in distribution of probabilistic Boolean networks, and how to solve a disturbance decoupling problem by event triggered control for logical control networks. Finally, several research problems in future works are predicted.

Stabilization of Boolean control networks with state-triggered impulses

Stabilization of Boolean control networks with state-triggered impulses

Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set

The traditional set stability of Boolean networks (BNs) refers to whether all the states can converge to a given state subset. Different from the existing results, the set stability investigated in this paper is whether all states in a given initial set can converge to a given destination set. This paper studies the set stability and set stabilization avoiding undesirable sets of BNs and Boolean control networks (BCNs), respectively. First, by virtue of the semi-tensor product (STP) of matrices, the dynamics of BNs avoiding a given undesirable set are established. Then, the set reachability and set stability of BNs from the initial set to destination set avoiding an undesirable set are investigated, respectively. Furthermore, the set stabilization of BCNs from the initial set to destination set avoiding a given undesirable set are investigated. Finally, a design method for finding the time optimal set stabilizer is proposed, and an example is provided to illustrate the effectiveness of the results.

Asynchronous Stabilization of Boolean Control Networks With Stochastic Switched Signals

This paper includes some results of switched Boolean control networks. The switched signals considered in this paper is time variant and it follows a certain probabilistic distribution vector. Given a concept of stabilization with stochastic switched signals, we obtained a necessary and sufficient condition for stabilization. Then a state feedback control depending on switched signals is designed to stabilize the system considered. Later we investigate a case when the switched signal θ(t) is unknown at time t, and what we have is the prediction switched signal ∧θ(t). For a given prediction matrix, a necessary and sufficient condition is given to preserve the stabilization. Except state feedback control, asynchronous pinning control for switched Boolean networks (BNs) is also considered. A necessary and sufficient condition is extended for the stability of BNs with stochastic switched signals. Moreover, algorithms are presented to find the minimal number of pinned nodes based on controlling minimal number of subsystems. Examples are shown to illustrate the effectiveness of the obtained results.

Pinning Stabilization of Boolean Control Networks via a Minimum Number of Controllers.

The stabilization problem of Boolean control networks (BCNs) under pinning control is investigated in this article, and the set of pinned nodes is minimized. A BCN is a Boolean network with Boolean control inputs in it. When the given BCNs cannot realize stabilization under existing Boolean control inputs, pinning control strategy is introduced to make the BCNs achieve stabilization. The Warshall algorithm is introduced to verify the stabilizability of BCNs, then novel computational feasible algorithms are developed to design the minimum number pinning controller for the system. By using our method, the minimum set of pinned nodes can be found with relatively low computational complexity. Finally, the theoretical result is validated using a biological example.

Set Invariance and Optimal Set Stabilization of Boolean Control Networks: A Graphical Approach

This article investigates set invariance and optimal set stabilization of Boolean control networks (BCNs) from a novel graph-theoretical perspective. First, we establish the relationship between the control invariant sets and the strongly connected components of the state transition graph (STG), and propose a new algorithm to compute the largest control invariant subset. Second, both set stabilizability and time-optimal set stabilization via state feedback are characterized by a breadth-first tree of the STG. Though the prior two problems have been attempted by existing algebraic methods, the primary advantage of our alternative graphical approach is the enhanced computational efficiency. Third, we consider for the first time, the optimal set stabilization problem with general cost criteria, not limited to time optimality. A state feedback controller is constructed for general optimal set stabilization using a shortest-path tree of the STG. Finally, it is straightforward to extend the proposed approach to handle various constraints as well as other types of logical networks by slightly modifying the STG. Two biological networks are used to test the performance of our approach. Results show that in accordance with time complexity analysis, our algorithms can dramatically reduce the running time for the first two problems compared with existing work, and effectively solve the general optimal set stabilization problem.

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

SummaryIn 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.

Sampled-Data State Feedback Control for the Set Stabilization of Boolean Control Networks

This paper studies the set stabilization of Boolean control networks (BCNs) under sampled-data state feedback control (SDSFC). The main research content is divided into two parts. First, the topological structure of BCNs under given SDSFC is investigated. The fixed point and sampled cycle are defined, respectively. It is found that sampled cycles allow elements to be repeated and not every element can be regarded as an initial state, and this is quite different from conventional cycles of BCNs. A theorem is presented to calculate the number of fixed points and an algorithm is given to find all fixed points and sampled cycles. Second, the set stabilization problem of BCNs by SDSFC is investigated based on the sampled point set and the sampled point control invariant set (SPCIS). A necessary and sufficient condition is derived for the global set stabilization of BCNs by SDSFC, and further sampled-data state feedback controllers are also designed. The interesting thing is that if a state enters the SPCIS as an unsampled point, then it may run out of the given set again, which is in sharp contrast to conventional BCNs. Finally, an example is given to illustrate the efficiency of the obtained results.

Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable

We aim to further study the global stability of Boolean control networks (BCNs) under aperiodic sampled-data control (ASDC). According to our previous work, it is known that a BCN under ASDC can be transformed into a switched Boolean network (SBN), and further global stability of the BCN under ASDC can be obtained by studying the global stability of the transformed SBN. Unfortunately, since the major idea of our previous work is to use stable subsystems to offset the state divergence caused by unstable subsystems, the SBN considered has at least one stable subsystem. The central thought in this paper is that switching behavior also has good stabilization; i.e., the SBN can also be stable with appropriate switching laws designed, even if all subsystems are unstable. This is completely different from that in our previous work. Specifically, for this case, the dwell time (DT) should be limited within a pair of upper and lower bounds. By means of the discretized Lyapunov function and DT, a sufficient condition for global stability is obtained. Finally, the above results are demonstrated by a biological example.

Set Stabilization of Boolean Control Networks With Impulsive Effects: An Event-Triggered Approach

This brief investigates the set stabilization of Boolean control networks (BCNs) with impulsive effects via event-triggered control (ETC) scheme. An algorithm is designed to find the largest control invariant set, then its efficiency is authenticated. An interesting phenomenon is that some states may leave from the control invariant set at impulsive time steps. Afterward, a necessary and sufficient criterion is derived to determine the set stabilization of event-triggered controlled BCNs with impulsive effects. Finally, a biological example is given to illustrate the obtained results.

Stabilization of Boolean control networks with stochastic impulses

This paper studies the stabilization problem of Boolean control networks with stochastic impulses, where stochastic impulses model is described as a series of possible regulatory models with corresponding probabilities. The stochastic impulses model makes the research more realistic. The global stabilization problem is trying to drive all states to reach the predefined target with probability 1. A necessary and sufficient condition is presented to judge whether a given system is globally stabilizable. Meanwhile, an algorithm is proposed to stabilize the given system by designing a state feedback controller and different impulses strategies. As an extension, these results are applied to analyze the global stabilization to a fixed state of probability Boolean control networks with stochastic impulses. Finally, two examples are given to demonstrate the effectiveness of the obtained results.

Set stabilization of boolean networks via sampled‐data control

AbstractThe paper investigates the sampled‐data state feedback control (SDSFC) for set stabilization of Boolean control networks (BCNs). Set stabilization means that a system converges to a subset of the state space under certain controllers. Assume that the given subset is , where and sampling period is τ. We consider two conditions q ≤ τ;q > τ and for any given subset , calculate the corresponding largest control invariant subset (LCIS). Moreover, a design procedure to calculate all possible SDSFCs for set stabilization of BCNs is obtained. Ultimately, we provide an example to demonstrate the efficiency of the results.

Function Perturbation Impact on Feedback Stabilization of Boolean Control Networks.

Function perturbation analysis of Boolean networks is an important topic in the study of gene regulation due to gene mutation or immeasurable variables. This brief studies the function perturbation impact on feedback stabilization of Boolean control networks (BCNs) by using the algebraic state space representation approach. First, the state feedback stabilization control design of BCNs is recalled and the function perturbation problem is formulated. Second, given a state feedback stabilizer, it is robust to the considered function perturbation if one of the following three cases happens: 1) the block where the function perturbation occurs is different from the block which is affected by the state feedback stabilizer (Case 1); 2) when Case 1 does not happen, the perturbed column converges to the equilibrium faster than the original column (Case 2); 3) when Cases 1 and 2 do not happen, the perturbed column does not belong to the reachable set of the original column (Case 3). Third, when the perturbed column belongs to the reachable set of the original column, a constructive procedure is proposed to modify the given state feedback stabilizer to be robust to the function perturbation. Finally, the obtained new results are applied to the function perturbation analysis of lactose operon in Escherichia coli. The main novelty of this brief is to develop a new theoretical framework for the robustness of feedback controllers of BCNs with respect to function perturbation, which is not solved in the existing literature.