Boolean Control Networks Research Articles

Set Restabilization of Perturbed Boolean Control Networks

This paper develops a parameter tuning method for solving the set restabilization problem of perturbed Boolean control networks (BCNs). First, the absorbable attractor, which we previously proposed, is recalled. Based on the relationship between attractors, a necessary and sufficient restabilizability criterion is derived. This criterion is used to check whether a perturbed BCN can be stabilized to the original target set by modifying the least number of parameters to the old controller. Furthermore, a constructive method for fine-tuning the old controller is provided if the criterion condition derived above is satisfied. Compared with the existing relevant results, ours have clear advantages, since they can address the set restabilization problem of BCNs subject to multi-column function perturbations, which has not been solved yet. Finally, two examples are employed to show the effectiveness and advantages of our results.

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.

Kullback-Leibler Control in Boolean Control Networks.

This article addresses the Kullback-Leibler (KL) control problem in Boolean control networks. In the considered problem, an extended stage cost function depending on the control inputs is introduced; in contrast to a stage cost of the conventional KL control problems in the Markov decision process cannot take into consideration the control inputs. An associated Bellman equation and a matrix-based iteration algorithm are presented. The theoretical analysis shows that the proposed KL control results in an approximated form of conventional dynamic programming (DP). Furthermore, the convergence analysis is presented, with the weight parameter converging to zero and diverging to infinity. In practical application examples, a comparison of the conventional DP and proposed KL control is illustrated.

Fault Detection of Boolean Control Networks via Reduced Systems

Fault Detection of Boolean Control Networks via Reduced Systems

Controllability of delayed generalized asynchronous Boolean control networks under disturbances

For delayed generalized asynchronous Boolean networks with random disturbances, it is still uncertain about their robust controllability. This paper uses the semi-tensor product to transform these Boolean networks into linear representations to derive the dependence matrix of the network transition on the control mode. After that, three different control modes are utilized to define controllability. Each control mode provides both reachable trajectories set under a specific initial trajectory and an initial trajectory set under a specific target trajectory. It is also calculated for the likelihood of a transition between two states. Lastly, two concrete examples validate the theoretical findings under various control modes.

Restabilization of perturbed Boolean control networks based on absorbable attractors

Restabilization of perturbed Boolean control networks based on absorbable attractors

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

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

A matrix approach to the analysis and computation of robust cycles for Boolean control networks with disturbances

A matrix approach to the analysis and computation of robust cycles for Boolean control networks with disturbances

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

Lossless State Compression of Boolean Control Networks

Lossless State Compression of Boolean Control Networks

Optimal control of Boolean control networks with state-triggered impulses

In the real world, abrupt changes caused by external environment and system interaction can exhibit a pattern resembling an “impulse” response. A novel model, known as the hybrid-index model, has recently been introduced for Boolean control networks (BCNs) to characterize such impulsive responses. The optimal control problem is a fundamental issue in control theory, and many control problems can be classified as special cases of optimal control problems. Nevertheless, the optimal control problem for the hybrid-index model remains unresolved. This study delves into the optimal control problem of impulsive Boolean control networks (IBCNs) under the hybrid-index model framework. Forward completeness serves as a crucial condition to avert Zeno behavior in the hybrid-index model of IBCNs. In contrast to prior studies on the hybrid-index model of IBCNs, the study shows that the optimal control problem of IBCNs can be addressed even in cases where the system is not forward complete. Leveraging the theory of semi-tensor product, both finite-horizon and infinite-horizon optimal control problems of IBCNs are tackled using the quotient mapping method and the recursive method for optimal control of Boolean control networks. The study yields the optimal cost and optimal control law through state feedback. To illustrate the efficacy of the proposed approach, a mathematical example and a biological example known as the λ switch are presented.

Finite-time observability of probabilistic Boolean multiplex control networks

Finite-time observability of probabilistic Boolean multiplex control networks

State Estimation via Designing Controller and State Estimation-Based Stabilization for Boolean Control Networks.

This article investigates the issues of state estimation and state estimation-based stabilization for Boolean control networks (BCNs). Unlike previous state observers, this article proposes an optimal state estimator by designing a particular input sequence for the first time, where the maximum-minimum method is employed such that the state of BCNs can be uniquely estimated in short time steps. A minimum reconstructible state set (MRSS) is constructed to determine this input sequence. Next, based on the estimated state, a finite-time stabilization scheme is proposed by constructing a switching controller consisting of three stages. A controller is first developed to estimate the state of BCNs in finite-time steps, and a state reachable controller is also provided to make the state of BCNs reachable to a given equilibrium point. Subsequently, a constant controller is further developed to stabilize the state of BCNs to the equilibrium point. Finally, an oxidative stress response model is used to illustrate the effectiveness of the proposed results.

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.

Parameter Learning of Probabilistic Boolean Control Networks with Input-Output Data

Article Parameter Learning of Probabilistic Boolean Control Networks with Input-Output Data Hongwei Chen 1,*, Qi Chen 1, Bo Shen 1, and Yang Liu 2 1 College of Information Science and Technology, Donghua University, Shanghai 201620, China 2 School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China * Correspondence: hongwei@dhu.edu.cn Received: 23 September 2023 Accepted: 27 November 2023 Published: 26 March 2024 Abstract: This paper investigates the parameter learning problem for the probabilistic Boolean control networks (PBCNs) with input-output data. Firstly, an algebraic expression of the PBCNs is obtained by taking advantage of the semi-tensor product technique, and then, the parameter learning problem is transformed into an optimal problem to reveal the parameter matrices of a linear system in a computationally efficient way. Secondly, two recursive semi-tensor product based algorithms are designed to calculate the forward and backward probabilities. Thirdly, the expectation maximization algorithm is proposed as an elaborate technique to address the parameter learning problem. In addition, a useful index is introduced to describe the performance of the proposed parameter learning algorithm. Finally, two numerical examples are employed to demonstrate the reliability of the proposed parameter learning approach.

Set stabilization of logical control networks: A minimum node control approach

In network systems, control using minimum nodes or pinning control can be effectively used for stabilization problems to cut down the cost of control. In this paper, we investigate the set stabilization problem of logical control networks. In particular, we study the set stabilization problem of probabilistic Boolean networks (PBNs) and probabilistic Boolean control networks (PBCNs) via controlling minimal nodes. Firstly, an algorithm is given to search for the minimum index set of pinning nodes. Then, based on the analysis of its high computational complexity, we present optimized algorithms with lower computational complexity to ascertain the network control using minimum node sets. Moreover, some sufficient and necessary conditions are proposed to ensure the feasibility and effectiveness of the proposed algorithms. Furthermore, a theorem is presented for PBCNs to devise all state-feedback controllers corresponding to the set of pinning nodes. Finally, two models of gene regulatory networks are considered to show the efficacy of obtained results.

Optimal control for reachability of Markov jump switching Boolean control networks subject to output trackability

This article aims at designing the finite horizon optimal control sequence (FHOCS) for ensuring the reachability of Markov jump switching Boolean control networks (MJSBCNs) subject to output trackability. The key step in solving such a problem is to construct a Luenberger-like observer (LLO). Our approach includes a few steps as follows. We firstly propose the formulation of the optimal control problem (OCP) of maximising the probability of finite-time reachability subject to output trackability. Then, by converting the dynamics of MJSBCNs into an equivalent expectation system, an LLO is established for MJSBCNs. In this setup, a Luenberger-like observation matrix is constructed, which is an effect tool to solve the finite-time reachability problem. Finally, an LLO method is developed to find the FHOCS by maximising the T -step Luenberger-like observation matrix. In a biological example, we show the effectiveness of our developed methods.

On Connections Between Invariant Subspace and Quotient Approaches for Analysis and Control of Boolean Networks

On Connections Between Invariant Subspace and Quotient Approaches for Analysis and Control of Boolean Networks

Set Controllability of Boolean Control Networks Under Stochastic Function Perturbation

Set Controllability of Boolean Control Networks Under Stochastic Function Perturbation

Design of all feasible output feedback controllers for robust output tracking of Boolean control networks

This paper devotes to the design of all feasible output feedback controllers for the robust output tracking of Boolean control networks with disturbances (DBCNs). First, the output feedback–based robust control invariant set (RCIS) is defined, and a calculation method to find all output feedback–based RCISs of a given set is derived via the truth matrix technique. Second, a class of complete family of robust reachable sets (CFRRSs) is developed; the solvability of robust output tracking problem by output feedback control is verified. Furthermore, a constructive algorithm of all feasible output feedback controllers is presented. Finally, the study of a network about Escherichia coli lactose operon shows the effectiveness of the theoretical results.