Boolean Control Networks Research Articles

Aggregation method to reachability and optimal control of large-size Boolean control networks

Aggregation method to reachability and optimal control of large-size Boolean control networks

Reconstructibility analysis and set‐observer design for Boolean control networks

AbstractThis paper deals with the issues of reconstructibility analysis and set‐observer design for Boolean control networks (BCNs). A state estimation set is considered to find the state estimation of BCNs, and a reconstructibility judgment matrix (RJM) is obtained by compact vector of state estimation set. Then, a kind of state‐reconstructible tree is constructed, and algorithms are also provided to construct it. The state‐reconstructible tree can categorize BCNs to be globally reconstructible, locally reconstructible, and unreconstructible. The sufficient and necessary conditions for the reconstructibility of BCNs are given. Meanwhile, the relationship between input–output trajectory and estimated state is derived. Next, with the knowledge of input–output sequence, a set‐observer is designed such that the state of BCNs for any global reconstructible BCNs is uniquely determined in a finite time. Some examples are also given to illustrate the effectiveness of the proposed methods.

Sampled-data Control of Probabilistic Boolean Control Networks: A Deep Reinforcement Learning Approach

The rise of reinforcement learning (RL) has guided a new paradigm: unraveling the intervention strategies to control systems with unknown dynamics. Model-free RL provides an exhaustive framework to devise therapeutic methods to alter the regulatory dynamics of gene regulatory networks (GRNs). This paper presents an RL-based technique to control GRNs modeled as probabilistic Boolean control networks (PBCNs). In particular, a double deep-Q network (DDQN) approach is proposed to address the sampled-data control (SDC) problem of PBCNs, and optimal state feedback controllers are obtained, rendering the PBCNs stabilized at a given equilibrium point. Our approach is based on options, i.e., the temporal abstractions of control actions in the Markov decision processes (MDPs) framework. First, we define options and hierarchical options and give their properties. Then, we introduce multi-time models to compute the optimal policies leveraging the options framework. Furthermore, we present a DDQN algorithm: i) to concurrently design the feedback controller and the sampling period; ii) wherein the controller intelligently decides the sampled period to update the control actions under the SDC scheme. The presented method is model-free and offers scalability, thereby providing an efficient way to control large-scale PBCNs. Finally, we compare our control policy with state-of-the-art control techniques and validate the presented results.

Robust Output Tracking of Boolean Control Networks over Finite Time

With an increase in tracking time, the operating cost of the controller will increase accordingly. Considering the biological applications of Boolean control networks (BCNs), it is necessary to study the control problem of BCNs over finite time. In this paper, we study the output tracking problem of a BCN with disturbance inputs in a given finite time. First, the logical form of BCNs is transformed into an algebraic form using the semi-tensor product (STP) method. Then, the robust output tracking problems of a reference output trajectory and the outputs of a reference system over finite time are transformed into the robust reachability problem of the BCNs. Based on the truth matrix technique, two necessary and sufficient conditions are provided for the trackability of the reference outputs over finite time. Moreover, two algorithms are proposed to design the controllers in the case of the traceable outputs. It should be pointed out that the truth matrix method we used here has some unique features, including its simple computation and concise expression. Finally, two illustrative examples are presented to demonstrate the results in this paper.

Observability Criteria for Boolean Networks

This article investigates observability of Boolean control networks (BCNs) and probabilistic Boolean networks (PBNs). First, weak observability of BCNs is discussed via the nonaugmented approach. The obtained result is then applied to determine (asymptotic) observability of PBNs. Finally, complexity of algorithms based on new criteria is analyzed. Compared with existing ones, time and space complexity do not get worse, even are improved under some mild conditions.

Robust Stabilization of Impulsive Boolean Control Networks with Function Perturbation

This paper studies the robust stabilization of impulsive Boolean control networks (IBCNs) with function perturbation. A Boolean control network (BCN) with a state-dependent impulsive sequence is converted to an equivalent BCN by the semi-tensor product method. Based on the equivalence of stabilization between the IBCN and the corresponding BCN, several criteria are proposed for the robust stabilization of IBCNs. Furthermore, when the IBCN is not robustly stabilizable after the function perturbation, an algorithm is presented to modify the control or the impulse-triggered set. Finally, an example is given to verify the obtained results.

Reduced-order observer design for fault diagnosis of Boolean control networks

In this paper, we propose an approach to design reduced-order observer of Boolean control networks (BCNs) for fault diagnosis by applying the semi-tensor product (STP) of matrices. At first, for observability analysis a computationally efficient approach based on the relational coarsest partition problem (RCP) is proposed. Then a necessary and sufficient condition for fault detectability analysis is introduced. After that an approach is introduced to design a reduced-order observer for fault detection. If fault occurrence has been detected, then an approach is proposed to solve fault isolation problem of BCNs. The basic idea is to separate dynamics of the faults into different independent subsystems by using graph theory. For each subsystem a residual generator is constructed based on reduced-order observer by getting rid of indistinguishable states. By theoretical analysis and simulation study it is shown that the approach proposed in the paper for fault isolation requires lower computational effort than the conventional scheme of a bank of full-order observers.

Stabilization of Markovian Jump Boolean Control Networks via Sampled-Data Control.

In this article, we study the finite-time stabilization and the asymptotic stabilization with probability one of Markovian jump Boolean control networks (MJBCNs) by sampled-data state feedback controls (SDSFCs). Based on the semi-tensor product (STP), we introduce an augmented variable multiplied by the vector form of the switching signal and the state of MJBCN. We find that under SDSFC, the sequence of the states of the augmented variable at sampling instants satisfies the Markov property. Based on the convergences of the switching signal and the augmented variable, we obtain the sufficient and necessary criteria for the finite-time stabilization and the asymptotic stabilization of MJBCNs by SDSFCs, respectively. Moreover, for the two kinds of stabilization, the feedback matrices of SDSFCs are constructed, respectively. Finally, the obtained results are applied to an apoptosis network and a model of the lactose operon in the Escherichia Coli.

Output Feedback Observability of Switched Boolean Control Networks

This paper investigates the output feedback observability of switched Boolean control networks. According to time-varying output feedback (TVOF) and time-invariant output feedback (TIOF) controls, six types of observability are proposed and their relation is discussed. A technique called parallel extension and a new system named induced logical dynamic system are developed. Based on them, some necessary and sufficient conditions are obtained for these TVOF and TIOF observabilities. In addition, the relation between output feedback observability and the existing results about observability is analyzed. Furthermore, some examples are given to illustrate the validity of the main results.

New Method for Disturbance Decoupling of Boolean Networks

The coordinate transformation technique is a traditional method for solving the disturbance decoupling problem (DDP) of Boolean control networks (BCNs). But under this technique, the obtained conditions are not necessary for the solvability of DDP of original systems. Thus, this article investigates the DDP of Boolean networks (BNs) and BCNs in a new perspective. Based on the new definition of disturbance decoupling, the one-step evolutionary dynamic of states of BNs, shown as a table, is presented for solving the DDP. Besides, a matrix discriminant is introduced to use MATLAB to test whether a BN is disturbance decoupled. For discussing the solvability of DDP of BCNs, a truth matrix is constructed to provide a necessary and sufficient condition and find all possible state feedback controllers. It is worth noting that the computation complexity of the main results is lower than that of the existing results. Furthermore, two examples are given to show the validity and advantages of the main results.

Event‐triggered control for sampled‐data set stabilization of switched delayed boolean control networks

This paper considers the event‐triggered control design for the uniform sampled‐data set stabilization of switched delayed Boolean control networks (SDBCNs). First, using the algebraic state space representation method, SDBCNs are converted into the equivalent algebraic form. Second, using the algebraic form, the uniform sampled‐data reachable sets are constructed, based on which, a necessary and sufficient condition is obtained for the uniform sampled‐data set stabilization of SDBCNs. Finally, the event‐triggered mechanism is presented, and a sufficient condition is proposed to design the time‐variant state feedback event‐triggered controller for the uniform sampled‐data set stabilization of SDBCNs.

Model Evaluation of the Stochastic Boolean Control Networks

This article investigates the model evaluation problem for the stochastic Boolean control networks (SBCNs). First, an algebraic expression of the SBCN is obtained based on the semitensor product method, and a straightforward approach is then proposed to compute the probability that the given observed output sequence is produced by the considered model. Second, two recursive algorithms, namely the forward and the backward algorithms, are designed for model evaluation by resorting to the forward-backward technique. In addition, scaling factors are introduced to deal with the numerical issues arising in the implementation of the developed algorithms. Finally, to illustrate the applicability and effectiveness of the proposed algorithms, a Boolean model of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">lac</i> operon is employed as an example for numerical simulation.

Passive-active fault detection of Boolean control networks

This paper investigates the fault detectability of Boolean control networks. To deal with different circumstances, passive fault detectability and four types of active fault detectability are proposed for the first time. For passive fault detectability, in line with observed input-output data, several discriminant conditions are put forward. For active fault detectability, by resorting to an auxiliary system, the essence of active fault detectabilty is revealed via reachability. Subsequently, corresponding to different types of active fault detectability, algebraic criteria that facilitate verification are provided. At the same time, the relationships of four types of active fault detectability are discussed as well. In addition, an approach for calculating fault detection time is given by combining passive fault detectability with active fault detectability. Finally, the effectiveness of the results obtained is elaborated by several examples.

Controllability and set controllability of periodically switched Boolean control networks

This paper investigates the controllability and set controllability of periodically switched Boolean control networks (PSBCNs) via the semi-tensor product. Firstly, the algebraic form of switching signal is given and a parallel system is formed by combining the switching signal and the state. Then the controllability problem of PSBCNs is transformed into the set controllability problem of the new system, further, the criterion for controllability is obtained. Secondly, the set controllability matrix of PSBCNs is constructed, and the necessary and sufficient condition of set controllability for PSBCNs is presented. In addition, a more general PSBCN is considered and the criteria for its controllability and set controllability are proposed. Finally, a practical example is given to illustrate the obtained results, which shows that our new results are correct and effective.

Self-triggered control of probabilistic Boolean control networks: A reinforcement learning approach

In this work, strategies to devise an optimal feedback control of probabilistic Boolean control networks (PBCNs) are discussed. Reinforcement learning (RL) based control is explored in order to minimize model design efforts and regulate PBCNs with high complexities. A Q-learning random forest (QLRF) algorithm is proposed; by making use of the algorithm, state feedback controllers are designed to stabilize the PBCNs at a given equilibrium point. Further, by adopting QLRF stabilized closed-loop PBCNs, a Lyapunov function is defined, and a method to construct the same is presented. By utilizing such Lyapunov functions, a novel self-triggered control (STC) strategy is proposed, whereby the controller is recomputed according to a triggering schedule, resulting in an optimal control strategy while retaining the closed-loop PBCN stability. Finally, the results are verified using computer simulations.

On Identification of Boolean Control Networks

On Identification of Boolean Control Networks

Minimal observability of Boolean control networks

In this paper, the minimum observability of Boolean control networks (BCNs) is investigated. An augmented system is proposed to analyze the dynamical trajectories of state pairs, followed by an effective criterion for observability of BCNs utilizing graphic tools. A minimal observability problem is formulated based on the fact that observability of the underlying network is facilitated by injecting new measurements. By introducing an indicator matrix, the solution of added measurements in vector form can be converted into dealing with the equations, by which, all the feasible measurements can be derived. Furthermore, the solution of the least added measurements can be solved by a minimum set covering problem. Meanwhile, two examples are given to illustrate the theoretical results.

Controllability of Markovian jump Boolean control networks: A graphical approach

This paper investigates the controllability of Markovian jump Boolean control networks (MJBCNs) by using graphical approach. To solve this problem, a deterministic directed graph is constructed to describe the stochastic evolutionary process of the considered MJBCN under the framework of semi-tensor product of matrices. Then, combining with breadth-first search, the special subgraph with breadth-first tree as the principal part is obtained. Based on this, the necessary and sufficient conditions to verify the controllability of MJBCNs are deduced, and the problem of determining the minimal controllable time is solved completely. Subsequently, two examples are given to illustrate the validity and correctness of the method.

Control in Boolean Networks With Model Checking

Understanding control mechanisms in biological systems plays a crucial role in important applications, for instance in cell reprogramming. Boolean modeling allows the identification of possible efficient strategies, helping to reduce the usually high and time-consuming experimental efforts. Available approaches to control strategy identification usually focus either on attractor or phenotype control, and are unable to deal with more complex control problems, for instance phenotype avoidance. They also fail to capture, in many situations, all possible minimal strategies, finding instead only sub-optimal solutions. In order to fill these gaps, we present a novel approach to control strategy identification in Boolean networks based on model checking. The method is guaranteed to identify all minimal control strategies, and provides maximal flexibility in the definition of the control target. We investigate the applicability of the approach by considering a range of control problems for different biological systems, comparing the results, where possible, to those obtained by alternative control methods.

Finite-time sampled-data set stabilisation of delayed probabilistic Boolean control networks

In this paper, the finite-time constrained set stabilisation of delayed probabilistic Boolean control networks (DPBCNs) is considered via sampled-data control (SDC). The main mathematical tool is semi-tensor product of matrices, which is used to convert the dynamics of DPBCNs into an equivalent algebraic state space representation (ASSR). Based on the ASSR of DPBCNs, the constrained sampled-data transition probability matrix is constructed. Then, new criteria are proposed for the finite-time constrained reachability of DPBCNs under uniform SDC. By virtue of finite-time constrained reachability, a procedure is established to design state feedback sampled-data stabilisers for DPBCNs. The obtained results are applied to the ‘minimal’ model of lactose operon in E. coli.