Probabilistic Boolean Control Networks Research Articles

Robust Event-Triggered Control Invariance of Probabilistic Boolean Control Networks.

In this brief, the robust control invariance problem of probabilistic Boolean control networks (PBCNs) is investigated by a class of event-triggered control (ETC), which is an intermittent control scheme in essential. By resorting to the semi-tensor product (STP) technique, a PBCN with ETC can be equivalently described in a form of an algebraic linear system. Based on which, a matrix testing condition is derived to judge whether the given set can be a robust ETC invariant set (RETCIS). Subsequently, a necessary and sufficient condition is developed for the existence of event-triggered controllers. Meanwhile, all feasible event-triggered controllers are designed for guaranteeing the given set to be an RETCIS. Finally, a biological example is employed to demonstrate the availability of theoretical results.

State feedback design for set stabilization of probabilistic Boolean control networks

Set stabilization of probabilistic Boolean control networks (PBCNs) is investigated in this paper and some interesting results are derived. The main results consist of three parts. (1) A definition of set stabilizability with probability one by closed-loop control is proposed for PBCNs, which is not a natural extension from deterministic Boolean control networks to PBCNs due to the random feature of PBCNs. (2) A necessary and sufficient set stabilizability condition is provided for PBCNs. (3) An algorithm for designing a state feedback controller is developed. It is guaranteed that all designed controllers can stabilize a PBCN to a given subset with probability one. The design method is constructive, so it is convenient to use this method in practical application. The results derived above are fundamental and important, since based on them many problems about PBCNs can be solved, for example partial stabilization, synchronization, and so on. Finally, a practical example is employed to show the effectiveness of our results.

Sampled-data stabilization of probabilistic Boolean control networks

Probabilistic Boolean networks (PBNs) are discrete-time systems composed of a family of Boolean networks (BNs), between which the PBN switches in a stochastic fashion. In this paper, we address the stabilization of probabilistic Boolean control networks (PBCNs) via a sampled-data state feedback controller (SDSFC). Based on the algebraic representation of logical functions, a necessary and sufficient condition is derived for the existence of SDSFCs for the global stabilization of PBCNs, and the controller is further designed. A biological example is presented to illustrate the effectiveness of the obtained results.

Output tracking of probabilistic Boolean networks by output feedback control

In this paper, we deal with the output tracking of probabilistic Boolean control networks (PBCNs) via output feedback control. Firstly, the algebraic representation of PBCNs is obtained by resorting to semi-tensor product (STP) technique. Then, a novel notion, named as output feedback based control invariant set (OFBCIS), is offered. Meanwhile, an algorithm is developed to find all OFBCISs in a given set. Consequently, some necessary and sufficient conditions are derived for the solvability of output tracking problem under output feedback control. Besides, all feasible output feedback laws are solved by another constructed algorithm. Finally, two numerical examples are exhibited to illustrate the effectiveness of the theoretic results.

Stabilization and Finite-Time Stabilization of Probabilistic Boolean Control Networks

In this paper, we study the stabilization and finite-time stabilization of probabilistic Boolean control networks (PBCNs). A complete family of reachable sets is defined first, based on which, feedback stabilization conditions are obtained. Then a way to find all possible state feedback controllers are presented for the stabilization of PBCNs accordingly. Moreover, it has been stated that the approach in this paper can also be applied to finite-time stabilization via some changes in the construction of set sequence. Finally, an evolutionary networked game is given as an example to illustrate the efficiency of the obtained results.

Event-Triggered Control for the Stabilization of Probabilistic Boolean Control Networks

This paper realizes global stabilization for probabilistic Boolean control networks (PBCNs) with event-triggered state feedback control (ETSFC). Via the semitensor product (STP) of matrices, PBCNs with ETSFC are converted into discrete-time algebraic systems, based on which a necessary and sufficient condition is derived for global stabilization of PBCNs. Furthermore, an algorithm is presented to design a class of feasible event-triggered state feedback controllers for global stabilization. Finally, an illustrative example shows the effectiveness of the obtained result.

Reconstruction of probabilistic Boolean networks

Probabilistic Boolean control networks (PBCNs) have received a great amount of attention in the field of opinion dynamics in social networks and gene (or genetic) regulatory networks. PBCNs have been transferred to state transition probability matrices. Using a Markov chain theory, the PBCN is investigated under a state space framework. In this paper, we address the problem of constructing a probabilistic Boolean control network from a prescribed transition probability matrix. First, an algorithm is given to obtain the realization of a PBCN. Second, because of the non-uniqueness of the logical realization of a PBCN, a modified algorithm is introduced to obtain other realizations of PBCNs. Finally, an illustrative example is given to demonstrate both the efficiency and effectiveness of the proposed algorithms. In addition, the future direction of the research is discussed.

Static output feedback set stabilization for context-sensitive probabilistic Boolean control networks

In this paper, we investigate the static output feedback set stabilization for context-sensitive probabilistic Boolean control networks (CS-PBCNs) via the semi-tensor product of matrices. An algorithm for finding the largest control invariant set with probability one is obtained by the algebraic representations of logical dynamics. Based on the analysis of the set stabilization, necessary and sufficient conditions for S-stabilization are obtained. Static output feedback controllers are designed to achieve S-stabilization for a CS-PBCN. At last, examples to study metastatic melanoma are given to show the effectiveness of our main results.

Robust Control Invariance of Probabilistic Boolean Control Networks via Event-Triggered Control

This paper investigates the robust control invariance of probabilistic Boolean control networks via the technique of semi-tensor product. Some essential conditions are obtained to check whether the set is a robust event-triggered control invariant set (RETCIS) through the given event-triggeredcontroller (ETC). Moreover, an algorithm is designed for ETC to ensure that the given set is RETCIS. At last, a model of the apoptosis network shows the effectiveness of the main results.

Controllability of probabilistic Boolean control networks with time-variant delays in states

Controllability of probabilistic Boolean control networks with time-variant delays in states

State feedback based output tracking control of probabilistic Boolean networks

This paper studies the state feedback based output tracking control of probabilistic Boolean control networks (PBCNs) by using the semi-tensor product of matrices. A series of reachable sets (with probability 1) is defined inductively for PBCNs, and some useful properties are obtained for the reachable sets. Based on the properties of the reachable sets, a necessary and sufficient condition is presented for the state feedback based output tracking control of PBCNs. Meanwhile, a constructive procedure is proposed to design state feedback laws for PBCNs to track a constant reference signal. The study of two illustrative examples shows that the obtained new results are very effective.

Controllability of probabilistic Boolean control networks based on transition probability matrices

In this paper, we propose a new approach to investigate the controllability and reachability of probabilistic Boolean control networks (PBCNs) with forbidden states. We first give a simple algebraic formula for the transition probability between two states in a given number of time-step, while avoiding a set of forbidden states. Then we construct the controllability matrix based on a new operator, and some necessary and sufficient conditions are obtained for the controllability and reachability of PBCNs. A numerical example is given to illustrate the efficiency of the obtained 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 sufficient 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 sufficient 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 sufficient condition of the stabilization of PBCNs. Both necessary and sufficient conditions for controllability and stabilizability are based on reachability matrix, which are easily computable. Hence the two necessary and sufficient conditions are straightforward verifiable. Numerical examples are provided from case to case to demonstrate the corresponding theoretical results.

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.