Stabilization Of Boolean Control Networks Research Articles

Robust set stabilization of Boolean control networks with impulsive effects

This paper addresses the robust set stabilization problem of Boolean control networks (BCNs) with impulsive effects via the semi-tensor product method. Firstly, the closed-loop system consisting of a BCN with impulsive effects and a given state feedback control is converted into an algebraic form. Secondly, based on the algebraic form, some necessary and sufficient conditions are presented for the robust set stabilization of BCNs with impulsive effects under a given state feedback control and a free-form control sequence, respectively. Thirdly, as applications, some necessary and sufficient conditions are presented for robust partial stabilization and robust output tracking of BCNs with impulsive effects, respectively. The study of two illustrative examples shows that the obtained new results are effective.

On algorithms for state feedback stabilization of Boolean control networks

This paper deals with the algorithms for state feedback stabilization of Boolean control networks (BCNs). By resorting to the semi-tensor product (STP) technique, the labelled digraph that can be used to completely characterize the dynamics of BCNs is derived, which leads to an equivalent graphical description for the stabilization of BCNs. What is more interesting is the fact that the existence of a state feedback control law stabilizing the BCN to some given equilibrium point can be characterized in terms of its spanning in-tree. Consequently, two in-tree search algorithms, namely, the breadth-first search and the depth-first search, are proposed to design the state feedback stabilizing law when global stabilization is feasible. Besides, some basic properties about the tree-search algorithms are addressed. A biological example is employed to illustrate the applicability and usefulness of the developed algorithms.

Delayed Feedback Control for Stabilization of Boolean Control Networks With State Delay.

In this brief, we study the delayed feedback stabilization problem for Boolean control networks (BCNs) with state delay. Using the semi-tensor product of matrices, some necessary and sufficient conditions are obtained. For the stabilization of BCNs, detailed procedure to construct the feedback controllers is also presented. We further derive the number of different feedback controllers, which can successfully stabilize the BCN in a finite time. Finally, an illustrative example is presented to show the effectiveness of our method.

Minimum‐Time State Feedback Stabilization of Constrained Boolean Control Networks

AbstractMinistry in 2005, and the National Prize of Natural Science of China in 2008. Currently, he is Associate Editor IMA Journal of Math Control and Inform., and a Technical Committee member of IFAC (TC2.3).This paper investigates the state feedback stabilization of Boolean control networks (BCNs) with state and input constraints by using the semi‐tensor product of matrices. Firstly, a kind of constrained input‐state incidence matrix is proposed for constrained BCNs, which contains all the reachability information of the constrained systems. Secondly, based on the constrained input‐state incidence matrix, a necessary and sufficient condition is presented for the stabilization of constrained BCNs via state feedback. Thirdly, a general procedure is proposed to design all possible minimum‐time state feedback stabilizers. The study of an illustrative example shows that the new results obtained are effective in analyzing the stabilization of constrained BCNs.

Set stability and set stabilization of Boolean control networks based on invariant subsets

This study addresses the set stability of Boolean networks (BNs) and set stabilization of Boolean control networks (BCNs). Set stability determines whether a BN converges to a given subset, whereas set stabilizability addresses the issue of whether a BCN can be stabilized to a given subset. Many problems can be viewed as special cases of set stability and set stabilization, including synchronization, partial stability, and partial stabilization problems. The concepts of invariant subset and control invariant subset are introduced. Then, algorithms for the largest invariant subset and the largest control invariant subset contained in a given subset are proposed. Based on the invariant subsets obtained, the necessary and sufficient conditions for set stability and set stabilizability are established, and formulae are provided to calculate the shortest transient periods for respective initial states. A design procedure is proposed for finding all the time-optimal set stabilizers. Finally, an example is used to show the application of the proposed results to the synchronization problem of BNs.

Output feedback stabilization of Boolean control networks

In the paper output feedback control of Boolean control networks (BCNs) is investigated. First, necessary and sufficient conditions for the existence of a time-invariant output feedback (TIOF) law, stabilizing the BCN to some equilibrium point, are given, and constructive algorithms to test the existence of such a feedback law are proposed. Two sufficient conditions for the existence of a stabilizing time-varying output feedback (TVOF) are then given. Finally, an example concerning the lac Operon in the bacterium Escherichia Coli is presented, to illustrate the effectiveness of the proposed techniques.

Partial state stability and stabilization of Boolean control networks

The paper deals with problems on the stability and stabilization of Boolean networks with respect to a given part of variables characterizing the Boolean network. Using the semi-tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean (control) network can be converted to discrete time linear (bilinear) dynamics called the algebraic form of the Boolean (control) network. The two main results are as follows: (i) From the algebraic form of a Boolean (control) network, two partial stability definitions are introduced. One is partial stability with respect to another variable set, and the other is partial stability with respect to arbitrary initial states. (ii) Based on the algebraic form, necessary and sufficient conditions for the stability of global partial states with respect to the variable set and arbitrary initial states are obtained. Examples are provided to illustrate the effectiveness of our results.

STABILITY AND STABILIZATION OF BOOLEAN NETWORKS

The stability of Boolean networks and stabilization of Boolean control networks are discussed.By using the method of semi-tensor product of matrices and the matrix expression of logic,the dynamics of Boolean network can be represented as a discrete-time dynamic system,then it is converted into an algebraic form.Then the one-to-one correspondence between the structure matrix of the algebraic form and a digital transformation is established.Finally,by using the method of digital transformation,necessary and sufficient conditions for the stability and stabilization of Boolean networks are obtained.

Output feedback stabilization control design for Boolean control networks

This paper investigates the output feedback stabilization of Boolean control networks (BCNs) by using the semi-tensor product method and presents a number of new results. First, based on the algebraic expression of BCNs, a necessary and sufficient condition is presented for the existence of output feedback stabilizers. Second, a constructive procedure is proposed to design output feedback stabilization controllers for BCNs. The study of an illustrative example shows that the new results obtained in this paper are very effective in designing output feedback stabilizers for BCNs.

Stability and stabilization of Boolean networks

AbstractThe stability of Boolean networks and the stabilization of Boolean control networks are investigated. Using semi‐tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean (control) network can be converted to a discrete time linear (bilinear) dynamics, called the algebraic form of the Boolean (control) network. Then the stability can be revealed by analyzing the transition matrix of the corresponding discrete time system. Main results consist of two parts: (i) Using logic coordinate transformation, the known sufficient condition based on incidence matrix has been improved. It can also be used in stabilizer design. (ii) Based on algebraic form, necessary and sufficient conditions for stability and stabilization, respectively, are obtained. Copyright © 2010 John Wiley & Sons, Ltd.