http://lsc.amss.ac.cn/~dcheng/files/Automatica-45(7)-P1659_2009.pdf

Controllability and observability of Boolean control networks

http://lsc.amss.ac.cn/~dcheng/preprint/bn_isim.pdf

Input-state incidence matrix of Boolean control networks and its applications

State feedback stabilization for Boolean control networks is investigated in this technical note. Based on the algebraic representation of logical dynamics in terms of the semi-tensor product of matrices, a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller, and a general control design approach is proposed when global stabilization is feasible via state feedback. Instead of designing the logical form of a stabilizing feedback law directly, we first construct its algebraic representation and then convert the algebraic representation back to the logical form. An example is worked out to illustrate the proposed design procedure.

State Feedback Stabilization for Boolean Control Networks

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

This study presents a detailed survey on recent development of logical networks and its applications, including the background of logical networks, the theory of a new matrix product called semi-tensor product (STP) of matrices, some fundamental works on logical networks, and some current research works. Particularly, some fundamental works on logical networks are presented for the past years, including controllability, stability and stabilisation, synchronisation, disturbance decoupling and so on. Due to the great potential of STP in dealing with logical networks, a surge of attraction from overseas is paid on the study of STP and its applications. Currently, some new research areas are widely studied including pinning control, function perturbations, system decomposition, trajectory control, output tracking issues, symbolic dynamics and so on. The main concern of this study is to present a comprehensive introduction to logical networks and some other applications under the framework of STP of matrices.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2016.1659

Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems

The 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.

/pdf/stability-and-stabilization-of-boolean-networks-2lv6kbarzp.pdf

Stability and stabilization of Boolean networks

This paper addresses stabilization of switched linear control systems with unstabilizable individual switching models. First we consider the stabilization of switched systems via a controllable switching strategy. Then stabilization by both controls and switching laws is investigated. Certain sufficent conditions are obtained.



ABSTRACT

Stabilization of switched linear systems

We have developed a distributed data mining algorithm based on the progressive knowledge extraction principle. The knowledge factors, the data attributes that are significant statistically or based on a predefined mining function, are extracted progressively from the distributed data sets. The critical data attributes and sample data set are selected iteratively from distributed data sources. The experiments showed that the algorithm is valid and has the potentials for the large distributed data mining practices.

Jiang B. Liu

Papers

Stability and stabilization of Boolean networks

Stabilization of switched linear systems

A distributed knowledge extraction data mining algorithm