Analysis And Pinning Control Of Serial Logical Networks

In recent years, with the development of genetic regulatory networks and the-oretical biology, logical networks have been widely used in gene regulation, multi-valued logic circuit design, network game theory, fuzzy control, finite automata,optimal control, and so on. The basic properties and applications of logical net-works have attracted many scholars' attention, and some excellent results have been obtained. This thesis studies the stability and pinning control problems of serial logical networks (SLNs) based on difference equation and semi-tensor product of matrices.In chapter 1, we present the historical background and current results of log-ical networks, and give some important notations and preliminaries. In chapter 2, the algebraic representations of serial logical networks and serial logical control networks (SLCNs) with pinning control are established via the semi-tensor product of matrices, respectively. Moreover, we present the mutual conversion method be-tween parallel logical networks and serial logical networks. In chapter 3, a necessary and sufficient condition is given for the stability of SLNs. Also, we study the rela-tions of fixed points between serial logical networks and parallel logical networks.In chapter 4, we present a necessary and sufficient condition for the reachability of constrained SLCNs. Meanwhile, the problems of feedback stabilization (including state feedback and output feedback) of SLCNs with pinning control are studied,and an effective method is proposed to calculate the feedback gain matrices. In chapter 5, the obtained theoretical results are applied to gene regulatory networks and networked evolutionary games.