Research On Stability And Output Tracking Of Switched Logical Networks

Logical networks are a class of discrete nonlinear systems formed by the interaction of a finite number of state through logical relationships.Logical networks are also known as k-valued logical networks,which include Boolean networks(k= 2)and multi-valued logical networks(k? 3),and they have a wide range of applications in gene regulation,circuit fault detection,formation control,etc.While the switched logical networks are a type of system which consider the switching modes among the logical networks,and their dynamic behaviors are more complicated.Based on the semi-tensor product method of matrices,this thesis studies the problems related to stability and output tracking of switched logical networks.For the stability of switched logical networks: firstly,the paper studies the global stability at a limit cycle for switched k-valued logical networks(k? 2),and a necessary and sufficient condition is presented by using the method of digital transformation;then the set stability of switched k-valued logical networks is considered,we summarize an algorithm to obtain the largest switched invariant set,and by utilizing the property of switching point reachability,a sufficient and necessary condition for judging the set stability of the system is derived.In addition,the above results are further extended to the switched logical control networks with state-dependent switching signals.For the output tracking problem of switched logical networks,this article studies the problem of optimal output tracking and event-trigged pinning control of switched Boolean networks: when the switching signal is open loop,necessary and sufficient conditions are presented to judge the output trackability of the system by resorting to the result of set stability,then by using the method of graph theory,an optimal switching sequence is designed,which enables the system to track a given reference signal with the minimum cost;next,for the case where the switched Boolean networks cannot track the reference signal under the given closedloop switching law,this paper designs an event-triggered pinning controller,and verifies its feasibility through a biological example of apoptosis networks.