Stability Analysis And Synthesis Of Several Kinds Of Logical Dynamic Systems

Logical dynamic system(LDS)is a kind of nonlinear discrete-time dynamic system based on a directed graph.In an LDS,each node takes values from a finite set,and the update of the state of each node is determined by the logical operation of the state of the adjacent nodes.Since Boolean algebra was founded,especially since Kauffman introduced Boolean network(BN)to study gene regulatory networks,the LDS has become an important research tool in many fields,such as biological systems,social networks,game theory,and so on.Taking multi-valued logical networks(LNs)as the basic research object,this paper discusses two kinds of typical hybrid LNs,namely switched logical networks(SLNs)and impulsive logical networks(ILNs).The stability analysis and the design of switching signals/impulsive instant sequences of the above two kinds of networks are further discussed by means of the semi-tensor product of matrices and Lyapunov stability theory,and with the help of SLN model,some control problems of LNs are discussed.In addition,using the LDS to model,this paper further discusses the optimal strategy estimation of a class of n-person random evolutionary Boolean games(REBGs).The main work of this paper is summarized as follows:· For LNs,a new class of constrained switching signals,namely logical switching,is considered.Combining the Lyapunov theory with the concept of average dwell time,the point stability and set stability of LNs under this kind of constrained switching signals are analyzed,and some sufficient criteria are given.· The point stability and set stability analysis of LNs under the influence of instantaneous impulses are considered.Firstly,a necessary and sufficient condition for the global stability of impulse ILNs under arbitrary impulsive instant sequences is given.Secondly,combined with the concept of average impulsive interval and the Lyapunov theory of LNs,the stability of ILNs is further analyzed based on the stability of the non-impulsive process,and some sufficient criteria are given.· The stabilization of LNs under event-triggered switching signals is studied.According to the existence of the switching Lyapunov function,a necessary and sufficient condition for the stabilization of LNs under event-triggered switching signals is obtained.Secondly,according to the obtained switching Lyapunov function,the design algorithms of the timeoptimal and cost-optimal switching sequences are given.Finally,the results are applied to the stabilization of LNs with logical switching as well as ILNs,and the event-triggered logical switching sequence and event-triggered impulsive control strategy are designed accordingly.· The stabilization problem under two kinds of controllers for logical control networks is transformed into the stability analysis of SLNs by using the idea of model transformation.On the one hand,the stabilization of SLNs under an asynchronous switching state feedback controller is considered,and a sufficient criterion is given.On the other hand,the stabilization of logical control networks,probabilistic logical control networks,and Markov logical control networks under the aperiodic intermittent control is studied,and the criteria for the stabilization under time-triggered intermittent control and event-triggered intermittent control are given respectively.· The problem of optimal strategy estimation for a class of n-person REBGs is discussed.By using the minimum mean square error criterion,the optimal strategy estimator of nperson REBGs is given.Moreover,the n-person REBG is modeled by an LDS,and then an iterative algorithm based on the matrix is established by the semi-tensor product of matrices to calculate the optimal strategy estimator and minimum mean square error of n-person REBGs.