Sampled-data Control Of Boolean Networks And Some Related Qualitative Problems

Boolean network is one of the simplest logical dynamic system with binary state variables.It has been confirmed to be a significant tool in depicting,analyzing,and simulating the neural networks,gene regulatory networks,and social systems With going deep into studying,Boolean network model has been applied to game theory and information science.Because of its wide application,Boolean network has always been a hot topic.This thesis investigates Boolean control networks under sampled-data control.The major work of this dissertation is as followsIn the first part,the research background of this thesis is presented.And some preliminaries are given,mainly focus on the definition and properties of semi-tensor product of matrices,the algebraic representation of Boolean functions,and so onThe Chapter two addresses the sampled-data state feedback control for set sta,bilization of Boolean control networks.Set stabilization means that a Boolean control network converges to a subset of the state space.The concept of sampled-data con,trol invariant subset is introduced.Then consider two conditions q??q>?,where q is the cardinal number of any given nonempty subset ? and ? is sampling period,and calculate the corresponding largest sampled-data control invariant subset.Based on the largest sampled-data control invariant subset obtained,a design procedure is proposed to calculate all possible sampled-data state feedback controllers for set stabilization of Boolean control networks.Ultimately,an example is provided to demonstrate the efficiency of the above resultsStabilization of Boolean control networks under aperiodic sampled-data con-trol is investigated in Chapter three.The sampling period is allowed to be taken from a limited number of values.Using the semi-tensor product of matrices,a Boolean control network under aperiodic sampled-data control can be converted in-to a switched Boolean network.Here,the switched Boolean network can only switch at sampling instants,which does not mean that the switches occur at each sampling instant.For the switched Boolean network,consider two cases:(i)switched Boolean network with all stable subsystems;(ii)switched Boolean network containing both stable subsystems and unstable subsystems.For these two cases,the techniques of switching-based Lyapunov function and the average dwell time method are used to derive sufficient conditions for global stability of Boolean control networks under aperiodic sampled-data control,respectively.The upper bounds of the cost function,which is defined to guarantee that the considered Boolean control network is not only globally stabilized but also can assurance the performance at an appropriate level,are determined,respectively.Moreover,an algorithm is presented to construct the aperiodic sampled-data controllers.At last,the obtained results are demonstrated by several examplesThe purpose of Chapter four is to further study the global stability of Boolean control networks under aperiodic sampled-data control.According to Chapter three,it is known that a Boolean control network under aperiodic sampled-data control can be transformed into a switched Boolean network,and further global stability of the Boolean control network under aperiodic sampled-data control can be obtained by studying the global stability of the transformed switched Boolean network.Unfor-tunately,since the major idea of Chapter three is to use stable subsystems to offset the state divergence caused by unstable subsystems,the switched Boolean network considered requires at least one stable subsystem.While the main thrust of this chapter is that switching behavior also has a good characteristic of stabilization,i.e.,when all subsystems are unstable,the switched Boolean network can also be stable by designing appropriate switching laws.Specifically,for this case,the dwell time needs to be confined by a pair of upper and lower bounds,and then the techniques of discretized Lyapunov function and dwell time method are used to derive sufficient condition for global stability.Ultimately,the obtained results are illustrated by a biological exampleFinally,Chapter five summarizes the whole paper and looks forward to future research work.