Dynamic Characteristics Analysis Of Discrete Control System Under Networked Environment

In recent years,with the rapid development of the computer networks,communication technology and system control,the cyber physical systems(CPSs)have emerged,which are a kind of intelligent systems closely integrating the computing ability with the communication environment and the control method,and hence can make the addressed systems more automatic,informatized and intelligent.Among them,the discrete control system is a kind of model used to characterize the CPSs,such as the smart grid system,the intelligent transportation system and so on.Under the framework of Boolean networks(BNs)and finite state automata(FSA),by resorting to the semi-tensor product(STP)technique of matrices,the dynamic characteristics are investigated in this dissertation for these types of discrete control systems under the networked environment,which include the stabilization,observability,antisynchronization,cluster synchronization and fault detection of BNs as well as the initial state estimation of FSA.The specific works are summarized as follows.The first chapter mainly introduces the research background and significance,the research contents and innovation of this dissertation.Firstly,the research status/progress of the BNs and FSA are introduced.Then,the main results obtained and the contributions of this dissertation on BNs and FSA are presented.The second chapter introduces firstly the theory on STP of matrices,including the basic properties of the STP and the matrix representation of the logical operators.Then,by resorting to the STP of matrices,the corresponding algebraic expression of the BN is established.Finally,some basic concepts of FSA are introduced.The third chapter addresses the stabilization problem of impulsive BNs under the influence of stochastic disturbances.By resorting to the STP method of matrices,the dynamic evolution of the impulsive BN is transformed into an algebraic form.Then,through the analysis of the reachable set,the concept of the distance between each state of the network and the equilibrium is defined,based on which the algorithm is then proposed for designing the appropriate aperiodic impulsive sequences.In addition,based on the state feedback control method,some criteria are proposed to stabilize the periodic impulsive Boolean control networks(BCNs)with stochastic disturbances.Finally,numerical examples are given to demonstrate the feasibility of the established theoretical results.The fourth chapter is concerned with the observability problem of BCNs under stochastic disturbances,which is investigated via two kinds of control schemes: deterministic control and state feedback control.Firstly,based on the proposed indicator matrix,a simplified system of the original augmented Boolean system is constructed.Based on the analysis of the auxiliary system,observability of the original BCN is converted to determining whether an observable set can be reached from another unobservable set.After that,some necessary and sufficient criteria are obtained to judge the observability of BCNs.At the same time,two algorithms are proposed for designing these two types of control sequences.Finally,numerical simulations are also provided to demonstrate feasibility of the theoretical results.The fifth chapter investigates the anti-synchronization and generalized cluster synchronization problems of BCNs,respectively.Firstly,two equivalent properties of the driveresponse BCN are proposed through an algebraic representation of the logic dynamics.Then,based on the analysis of the event conditions,an algorithm of the event-based state feedback control matrix is designed,and a necessary and sufficient criterion guaranteeing the antisynchronization of the drive-response coupled BCNs is formulated.In addition,by using the STP method of matrices,the BCNs with delays in both the states and the inputs is transformed into an equivalent extended system.Next,based on the updated iterative equation of the system,two types of generalized cluster synchronization problems are studied: 1)generalized internal cluster synchronization within the BCN,and 2)generalized cluster synchronization between the BCN and the target reference network.Moreover,necessary and sufficient conditions are proposed satisfying the above two types of generalized cluster synchronization.More importantly,the algorithm for designing the gain matrix of the state feedback controller is also derived.The sixth chapter considers the problem of fault detection for asynchronous delayed BCNs with sampled-data control.Applying the STP method,the asynchronous update rules of the separate states are firstly converted into the synchronous update scheme of the multi-states.After that,the original fault detectable states are regarded as a compact set,based on which a dimension reduction model is established,and then the fault detection problem of the original system is reduced into a global stabilization issue.Subsequently,through the sampled-data control scheme,some fault detection criteria are proposed for the considered asynchronous delayed BCN.Meanwhile,the sampled-data control matrix can be constructed step by step by resorting to an elegant algorithm provided.Finally,an example is provided to demonstrate the feasibility and importance of the results obtained.The seventh chapter is concerned with the initial state detectability problem of finite state automata(FSA).First,by resorting to the Boolean STP method of matrices,the corresponding algebraic forms of the partially-observed FSA are separately constructed,and the dimension reduction tracking observation system of the corresponding original system is established.Simultaneously,based on the newly defined dimension reduction output–event observation matrix,the sufficient and necessary criteria of the strong(or weak)initial state(I-S)detectability of the system are obtained,and the relevant algorithm of I-S detectability is designed,respectively.At the same time,the computational complexity of the considered system is reduced to some degree.In addition,the reversal observation system of the original system is also considered.Based on the state transition reversal output–event observation matrix,the sufficient and necessary criterion is established to determine the weak I-S detectability of the addressed system.Subsequently,several illustrative examples of FSA are used to demonstrate the validity of the derived results.The eighth chapter summarizes the whole paper based on the previous contents,and provides some prospects of our future works.