Stability And Differentially Private Consensus Of Two Types Of Switched Systems

As an important class of hybrid systems,switched systems have been widely used in mobile communication,traffic management,electric power generation,military command,and other fields in recent years.Since the switched system contains both continuous and discrete dynamics,its dynamic behavior is not a simple superposition of the behaviors of various subsystems,but rather has particularity and complexity.In general,the stability of a switched system is not equivalent to the stability of its subsystems,but depends on the design of switching rules.Different switching rules can lead to different dynamic behaviors of the system,so it is necessary to study the stability of switched systems,which has extremely rich theoretical connotation.The study of switched systems can not only promote the theoretical development of hybrid systems,but also enrich the theoretical systems of automatic control.Considering the rapid development of intelligent control and the importance of information security,the consensus and privacy protection of multi-agent systems have attracted more and more scholars’ attention.In particular,with the improvement of the intelligent level of sensors and robots,as well as the increasing trend of automation,it is difficult for systems with fixed topology to meet the current complex practical application requirements.Since the topology structure of multi-agent systems depicts the coordination and cooperation between different agents,which directly affects the dynamic behavior of the system,the hybrid nature of switching topology greatly increases the analysis difficulty of consensus and privacy protection compared with fixed topology.Based on this,this dissertation uses the basic theories such as algebraic graph theory,matrix theory,and control theory,to deeply study the stability and differentially private consensus of switched systems.The main research work is divided into the following aspects:(1)Compared with the classical average dwell time switching and mode-dependent average dwell time switching,this dissertation considers a more flexible and practical mode-dependent average dwell time switching based on transition probability to study the global exponential stability of discrete-time switched systems with stable and unstable subsystems.On account of the fact that the state of the system cannot be measured directly and the limited channel resources in the actual environment,this dissertation designs a novel class of observer-based quantized control scheme that incorporates the quantization of three kinds of signals: the measurement output,the state of observer,and the measurement output of observer.Further,to reduce the conservativeness of the obtained results,this dissertation constructs new multiple Lyapunov functions with negative terms to deal with the infinitely distributed delay,obtains stability criteria in the form of linear matrix inequality that is easy to verify,and gives the design algorithm of controller parameters.The results of this dissertation show that even if only one subsystem is controlled,the stability of the whole switched system can still be guaranteed,and the lower bound of the dwell time of the controlled subsystem can be very small.In addition,the above conclusions are also extended to the stability study of discrete-time systems with Markovian switching.(2)Different from the existing results,this dissertation extends the differentially private consensus algorithm to the research of multi-agent systems under switching network topology for the first time and studies the differentially private consensus of discrete-time multi-agent systems over connected switching networks.By designing a novel distributed communication mechanism and using the analysis method combining iterative idea and matrix theory,the mean-square consensus of the multi-agent system under the influence of random noise is achieved,and the introduced random noise satisfies a weaker constraint condition.In order to analyze the differential privacy of the system,this dissertation presents a specific noise selection method and discusses the differentially private consensus problem of the system with random noises obeying the Laplace distribution under the weaker constraint condition.The explicit expression of the privacy level is given,and each agent can independently choose its privacy level according to the actual situation.It is worth noting that in order to highlight the advantages of the research method in this dissertation,this dissertation compares the proposed research method with that under fixed topology,and finds that the existing methods are only suitable for the differentially private consensus of switched systems whose network topology meets certain structures,while this dissertation does not have any restrictions on the network structure of the system except for connectivity.(3)Considering the limited communication resources,noise interference,or system failure in the actual environment,this dissertation further studies the differentially private consensus of multi-agent systems under the jointly connected switching topology.Because the network topology under the jointly connected condition is not connected at each moment and there are no other requirements for the network structure of the system in this dissertation,the theoretical analysis becomes particularly difficult compared with fixed topology and connected topology.Based on this,by proposing a distributed communication mechanism and using the combination of matrix theory,limit idea and iterative method,this dissertation not only proves the existence of the control gain in the communication mechanism that enables the system to achieve mean-square consensus,but also quantitatively provides a method for selecting the control gain.At the same time,it is pointed out that when the system achieves mean-square consensus,the final consensus state of the system will randomly fall near the average value of the initial state with a finite variance,and a calculation method for convergence accuracy is clearly given.Further,in order to reveal the essence of the differential privacy protection effect of noise on the system when the time tends to infinity,this dissertation presents a necessary and sufficient condition for the probability density function of random noise to satisfy,thereby revealing the effectiveness of noise obeying the Laplace distribution in protecting the differential privacy of the system.Finally,a series of simulation examples verify the validity of the results and show the relationship between different performance indicators.