Research On Event-triggered Control For Markov Jump Systems Under DoS Attacks

Due to the environment influences,component faults,actuator failures and oth-er factors,random and abrupt changes of structures and parameters occur in practical physical systems.As a kind of hybrid systems that contains multiple subsystems and jump law obeying Markov process,Markov jump systems can accurately describe such phenomenon.In this regard,Markov jump systems have been deeply studied and wide-ly applied to aerospace,power systems,industrial networks and other fields in the past few decades.In network environments,compared with the traditional periodic sam-pling scheme,event-triggering scheme（ETS）is able to reduce the system signal sampling frequency and further save network resources while ensuring system performance.In ad-dition,due to the limitation of network communication technology,the data transmitted over networks are vulnerable to various malicious attacks,which can deteriorate system performance or even crash system.Therefore,this paper focuses on the analysis of event-triggered control problem for Markov jump systems under denial-of-service（Do S）attacks.The main research contents can be summarized as:1.The event-triggered and self-triggered control problem for continuous-time Markov jump systems under Do S attacks are investigated.Instead of static ETS,dynamic ETS is used to further reduce sampling frequency of system signals.Since Do S attacks make controller lose effect,the switched Markov jump closed-loop system is established.Fur-thermore,multiply Lyapunov function method is utilized to obtain sufficient conditions of stochastic stability and the design of controller gain and event-triggering parameter.Meanwhile,self-triggering scheme（STS）is provided on the basis of dynamic ETS.Such scheme can predict the next triggering instant in advance and avoid the real-time mea-surement of triggering conditions.Compared with the previous STS derived under static ETS,the STS proposed in this paper can reduce more signal sampling.2.Considering that there exist exogenous disturbance and random noise,the event-triggered and self-triggered L_∞control problem for continuous-time Markov jump s-tochastic nonlinear systems under Do S attacks is discussed.Because random noise may lead to Zeno behavior,an ETS based on mathematical expectations is constructed and multiply Lyapunov function method is used to obtain sufficient conditions for ensur-ing L_∞performance.Since ETS with mathematical expectation is difficult to achieve,STS that can be implemented based on sample trajectories is given.In the presence of STS,when no exogenous disturbance is contained,the almost sure exponential stability performance are investigated.In particular,the exponent parameters are introduced in triggering scheme to further reduce triggering frequency.3.In the above contents,Do S attacks are modeled as open-loop control,which may cause a sharp drop in system performance.In this regard,zero-order holder（ZOH）is used to maintain the old transmission data.On such basis,the issue of event-triggered L_∞control for continuous-time Markov jump system under Do S attacks is studied.Un-der the influence of ZOH,in order to avoid exogenous disturbance and Do S attacks from causing Zeno behavior,an ETS with fixed triggering lower bounds is proposed and the influence of Do S attacks on ETS is analyzed,and the new triggering inequality in the presence of attacks is estimated.Furthermore,via using Lyapunov function method and cooperating with the constraints of Do S attacks,sufficient conditions for ensuring the L_∞performance is obtained,and then the design of state feedback gain and event-triggering parameter is provided.4.Considering that discrete-time systems also widely exist in actual physical mod-els,the event-triggered L₂-L_∞asynchronous control problem of discrete-time Markov jump systems under Do S attacks is further investigated.In the event-triggered control design of Markov jump systems,the mode-dependent ETS is most adopted to reduce the conservativeness of controller design.The above contents assume that the subsystems,controller and ETS are synchronized.However,since the system modal information may be difficult to obtain and hidden in the controller,it may cause asynchronous problem among subsystems,controller and ETS.For this reason,Hidden Markov Model（HMM）is used to describe such asynchronous behavior.Based on HMM,considering the impact of periodic Do S attacks,Lyapunov function method and iterative technology are used to obtain sufficient conditions to ensure the stochastic stability and L₂-L_∞control perfor-mance,and then the design of controller and event-triggering parameter is given.5.Due to the modeling advantages of Takagi-Sugeno（T-S）fuzzy model in terms of nonlinearity and uncertainty,the event-triggered H_∞control problem of discrete-time T-S fuzzy Markov jump systems under Do S attacks is studied.Compared with periodic Do S attacks in the fourth content,a more general aperiodic Do S attacks is introduced.In particular,in order to address the conservative problem of controller design caused by mismatching behavior between membership functions of fuzzy controller and fuzzy sys-tem,ETS including membership functions is designed.Furthermore,by using multiply Lyapunov function method and iterative technique,sufficient conditions for ensuring H_∞performance and the specific controller and event-triggered parameter design are given.