Composite Anti-disturbance Control For Semi-markovian Jump Systems Based On Event-triggered Mechanism

In the field of control,the research and application of stochastic systems have been widely concerned.Markovian Jump Systems(MJSs)is a typical multi-modal stochastic system.It can switch between different sub-systems by jumping between different modal to describe the sudden changes of system parameters or structures.It has strong modeling capabilities and rich engineering background.Therefore,it has been widely concerned by engineering and academia,and its research results are increasingly applied to actual systems,such as power systems,communication systems,network control systems.However,in the MJSs,its dwell time obeys exponential distribution,so its transition probability is time-invariant.But,most of the practical systems cannot meet this condition,and applying MJSs in reality can only give approximate results or even cannot be applied at all.The semi-Markovian Jump Systems(S-MJSs),its transition probability matrix is a time-varying matrix that depends on the probability distribution function,so it has more important research value.On the other hand,due to environmental noise,severe weather or frictional losses of system components,the actual control system inevitably generates disturbance.Therefore,how to reduce and avoid the influence of various disturbances becomes crucial.The event-triggered method is generally welcomed for effectively reducing the communication burden and solving the resource limitation problem.In this paper,based on the event-triggered method,the composite control based on disturbance observer for continuous time nonlinear S-MJSs under multiple disturbances and actuator saturation is studied.The main innovations are as follows:(1)The composite control problem of S-MJSs with multiple disturbances and nonlinearity is studied,based on the combination of disturbance observer-based control and event-triggered control.In this paper,the disturbances existing in the system are divided into two types,one is norm-bounded disturbance,and the other is modelable disturbance generated by exogenous systems.Using the upper and lower bounds of the dwell time of the given transition probability to effectively solve the time-varying transition probability problem of S-MJSs.In addition,by solving the LMI,the disturbance observer gain,state feedback controller gain,and event-triggered dynamic matrix are obtained.Finally,a simulation example is given to verify the effectiveness of the proposed control algorithm.(2)The problem of composite anti-disturbance control for continuous time S-MJSs with actuator saturation,multiple disturbances and nonlinearity is studied.Based on the linear convex hull method,the auxiliary matrix and parameters are used to give the attracting domain of the closed-loop system,and the linearization problem of matching disturbance is solved.In addition,for the event-triggered mechanism,Zeno behavior will bring great difficulty to the calculation and implementation of information exchange process.In order to avoid the Zeno behavior,the minimum time interval between adjacent trigger events is given and its effectiveness is proved.Finally,a series of LMIs easily solving are obtained.(3)For S-MJSs with actuator saturation and multiple disturbances,a more general unknown nonlinear situation is studied.On the basis of the original event-triggered mechanism,improvements are made and exponential function related parameters are added to avoid the Zeno behavior more scientifically.In addition,the passive control of the system based on disturbance observer is studied.Under the condition of bounded input,the energy of passive system is attenuating,so passive system can keep the internal stability of the system.The specific analysis process is given from the aspects of system passivity and passive control.it was verified by a set of simulation examples.