Stability Analysis And Control Of One-dimensional/Two-dimensional Discrete-time System Via Event-triggered Scheme

With the development and progress of computer technique,the network begins to be inserted to control systems to transmit and exchange information,thus the networked control system is proposed.However,the insertion of communication network brings certain perfections,such as time-delay,packed dropouts etc.These factors not only degrade the system performance,but also lead to system instability.For these typical issues,some control strategies have been put forward to ensure a satisfactory system performance.Among them,the networked predictive control technique proposed by Liu et al is effective for compensating the network-induced phenomenon in systems by predicting the future system information.Nevertheless,the predictive control sequence may generate a large number of data and more resources are needed,which undoubtedly limits the applications of this method.Furthermore,the traditional time-triggered control transmits some data that no impact on system performance,which also increases the transmission burden.Inspired by these considerations,the event-based NPC method will be designed in this paper to compensate the network-induced time-delay.The consideration of event-triggered mechanism can not only suppress the generation of network-induced phenomenon,but also reduce the number of data transmission and save the bandwidth resource.Firstly,the case of single channel delay is considered,that is,the transmission delay only exists in the sensor-to-controller channel.Particularly,two methods include the augmented model and the piecewise linear model are proposed,and Lyapunov theory is applied to analyze the stability of the control system.Secondly,the results are extended to the case of two-channel delays,that is,the transmission delay exists in both the sensor-to-controller and the controller-to-actuator channels.The event-triggered conditions are established in the sensor system and the actuator system respectively to further save the limited-bandwidth.On the other hand,the design problem of event-triggered control for two-dimension(2-D)system is further considered.2-D system is a class of systems that the states vary with the variables in both horizontal and vertical directions.Due to the 2-D attribute entail the times of data transmission is multiple,the research of event-triggered problem is more theoretical significance and application value.Therefore,the event-triggered control of 2-D system will be considered from the following two aspects:1.Similar to the one-dimensional system,sudden changes or failures often occur in the actual 2-D systems.Thus,the designing of event-triggered for 2-D switching system is necessary.In this paper,a control method based on event-triggered scheme is designed for 2-D switching system.The sufficient conditions for guaranteeing the stability of systems under arbitrary switching signal and restricted switching signal are obtained by stability analysis.2.For the 2-D system with external disturbances,the combination of sliding mode control and event-triggered scheme can not only adapt the disturbance,but also reduce the number of the data transmission and save the bandwidth resource effectively.Firstly,the event-triggered scheme and sliding surface function are designed,and then the stability analysis is developed by obtaining the sliding mode dynamics.Furthermore,two different event-triggered sliding mode controllers in term of Lyapunov function approach and reaching law approach are presented.At the same time,the conditions to ensure the existence of the event-triggered sliding mode controller is given.Then,the effectiveness and validity of the research results are demonstrated by accomplishing a group of simulations.Finally,a summary of this paper is given and the future research direction is expected based on the current research gains.