Event-triggered Based Piecewise-continuous Observer Design For Networked Systems

In networked systems,compared to the conventional periodic time-triggered mechanism for data transmission,the aperiodic event-triggered mechanism brings lots of advantages,such as saving bandwidth,prolonging the service life of sensors,strengthening the security of information,etc,which is one of the current research hotspots.Compared to the problem of event-triggered control,the study for the problem of event-triggered observation hasn't draw enough attention currently,and has the limitations as follows:First,about the observer structure.The piecewise-continuous hybrid observer is more suitable for the sampled data systems.However,the current researches on hybrid observer are mostly based on the periodic sampled system output,and the research on event-triggered hybrid observer is still rare;Second,about the event-triggered mechanism.For the error based conventional event-triggered mechanism which is widely used currently,no matter how the controlled object,the observer or the network environment change,its form is always unchangeable or similar,and the real-time information of the system used for judging whether to execute the transmission task is also unchangeable(usually is the system output data),so it has certain conservatism in the theoretical design;Third,about the event-triggered observer.The studies of event-triggered observers are based on various systems currently.However,for a special type of nonlinear systems called state affine systems,it's hybrid observer design is mostly based on the periodic time-triggered mechanism,and the hybrid observer research for state affine systems based on the event-triggered mechanism is still rare.Based on the above considerations,in order to make up for the shortcomings of the existing results,it is necessary to study how to design a class of event-triggered hybrid observers for the sampled data systems,and then improve the existing conventional event-triggered mechanism,design a more flexible type of event-triggered mechanism,which can make use of more abundant real-time information of the system and has lower conservatism,and finally extend the results to nonlinear state affine systems.Based on this,in line with the basic idea of ”from simple to difficult”,the main contents of this paper can be summarized as follows:(1)Aiming at the observation problem of linear system with aperiodic sampled and delayed output,combined with the conventional event-triggered mechanism technology,a class of event-triggered piecewise-continuous hybrid state observers is proposed.Firstly,by using the periodic detection method of event-triggered conditions,the conventional event-triggered mechanism technology,and the reduced order discrete-time Luenberger observer technology,the event-triggered reduced order discrete-time Luenberger observer model is established,which realizes the purpose of observing the periodically sampled and delayed state estimation from the aperiodically sampled and delayed output;Secondly,by using the technology of linear piecewise-continuous systems,the reconstruction calculation is designed,and the undelayed state estimation of continuous time is reconstructed from the periodically sampled and delayed state estimation;Thirdly,based on the proposed model of event-triggered piecewise-continuous hybrid observation system,the stability analysis is studied.Finally,the effectiveness and superiority of the proposed method are verified by simulation comparison with the existing Lyapunov–Krasovskii observer.(2)Aiming at the problem of event triggered mechanism design,considering the linear networked observation system with aperiodic sampling and delay,the conventional event-triggered mechanism is improved,and a kind of system(observation)performance based event triggered mechanism is proposed.For linear systems,the design of system performance based event-triggered piecewise-continuous observer is studied in two cases.In the first case,only aperiodic sampling is considered.By using the linear matrix inequality technique,a new system performance based event-triggered mechanism is proposed.Based on the high-gain observer technique and the reset predictor technique,an event-triggered piecewise-continuous hybrid observer model is established,and the sufficient conditions for its global exponential convergence are obtained;In the second case,the aperiodic sampling and delay are considered simultaneously.The case of only considering aperiodic sampling in the previous step is improved,and the design of system performance based event-triggered mechanism in the case of delay is studied.The event-triggered piecewise-continuous hybrid observer model is proposed,and the sufficient conditions to make it globally asymptotically convergent are obtained.By using the wirtinger-based inequality technique,a very small over estimation is realized,thus the stability conditions of low conservatism are obtained.Besides,the co-design of observer and event-triggered mechanism is further studied.For the above two cases,the effectiveness is verified by simulation.In addition,for the case of considering both the aperiodic sampling and delay,the superiority of the proposed system performance based event-triggered mechanism is verified by simulation comparison with the periodic time-triggered mechanism and the classical event-triggered mechanism.(3)Aiming at the observation problem of nonlinear state affine system with aperiodic sampled and delayed output,the theory of system performance based event-triggered hybrid observer is proposed.For nonlinear state affine systems,the design of system performance based event-triggered piecewise-continuous observer is also studied in two cases.In the first case,only aperiodic sampling is considered.For the special nonlinear state affine system,another type of system performance based event-triggered mechanism is proposed.Also,using the high-gain observer technology and reset predictor technology,the model of event-triggered piecewise-continuous hybrid observer is established,and the sufficient conditions for its global exponential convergence are obtained;In the second case,the aperiodic sampling and delay are considered simultaneously.The case of only considering aperiodic sampling in the last step is improved,the design of system performance based event-triggered mechanism in the case of delay is studied.The event-triggered piecewise-continuous hybrid observer model is proposed,and the sufficient conditions for its global exponential convergence are obtained.At the same time,the continuous detection method of event-triggered conditions in the previous case is improved.The periodic detection method is used to propose the periodic system performance based event-triggered mechanism.For the above two cases,the effectiveness and superiority are verified through the simulation comparison with the relevant literatures.Besides,the method in the first case is simplified and applied to the linear systems,and through the simulation research,it is compared with the system performance based event-triggered mechanisms proposed in(2)which is designed for linear system by using Linear matrix inequalities,and finally the advantages and disadvantages for the two methods are illustrated from points of the conservatism and the universality of application respectively.