Event-Triggered Control For Uncertain Linear Systems

With the rapid development of computer technology and communication technology,traditional wired network technology is rapidly being replaced by wireless network technology.Compared with wired network technology,wireless network technology has the advantages of convenience and low price,but the disadvantage is that the energy consumption is very high,and it is difficult to meet the application requirements by using the time sampling mechanism.Today in the 21st century,for human beings,resources are becoming more and more scarce,and the effective use of resources and low energy consumption are what society needs.In the face of this situation,the event trigger mechanism was introduced into the control system.The event-triggered mechanism is a non-periodic sampling,that is,the system only needs to recalculate the control amount when the error of a certain system parameter or system index exceeds a specified threshold,and the control task of the control system is executed.Due to external disturbances,unmodeled errors and various faults of the system,the mathematical model of the system inevitably has different forms of uncertainty.The exact model of the actual control object is difficult to obtain,so the research on robust control is This background has been produced and is constantly evolving.Uncertainty will occur in large and small systems.Studying and analyzing the uncertainties in the system will help to study the stability and robustness of the analysis system,and help to obtain the desired control requirements and performance indicators.It is conducive to the design and application of the system.Based on event-triggered mechanism,this paper studies uncertain linear systems.The main contents of the algorithm are divided into three parts.The main work is summarized as follows:In the first part,considering the uncertain system parameters,the event-triggered mechanism is used to design the output-feedback controller and form a closed-loop control system.Firstly,the stability criterion is established based on the linear matrix inequality method to ensure the exponential stability of the closed-loop system.Secondly,it is proved that there is a positive lower bound in the event-triggered interval time.Finally,it is verified by simulation that the designed output-feedback controller can ensure the system index is stable under the event-triggered condition and can improve the utilization of system resources.In the second part,based on the event-triggered mechanism,and considering the state observer-based state-feedback control problem.Firstly,the output of the system is transmitted to the state observer only when the event condition is not met,and the closed loop control system is formed by the control system and the state observer error system.Secondly,a form of linear matrix inequalities is given for the closed-loop system to ensure that the continuous-time linear system and the observer error system have Lyapunov stability.Finally,the feasibility and effectiveness of the theoretical results are verified by simulation.In the third part,considering the uncertainties of system parameters and external disturbances,based on the event-triggered conditions,the controller is designed based on the state observer and constitutes a closed-loop control system.Then,it is proved that the system not only has Lyapunov stability,but also meets certain performance indexes,and the controller gain is solved by linear matrix inequality,and the controller of the system is obtained.Finally,the feasibility and effectiveness of the theoretical results are verified by simulation.