Research On Event-Triggered Quadratic Optimal Control For Continuous Systems

Because most of today's system control methods are designed based on digital platform,more consideration should be given to the sampling of system state in this control platform;the traditional sampling method is periodic for a control system,so its sampling period is fixed,which is called time-triggered mechanism;however,for some systems that need to consider the sampling efficiency,this method may cause the waste of system computing and communication resources.Therefore,in the past decade,event-triggered control has attracted more and more attention.Event-triggering uses a sampling method called non-uniform(aperiodic),which can sample the state of the system dynamically.Therefore,compared with the periodic sampling control system,under the action of event-triggered mechanism,the average sampling period of the system is longer,that is,the state sampling frequency of the system is slower,and the corresponding controller update frequency will be slower,so event-triggered mechanism can reduce the use of system hardware computing resources.The optimal control theory can minimize the control input of the system under the preset cost function,so in the optimal control theory,the control input of the system can be obtained by using the minimum principle to realize the design of the system controller.In this paper,an appropriate optimal controller is designed under the event-triggered mechanism to control the whole closed-loop system,in which the design methods of the event-triggered mechanism or self-triggering mechanism are discussed respectively,and then the optimal controller of the system is obtained by the linear quadratic method,and then the stability of the system is analyzed.It is further divided into event-triggered optimal,self-triggered optimal control and event-triggered optimal control based on state observer.The details can be described as below:Firstly,combined with the optimal control theory,the design method of linear quadratic optimal controller for linear systems based on event-triggered mechanism is studied.In the aspect of controller design,given the performance index functional that makes the system reach the equilibrium point from the initial state,the optimal feedback controller of the system is solved by the minimum principle,and in the part of event-triggered mechanism,a triggering condition is given to make the closed-loop system reach input-state stability(ISS).Then the dynamic event-triggered condition is introduced to further reduce the sampling times,and then it is proved that there is no Zeno behavior in the system.Finally,it is verified by MATLAB simulation.Secondly,based on the event-triggered optimal control method,a self-triggeringcondition is designed,and the corresponding linear quadratic optimal controller is obtained by using the optimal control theory.In the stability analysis,it is proved that under the event-triggered and self-triggered optimal control,the system can be stable and has no Zeno behavior.Then the simulation analysis is carried out by MATLAB,and the two control methods used are compared and analyzed,which proves the advantages of self-triggered control compared with event-triggered control.Finally,in order to solve the problem that the state may be unmeasurable in the actual physical system,an event-triggered optimal control method based on state observer is proposed.Firstly,the control system with state observer is modeled and analyzed,then combined with the optimal control theory,by setting the performance index to make the system reach the equilibrium point from the initial state,the linear quadratic optimal optimal control law of the system is obtained according to the minimum principle.Then,the corresponding event-triggering condition are given,and two sufficient conditions are obtained to ensure the asymptotic stability of the control system and the observer error system.Finally,a specific example is given,and the simulation analysis is carried out by MATLAB.