Research On The Designs Of Impulsive Observers For Nonlinear Systems

In the field of nonlinear control,the research of observer is a very important and meaningful direction.In 2007,the German scholar Raff first proposed the concept of impulsive observer in order to realize the state estimation of the system by using the sampling of the system output at the discrete time,so as to improve the bandwidth utilization rate in the network control background.In recent years,scholars have made a lot of achievements in the research of impulsive observer,but still face some problems to be solved.In view of the research status of impulsive observer,this paper mainly studies the following problems: the design of impulsive observer controlled impulsive control,the design of impulsive observer which can eliminate unknown input,and the design of impulsive observer via event-triggered impulsive control.These problems related to impulsive observer are the international frontier of control science,which can be applied in robot intelligent control,military weapon system tracking control and so on.The main works include the following aspects:Firstly,based on impulse stabilization,the design problem of impulsive observer for impulsive nonlinear systems is studied.Through Lyapunov stability theory analysis and demonstration,the stability criteria for estimating the tracking state to the original system and the asymptotic convergence of the error system are obtained.Then,by using the average dwell time condition and the linear matrix inequality method,the gain matrix design method of the impulsive observer is obtained.Finally,the feasibility and effectiveness of the designed impulsive observer are verified by MATLAB numerical simulation.Secondly,we discuss the design of an impulsive observer for nonlinear systems with unknown inputs or external disturbances.An appropriate observer model is constructed to obtain the error system model.An appropriate Lyapunov functional is constructed by using Lyapunov stability theory,linear matrix inequality(LMI)and average dwell time conditions.The asymptotic stability criterion of the error system is obtained to realize the tracking of the original system by the observer.Finally,the feasibility and effectiveness of the proposed design method are verified by numerical simulation with MATLAB.Thirdly,in order to overcome the problems of the observer via time-based classic impulsive control such as high impulse frequency,an extremely strong control strength,etc.The issue of impulsive observers via event-triggered impulsive control for continuous-time dynamical system(CDS)is proposed.In the article observer model is given,then the error model is obtained,by using Lyapunov stability theory,event-triggered impulsive control method,designed the three levels of event condition,asymptotic stability criterion of error system is obtained.Finally,the feasibility and effectiveness of the proposed method are verified by numerical simulation with MATLAB.