Event-triggered Identification Of Linear Set-valued Systems

In today's era,with the development of networked communication and in-formation technology,set-valued systems have been widely utilized in practical ap-plications in industry and life,especially in the fields of digital signal transmission,smart sensor networks,and biological medicine,etc.,which closely connects with modern life.With the continuously increasing requirement of data transmission in networks,the event-triggered communication scheme is a typical solution with historical background for saving communication resources,as we remotely estimat-ing system parameters in a networked environment.However,the event-triggered strategy destroys the integrity of observed data.In addition,the set-valued obser-vation results in the relationship between the obtained measurement data and the system output is essentially nonlinear.All these characteristics bring difficulties to the design of identification algorithms and the analysis of convergence properties.For the linear set-valued systems,this thesis studies the system parameter es-timating problem,under the condition that the set-valued observations of system outputs are transmitted through the network with an event-triggered scheme.Based on empirical measure and stochastic approximation methods,the system parameter estimation algorithms and corresponding event-triggered mechanisms are designed.Besides,by adopting the theory of the Bayesian formula,the law of large numbers and the martingale convergence theorem,properties of the proposed algorithms,in-cluding the convergency of the algorithm,the convergence speed,the asymptotic efficiency and the communication rate are analyzed.The main content and results of this thesis include the following aspects:(1)For the linear finite impulse response systems with whose outputs are sub-ject to both the binary-valued observation and the scheduling communication scheme,a parameter estimation algorithm is designed under periodic inputs.The strong convergency of this algorithm is established,the mean-square convergence rate of the estimate error is given.Combined with its Cramer-Rao lower bound,it is proved that the algorithm is asymptotically efficient.The communication rate of this method is derived as well.(2)This thesis also introduces the concept of event-triggered identification for the binary-valued finite impulse response system identification based on the event-triggered communication mechanism.A recursive identification algorithm is pro-posed based on the a priori information of system parameters and statistical prop-erties of the noise.The strong convergency and convergence rate of the algorithm are proved under a class of persistently exciting inputs conditions,and the commu-nication rate of the algorithm is discussed.(3)An event-triggered communication mechanism called the either-or com-munication scheme is proposed for the identification of finite impulse response systems with binary-valued observations.By taking full advantage of the received data,the trigger indicators,and the trigger conditions,an auxiliary sequence can be constructed to recover the set-valued observations.The estimation algorithms of unknown parameters are given for both the binary-valued and the multi-threshold set-valued observation situations,respectively.The convergence property of the algorithm is analyzed based on the strong law of martingale difference sequences,and the communication rate as well as other properties of the algorithm are both obtained.(4)An event-triggered mechanism based on the prediction was proposed,com-bined with the empirical-measure-based identification method and the weighted least squares optimization,an identification algorithm is proposed to estimate the unknown parameters by full use of the received data,the trigger condition,the thresholds of set-valued observations,and the information in the statistical prop-erty of the system noise.The convergency of the algorithm,the convergence speed,the asymptotic efficiency,and how to balance the communication burden and the estimate performance of the algorithm,as well as how to calculate the average rate of communication are analyzed.(5)On the basis of the above research,a deviation compensation method is proposed,where the estimation deviation is caused by the packet loss in the event-triggered communication part of the set-valued system identification.The algo-rithm's unbiasedness,convergency and the communication rate before and after channel are studied theoretically and verified through numerical simulations.