Research On Nonlinear Filtering For Nonlinear Systems With Uncertainty

In practical applications,factors such as the environment in which the control system is located changes,the environment in which the system is located is very complex,or external disturbances during system operation can lead to problems such as nonlinear uncertain dynamics,uncertainty in noise statistical characteristics,abnormal measured values,and uncertainty in system parameter models,which can lead to uncertainty in system.In addition,the problem of excessive measurement transmission that can degrade the lifetime of the sensor is considered.Moreover,with the increasing demand for control accuracy,the accuracy of state estimation for single sensor systems cannot meet some applications.Therefore,how to perform fusion estimation for multiple states of multi-sensor systems and what type of fusion strategy to sample have become increasingly important research directions in system state estimation.Based on the existence of the above problems in nonlinear control systems,this paper designs a series of nonlinear filtering algorithms and state fusion estimation algorithms based on unscented Kalman filter(UKF)algorithm.The specific research results and content are as follows:Firstly,the nonlinear filtering problem for a class of systems with uncertain dynamics and noise is studied.For uncertain dynamics,the uncertain dynamics are expanded to a new state that can be estimated in real time through the method of expanding the state.For measurement noise with uncertain statistical characteristics,covariance matching technology is used to estimate the covariance of measurement noise in real time and online.Then,an adaptive extended state unscented Kalman filtering algorithm is designed by combining the extended state system and covariance matching technology with the unscented Kalman filtering algorithm.The sufficient conditions for ensuring the stability of the designed filter are given through analysis.Secondly,the problem of event-triggered nonlinear filtering for a class of systems with measurement outliers is studied.An event-triggered transmission scheme based on Send-on-Delta is introduced to minimize the impact of measurement anomalies on the event-triggered transmission scheme while reducing unnecessary measurement data transmission.Then,the adaptive saturation function is used to process the information affected by the measurement outliers.An eventtriggered unscented Kalman filtering algorithm with adaptive saturation function is designed considering the impact of event-triggered transmission scheme and measurement outliers.Then,analyzing the convergence of the filter gives sufficient conditions to ensure that the estimation error covariance has an upper bound.Finally,considering the event-triggered distributed fusion estimation problem when the model of a multi-sensor system is unknown.Using Gaussian Process Regression(GPR)in machine learning,the nonparametric Gaussian process model of multi-sensor systems is learned offline from the collected training data.For each transmission channel,a controllable random event-triggering transmission scheme is introduced to reduce excessive measurement data transmission.Combining Gaussian process model with unscented Kalman filtering algorithm and considering event-triggered transmission scheme,an event-triggered unscented Kalman filtering algorithm based on Gaussian process is designed.Then,based on the sequential covariance insertion fusion strategy adopted by the fusion center,an event-triggered sequential covariance insertion fusion estimation algorithm based on Gaussian process is designed.Finally,sufficient conditions are given to ensure the convergence of the designed algorithm.