Research On State Estimation Of Nonlinear Systems Based On Robust Ideas

State estimation refers to the accurate estimation and judgment of the internal state in the dynamic system according to all the measurement data that can be collected in the system.The information obtained by measuring each input or output of the whole system can only directly reflect the external attributes of the whole system,and each dynamic law of the system needs to be composed of and described by internal state variables.For most systems,when measuring internal state variables,the cost is high or cannot be measured directly.In real life,nonlinear system exists in the actual industrial system,and the state estimation of nonlinear system has been widely studied.Particle filter and extended Kalman filter are the main methods applied to state estimation of nonlinear systems in recent years.However,these filters are not ideal for the system with high nonlinear degree.Therefore,considering the nonlinear degree of the system and the efficiency or simplicity of the calculation is an important topic in the field of state estimation of nonlinear systems.Firstly,two robust state estimation algorithms for linear systems are introduced,which consider the uncertainty of the system and make up for the sensitivity of the traditional Kalman filter to the system model error,and the computational complexity of the two algorithms is equivalent to that of the traditional standard Kalman filter.The first robust state estimation algorithm based on the minimum expected value of estimation error considers the correlation between Kalman filter and regular least squares,and achieves the purpose of state estimation by calculating the expected matrix off-line.The other is a robust state estimator based on sensitivity penalty.This state estimator is asymptotically unbiased when there is no external input.In addition,the estimation error variance is still bounded when there is a definite input signal.The simulation results show the advantages of the two robust state estimators for uncertain linear systems.Secondly,the proposed robust state estimator based on the minimum expected value of estimation error is applied to a nonlinear system described by T-S fuzzy model for state estimation.The model error caused by the uncertainty of the system parameters is considered,which will have any form of influence on the system.Then,the robust filter algorithm is combined with the fuzzy model,and the nonlinear system is approximately expressed by fuzzy rules,and the new algorithm is used to estimate the state of the system.Finally,numerical simulation experiments are used to compare the state estimation results of the new algorithm with those of the fuzzy Kalman filter.The experimental results show that the robust filter is superior to the fuzzy Kalman filter.Thirdly,the problem of state estimation for nonlinear systems by polynomial approximation is considered.The polynomial of given order is used to approximate the original nonlinear system,and the lower order polynomial with parameter uncertainty is used to describe the higher order approximation term.Considering that the model error will affect the system model in any form for the polynomial system,and combining with the robust state estimation algorithm based on sensitivity penalty,the problem of state estimation for polynomial approximation time-varying systems with model errors is studied.Then,the analytical expression of the proposed robust filter is similar to that of the Kalman filter,which indicates that the proposed algorithm can be implemented recursively.The numerical simulation results show that the new robust filter has good performance in the state estimation of nonlinear systems,and can be widely used.