Iterative Estimation Of Parameters And States For Bilinear Systems

In the field of industrial process control,nonlinear phenomena widely exist,and the identification of nonlinear systems is a concern in this field.Bilinear systems are a type of nonlinear system with a special structure,between linear systems and nonlinear systems.Bilinear systems are widely used in actual industrial processes.For example,in fields such as fluid heat exchange and nuclear fission,bilinear systems can be described.This paper studies the iterative estimation of parameters and states of bilinear state space systems under random interference.The topic has important theoretical significance and practical value,and the research results have reference significance for further research on the identification of nonlinear systems.The following is the main research content of this article.1.For bilinear state space systems under the influence of white noise disturbances,there are unknown parameters and unknown states,as well as their product terms(bilinear terms)with control variables.The difficulty lies in simultaneously identifying the parameters and states of the system.By employing the principles of interactive estimation theory,when identifying system parameters,the algorithm substitutes the unknown states with their previous iterative estimates.Based on the obtained parameter estimates,a bilinear state estimator is constructed,and a moving data window least-squares based iterative algorithm based on the bilinear state estimator is proposed.To further reduce computational complexity,using the hierarchical identification principles and block matrix inversion,a hierarchical moving data window least-squares based iterative algorithm and a moving data window least-squares based iterative algorithm based on matrix decomposition are proposed.2.For bilinear state space systems that are interfered by colored noise,the challenge is that colored noise has great influence on parameter and state estimation,so improving the estimation accuracy is the key.In order to reduce the impact of colored noise on parameters and state estimation,data filtering technology is used to establish filters to filter the input and output data of the system,and simultaneously identify system parameters and data filter parameters.Building upon this foundation,we have introduced the filtering based extended gradient-based iterative algorithm and the filtering based moving-data-window gradient-based iterative algorithm.These algorithms have the potential to enhance the accuracy of parameter estimation.3.For bilinear state space systems that are disturbed by both process noise and measurement noise,the challenge is to deal with the dual interference of process noise and measurement noise,and propose a more robust identification algorithm.An expectation maximization algorithm is derived to identify bilinear systems by using unknown states as hidden variables.Specifically,the Rauch-Tung-Striebel(RTS)smoother is proposed to performs state estimation in the expectation step.In the Maximization step,numerical optimization is used to update the parameter estimates.This results an expectation maximization algorithm based on RTS smoother to simultaneously estimate the state and parameters of the system.4.For distributed parameters and state estimation of bilinear state space systems,it is necessary to consider how to decompose subsystems.By augmenting parameters to state vectors as virtual states,a method based on sensitivity analysis is proposed to check the observability of the system and distinguish which state and parameter variables are important to the dynamics of the system,and then select estimable states and parameters.For the augmented system,an approach based on community structure detection is proposed to determine the optimal subsystem decomposition,where states,parameters,and measurement outputs are treated as nodes in a network.Building upon the results of subsystem decomposition,a distributed moving horizon estimation method is put forward for simultaneous estimation of states and parameters.The paper conducts numerical simulations on the proposed iterative estimation algorithm of parameters and states.Part of the algorithm is applied to actual models such as neutron dynamics model,thyristor-driven DC motor,and continuous stirred tank reactor to verify the effectiveness of the algorithm.Some algorithms have been compared in terms of computational cost.