Iterative Parameter Estimation Methods For Two-input Nonlinear Equation Error Systems

With the continuous advancement of industrial control technology requirements and control theory,the research of nonlinear systems has received more attention.Due to the application of more nonlinear models in actual industrial processes,the study of nonlinear system identification has important theoretical and practical value.In this paper,the problem of parameter identification for the two-input nonlinear equation error system is proposed.On the basis of consulting and researching relevant literatures,the following research results were obtained:First,the research object of this thesis is the error system of two-input nonlinear equations.According to the expression form of the nonlinear system,the parameter vector and the information matrix are defined.When discussing the interference of white noise or colored noise,the identification model of two-input nonlinear equation error system can be obtained separately.Second,for a two-input nonlinear finite impulse response system,based on the principle of hierarchical identification,the model to be identified is decomposed into two sub-models,and the two sub-models are identified by the least squares iterative method and the gradient iterative method respectively.The unmeasured noise contained in the information vector is replaced with its estimated value,and the hierarchical least squares iterative algorithm and the hierarchical iterative algorithm for the two-input nonlinear finite impulse response system are derived.Third,for the dual-input nonlinear controlled autoregressive model,the identification model of the model is derived,and on this basis,the recursive least squares algorithm and the recursive step gradient iterative algorithm are derived.Simulation examples show that the error between the identification results of the two algorithms and the true value is declining,indicating the effectiveness.Fourth,for the two-input nonlinear controlled autoregressive moving average model,considering the addition of colored noise,first of all,according to the idea of hierarchical identification,the original more complex system is decomposed into two subsystems and each subsystem is identified separately.The least square iterative method and the gradient iterative method were used to identify the two-input nonlinear controlled autoregressive moving average model.The recursive least squares iterative algorithm and recursive stepwise iterative algorithm were derived,and the two examples were respectively illustrated the effectiveness of the algorithm by simulation examples.In summary,the least squares iterative identification method and gradient iterative method are studied for the three error models of the two-input nonlinear equations.The effectiveness of the algorithm is obtained through simulation comparison.Finally,the paper gives a summary and outlook,and gives a brief introduction to some of the difficulties and deficiencies faced by the algorithm research mentioned in this article.