Recursive Parameter Estimation Of Two-inputs Output-error Bilinear Parameter System

In industrial processes,most of the systems are nonlinear systems and the parameter estimation of nonlinear systems has been widely concerned.The output error bilinear parameter system is a special kind of nonlinear system which has been used in engineering practice.Based on the least square algorithm and gradient algorithm,this paper uses the hierarchical identification principle,multi-innovation identification theory and data filtering technology to study the recursive parameter estimation problem of a two-input output-error bilinear parameter system.The main work is as follows:(1)For the two-inputs output-error bilinear parameter system,the original system is decomposed into three subsystems using the decomposition technology: the first subsystem contains unknown parameters related to the first input,the second subsystem contains unknown parameters related to the second input,and the third subsystem contains unknown parameters related to the noise model.Combining the least squares search principle,a hierarchical recursive least squares algorithm is given.(2)For the two-inputs and output-error bilinear parameter system,combined with the hierarchical identification principle,the forgetting factor is introduced to further improve the parameter estimation accuracy.Using the multi-innovation identification theory,the scalar innovation is expanded into innovation vector,making full use of the known data.Based on the negative gradient search principle,a hierarchical forgetting factor multi-innovation stochastic gradient algorithm is presented.(3)For the two-inputs and output-error bilinear parameter system,the data filtering technology is adopted to filter input and output data,change the system structure,and change the autoregressive moving average noise into moving average noise.Combining the auxiliary model idea,using auxiliary model outputs instead of unknown intermediate variables,a filtering-based hierarchical forgetting factor multi-innovation stochastic gradient algorithm is proposed.The paper presents a variety of parameter estimation algorithms and numerical simulations which verify the effectiveness of the algorithms for a two-inputs outputerror bilinear parameter system.