Recursive Identification Methods For Multivariable Equation-error Systems Based On Decomposition

Multivariable systems exist widely in industrial control and applications,and they can more accurately describe the characteristics of objects than SISO systems.Multivariable systems have complex structures and numerous parameters.The identification of multivariable systems is a research hotspot and has important theoretical significance and broad application prospects.This thesis focuses on the recursive identification algorithms for multivariable equation-error systems based on decomposition.The main contents are as follows:1.For the multivariable equation-error system disturbed by white noises,based on theprinciple of least squares,a recursive least squares(RLS)algorithm with high pa-rameter estimation accuracy is derived.By using hierarchical identification theory,a decomposition-based recursive least squares(D-RLS)algorithm is proposed.Bycomparing the computation amount of two algorithms,it can be seen that the D-RLSalgorithm has less computation amount.2.For the multivariable equation-error system disturbed by white noises,using neg-ative gradient search,a stochastic gradient(SG)algorithm is proposed.Then themulti-innovation theory is introduced to derive a multi-innovation stochastic gradient(MISG)algorithm,which improves parameter estimation accuracy.Then,combin-ing with hierarchical identification theory,a decomposition-based stochastic gradient(D-SG)algorithm and a decomposition-based multi-innovation stochastic gradient(D-MISG)algorithm are obtained.3.For the multivariable equation-error system disturbed by colored noises,namely themultivariable equation-error autoregressive moving average system with the autore-gressive moving average noises.With the help of hierarchical identification theory,theoriginal identification model is decomposed into a system model and a noise model.The decomposition-based recursive generalized extended least squares(D-RGELS)algorithm is obtained,and it has close parameter estimation accuracy with recursivegeneralized extended least squares(RGELS)algorithm but has lower computationalburden.4.For the multivariable equation-error autoregressive moving average system,along hi-erarchical identification ideas,a decomposition-based generalized extended stochasticgradient(D-GESG)algorithm is derived.By introducing the multi-innovation theo-ry,a decomposition-based multi-innovation generalized extended stochastic gradient(D-MIGESG)algorithm with high parameter estimation accuracy is obtained.For all the algorithms proposed above,this thesis gives the derivation steps,flowcharts and simulation examples.In order to illustrate the effectiveness of these algorithms,the calculation burden and parameter estimation accuracy are compared.Finally,the thesis draws conclusions and prospects.After that,a brief introduction to the difficulties faced by the identification of multivariable systems and the directions worthy of further study are given.