Maximum Likelihood-Based Recursive Identification For Multivariable Equation-Error Systems

With the development of industrial technologies,most industrial processes are essentially multivariable systems with complex structures.Due to the disturbance of colored noises,the identification of multivariable systems becomes more and more difficult.The maximum likelihood identification is an estimation based on the probability and statistics principle and the estimates have good statistical characteristics.Thus the maximum likelihood identification is applied in multivariable system identification.The thesis considers the identification problems for multivariable equation-error systems with colored noises by utilizing the maximum likelihood principle.The major results are as follows.(1)For the linear multivariable equation-error system with mutual interference,the multivariable system is decomposed into several subsystems with lower dimensions and fewer variables.By applying the maximum likelihood principle,decomposition-based maximum likelihood recursive identification methods are derived for the submodels.A decomposition-based maximum likelihood multi-innovation extended stochastic gradient identification algorithm with improved parameter estimation accuracy is proposed by applying the multi-innovation identification theory.(2)For the linear multivariable equation-error system in which the noise model is a moving average process,the coupling identification concept is used to avoid the redundant parameter problem caused by Kronecker product operation,and coordinate the coupling relationship of some parameter vectors among subsystems.The coupled maximum likelihood recursive identification algorithms are presented for the identification model of the subsystems,and the accuracy of parameter estimation is improved.Moreover,the proposed algorithms are extended to the multivariable input nonlinear equation-error systems with colored noise model as scalar polynomials.(3)For the linear multivariable equation-error system in which the noise model is an autoregressive moving average process,a linear filter is introduced.By filtering the observation data without changing the input-output relationship of the systems,the filtering-based maximum likelihood recursive identification algorithms are presented,the parameter estimation accuracy is improved,and the redundant parameter problem caused by Kronecker product operation is avoided.(4)For the multivariable input nonlinear equation-error system in which the noise model is a moving average process,the key-term separation method is used to separate the parameters of the nonlinear blocks from the parameters of the linear blocks.By using the hierarchical identification principle,the subsystem identification model is decomposed into two fictitious sub-subidentification models,and the key term separation-based maximum likelihood recursive identification algorithms are presented to estimate the parameters of the two sub-submodels interactively.Some numerical simulation examples are provided to verify the effectiveness of each proposed method,and the simulation results of some algorithms are analyzed and compared.