
For the identification of a class of nonlinear multi‐input multi‐output (MIMO) Hammerstein systems with different types of coefficients: a matrix coefficient and scalar coefficients, it is difficult to parameterise such Hammerstein systems into an identification model to which the standard identification method can be easily applied to implement parameter estimation. By the matrix transformation and the over‐parametrisation idea, this study transforms an MIMO Hammerstein system with different types of coefficients into an over‐parametrisation regression identification model, and points out the aroused large computation problem. To overcome the large computational load of the over‐parametrisation method, by the matrix transformation and the hierarchical identification principle, this study recasts the MIMO Hammerstein system into two models, each of which is expressed as a regression form in the parameters of the nonlinear part or in the parameters of the linear part. Then a hierarchical extended stochastic gradient algorithm is presented to alternatively estimate the parameters of the nonlinear part and the parameters of the linear part. The simulation results indicate that the proposed algorithm can effectively identify the nonlinear MIMO Hammerstein system.
computational load, scalar coefficients, nonlinear parameters, nonlinear control systems, regression analysis, MIMO systems, hierarchical systems, Nonlinear systems in control theory, Stochastic systems in control theory (general), System identification, identification model, linear systems, Multivariable systems, multidimensional control systems, matrix algebra, hierarchical identification principle, nonlinear MIMO Hammerstein system, Hierarchical systems, recasted model-based hierarchical extended stochastic gradient method, matrix coefficient, nonlinear multiinput multioutput Hammerstein systems, linear parameters, stochastic processes, nonlinear implement Hammerstein systems, parameter estimation, matrix transformation, over-parametrisation regression identification model, gradient methods
computational load, scalar coefficients, nonlinear parameters, nonlinear control systems, regression analysis, MIMO systems, hierarchical systems, Nonlinear systems in control theory, Stochastic systems in control theory (general), System identification, identification model, linear systems, Multivariable systems, multidimensional control systems, matrix algebra, hierarchical identification principle, nonlinear MIMO Hammerstein system, Hierarchical systems, recasted model-based hierarchical extended stochastic gradient method, matrix coefficient, nonlinear multiinput multioutput Hammerstein systems, linear parameters, stochastic processes, nonlinear implement Hammerstein systems, parameter estimation, matrix transformation, over-parametrisation regression identification model, gradient methods
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