Recasted models‐based hierarchical extended stochastic gradient method for MIMO nonlinear systems

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.