Weighted multi-innovation extended stochastic gradient identification for multivariable Hammerstein nonlinear systems based on multi-signal processing

Multivariable Hammerstein nonlinear systems contain a sum of some bilinear parameter functions, which is hard to convert into a standard regressive form for processing. The identification system can be converted into two different regressive forms by using multiple sets of binary signals. By combining the multi-innovation theory with the weight matrix, a weighted multi-innovation extended stochastic gradient algorithm with a forgetting factor is presented to estimate the parameters of parallel nonlinear subsystems and a linear subsystem. The advantage of the proposed algorithm is that it achieves faster convergence rates and higher accurate estimates than hierarchical principle based extended stochastic gradient algorithm and over-parameterization based extended stochastic gradient algorithm. Examples of CSTR process and PV power generation system are provided respectively to demonstrate the feasibility of the identification algorithm. This indicates that the prediction accuracy of the proposed algorithm can be improved by weighting the innovation.