Data-driven design and implementation of an alternately adaptive residual generator for Hammerstein systems

This paper addresses the data-driven design and implementation of an adaptive observer-based residual generator for Hammerstein systems. The basic idea behind this study is the application of a one-to-one mapping between a parity vector and the solution of Luenberger equations, the identification of the parity space and the Hammerstein nonlinearity via the over-parameterization and least squares support vector machine (LS-SVM). For the realization of adaptivity, the linear and nonlinear parameters are separated and estimated recursively in a parallel manner, with each updating algorithm using the most up-to-date estimation produced by the other algorithm at each time instant. Hence the procedure is termed the alternately adaptive algorithm. Furthermore, the stability condition of algorithm is investigated.