APPROXIMATE GRADIENTS, CONVERGENCE AND POSITIVE REALNESS IN RECURSIVE-IDENTIFICATION OF A CLASS OF NONLINEAR-SYSTEMS

Recursive identification algorithms based on the Wiener model are pres ented in this paper. They estimate the parameters of a SISO linear dyn amic block in cascade with a known static output non-linearity. Invers ion of the non-linear function is avoided and approximations of gradie nts are utilized. This allows an exact treatment of output measurement saturation and of situations where output measurements are obtained f rom sensors with relay-type characteristics, such as EGO sensors in em ission control systems for cars. Exact compensation for coarse quantiz ation of output measurements can also be obtained by the algorithms. S tochastic averaging techniques using associated differential equations prove that local and global convergence of the schemes are tied to po sitive realness and sector conditions on the non-linearity. Conditions for local convergence to the correct parameters are established for t he case where the output non-linearity is an arbitrary quantizer.