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Summary This paper considers a block‐oriented nonlinear Wiener system that consists of a linear block with real time‐varying unknown coefficients and pure time delay followed by a static invertible nonlinearity. Consideration is concentrated on the joint linear block coefficients and time delay tracking by processing observation samples. Two problems are analyzed. The first one is the avoidance of mean‐squares prediction error function multiextremality for time delay while seeking the global minimum. The other problem consists of the applicability of unified adaptive algorithms, based on the schema with corrective operators for the Wiener system. An approach used to transform the multiextremal criterion into a unimodal function for a nonstationary linear system, in respect of the time delay, is developed and analyzed for a block‐oriented nonlinear Wiener system with time‐varying coefficients and a time delay. The recursive parametric identification approach, based on the method of corrective operators, is developed for the nonstationary dynamic Wiener system. Applicability of algorithms is supported by various simulation tests solved by a computer.

SUMMARYThe aim of the present paper was to increase the efficiency of self‐tuning minimum variance (MV) control of linear systems followed by the so‐called hard nonlinearities. To this end, an approach based on reordering of observations to be processed for the reconstruction of an unmeasurable internal intermediate signal, which acts between a linear dynamic time‐invariant (LTI) system and a static nonlinear block of the closed loop Wiener system with a saturation nonlinearity in an output, has been developed. The technique based on the ordinary least squares and on data partition is used for the internal signal extraction. The results of numerical simulation, identification, and self‐tuning MV control as well as generalized MV control of the second‐order discrete‐time closed loop LTI system with the saturation nonlinearity are given by the computer. Copyright © 2012 John Wiley & Sons, Ltd.

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