Extremal control of Wiener model processes

Extremal control of Wiener type processes is considered. These models consists of a linear part followed by a static nonlinearity. We consider nonlinearities having one extremum point. The purpose is to keep the output of the process as close as possible to the extremum point. The main problem in the control of this kind of processes is the non-uniqueness of the inverse of the nonlinearity. This causes problems, e.g., in the estimation of the states of the process and identification in the adaptive case. A one-step-ahead controller combined with a probabilistic estimator is proposed and analyzed.