Experiment design for the identification of a simple Wiener system

Results on experiment design for the identification of nonlinear systems are extremely scarce. This paper examines the identification and optimal input design for a very simple nonlinear system: a Wiener system composed of a Finite Impulse Response (FIR) system followed by a power nonlinearity: (.)ⁿ. We first show that an expanding power (n >; 1) increases the information about the estimated parameters, while a compressing power (0 <; n <; 1) decreases the information. We then formulate a simple optimal input design problem for the considered class of Wiener systems and show that solutions can be computed by restricting the class of considered input signals. We provide a solution which offers some intuitive insights for the case of a FIR(2) system with a square nonlinearity and where the inputs are restricted to be Gaussian.