Iterative learning control for Hammerstein-Wiener Systems

The iterative learning control(ILC) is considered for the Hammerstein-Wiener System, which is a cascading system composed of a static nonlinearity followed by a linear dynamic system and then again by a static nonlinearity. Besides, both the system noise and the measurement noise are taken into account. Under the tracking performance, the optimal control is first expressed, and then by using the system outputs and the objective trajectory, the ILC is constructed on the basis of the stochastic approximation algorithm. It is proved that the designed ILC converges to the optimal control with probability 1 and the tracking error tends to the minimal value.