Robust Iterative Learning Control of Output PDF in Non-Gaussian Stochastic Systems Using Youla Parametrization

In this paper a robust iterative learning control (ILC) based control strategy is proposed for the shape control of the output probability density functions (PDF) for dynamic stochastic systems subjected to non-Gaussian variables. Using the radial basis function neural network (RBFNN) approximations to instant output PDFs, the output PDF tracking problem has been reduced to the weight control of the neural network. Furthermore, by separating the whole control horizon into certain number of the time domain sub- intervals called Batches, a control algorithm is established where the Youla parametrization technique has been used together with a proportional plus differential (PD) version of the ILC. The proportional part of the ILC law looks after the tuning of the RBFNN basis function parameters (i.e., the RBF centers and widths) whilst the differential part of the ILC law is used to tune the parameters of Youla-parameterized controller so that the closed-loop output PDF tracking performance is improved versus the advances of batches along the time horizon. The analysis on the proposed ILC convergence is made and demonstrable simulation results are also provided to show the effectiveness of the obtained control algorithm.