Complex stochastic systems modelling and control via iterative machine learning

Complex stochastic systems require the control of their stochastic distributions (i.e., the shape of their output probability density functions (PDFs)). This paper will address both modelling and control of such systems and will consist of a brief survey of the recent developments and the description of a detailed design procedure on an iterative learning-based output PDF control algorithm. In this context, a radial basis function (RBF) neural network is used to approximate the output PDFs, and the system dynamics is represented by a mathematical model between the weights of the RBF neural networks and the control input. The whole control horizon is divided into a number of batches, where within each batch fixed RBFs are used. However, between batches, iterative machine learning for the shape update of the RBFs is developed so as to improve the closed loop performance batch-by-batch. A simulated example is given so as to demonstrate the design procedure.