Gradient descent optimisation for ILC-based stochastic distribution control

Stochastic distribution control (SDC) for non-Gaussian system is a mathematically complicated yet practical problem to solve. The most recent solution involves a radial basis function neural network (RBFNN) framework to approximate non-Gaussian output probability density function (PDF). The dynamic weights of such neural network are controlled within each batch of ILC, using a dedicated adaptive controller. Then, between adjacent batches, an iterative learning control (ILC) algorithm is applied to tune RBFNN centres and widths. The most practical ILC-based SDC applications use sum of squared PDF tracking errors (calculated within each batch of ILC) to tune RBFNN parameters through so called P-type ILC laws. This paper first analyses the practical disadvantages of P-type ILC laws to use in SDC applications which include robustness, sensitivity, and operational problems. Then, based on the gradients of squared PDF tracking errors (calculated within batches), it develops a new ILC-based non-Gaussian stochastic control. Simulation results demonstrate the effectiveness of proposed gradient descent optimisation method for non-Gaussian stochastic distribution control.