ILC-based Generalised PI Control for Output PDF of Stochastic Systems Using LMI and RBF Neural Networks

In this paper, a fixed-structure iterative learning control (ILC) control design is presented for the tracking control of the output probability density functions (PDF) in general stochastic systems with non-Gaussian variables. The approximation of the output PDF is firstly realized using a radial basis function neural network (RBFNN). Then the control horizon is divided to certain intervals called batches. ILC laws are employed to tune the PDF model parameters between two adjacent batches. A three-stage method is proposed which incorporates: a) identifying nonlinear parameters of the PDF model using subspace system identification methods; b) calculating the generalised PI controller coefficients using LMI-based convex optimisation approach; and c) updating the RFBNN parameters between batches based on ILC framework. Closed-loop stability and convergence analysis together with simulation results are also included in the paper