Radial Basis Function based Iterative Learning Control for stochastic distribution systems

In this paper, an Iterative Learning Control (ILC) scheme is presented for the control of the shape of the output probability density functions (PDF) for a class of stochastic systems in which the relationship between approximation basis functions and the control input is linear, and the stochastic system is not necessarily Gaussian. A Radial Basis Function Neural Network (RBFNN) has been employed for the output PDF approximation and the coefficients of the approximation are linearly related to the control input. A three-stage method for the ILC-based PDF control is proposed which incorporates a) identifying PDF model parameters; b) calculating the control input; and c) updating RFBN parameters. The latter is accomplished based on P-type ILC law and the difference of the desired and calculated output PDF within a batch. Conditions for the convergent ILC rules have been derived. Simulation results are included to demonstrate the effectiveness of proposed method.