Enhanced predictive PDF control of stochastic distribution systems with neural network compensation and its application

Abstract

Compared to the conventional control algorithms that use mean and variance as indicators, predictive probability density function (PDF) control can effectively handle the output PDF control problem of non-Gaussian stochastic distribution systems. However, the existing predictive PDF control method does not consider the construction error between output PDF and weight, thus the control performance is still unsatisfactory. Therefore, this paper proposes a new Enhanced Predictive PDF control method (En-PDF) to improve the output PDF control performance of stochastic distribution systems. The proposed method mainly consists of two parts: the predictive PDF control part and the neural network compensation control part aiming to reduce the bias of output PDF. First, the Radical Basis Functions (RBFs) are used to approximate the PDF of the stochastic systems output, and then a prediction model representing the relationship between input and weight is established using the subspace identification algorithm to design the predictive PDF control for the stochastic systems. Next, the Kullback-Leibler (KL) divergence is used to measure the similarity between the output PDF and the set PDF, combined with the weight error and compensation to design a new performance index. Based on this, the parameters of the neural network are adjusted using the gradient descent algorithm to obtain the optimal compensation, and the stability and tracking performance of the proposed algorithm are analyzed using inductive reasoning method. Finally, the predictive PDF control input with the compensation work together on the controlled plant to achieve high-performance control of the output PDF of non-Gaussian stochastic distribution systems. Both simulation experiments and physical control experiments validate the effectiveness and superiority of the proposed method.