A Novel Data-Based Stochastic Distribution Control for Non-Gaussian Stochastic Systems

This article presents a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this article, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimization problem. Then, data-based direct optimization and identification-based indirect optimization have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this article are as follows: 1) a new data-based probability density function transformation is given; 2) the optimization algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing stochastic distribution control.