Modeling and Control for 3D Output Stochastic Distribution System Based on 2D PDF Models

This paper presents a novel modeling and control method for 3D output probability density function (PDF) of stochastic distributed systems. Firstly, considering the boundary constraints of the output PDF, linear B-spline functions are used to approximate the PDF of the system output variables, and the linear dynamic models of the X-axis and Y-axis are established respectively. Afterwards, on the basis of the 2D PDF models, a 3D PDF model is established. A controller is designed by optimizing the quadratic performance index, which makes the output PDF track the desired PDF effectively. Finally, an example is used to illustrate the effectiveness of the algorithm, and the expected results are achieved.