PI Tracking Control with Mixed H2 and H∞ Performance of Descriptor Time Delay System for Output PDFs Based on B-Spline Neural Networks

This paper presents a robust PI tracking control strategy with mixed H2 and H∞ performance for general non-Gaussian systems based on the square root B-spline model for the probability density functions (PDFs).The main objective is to design a generalized proportional-integral (PI) control strategy such that the PDF can follow a target one with the enhanced robustness. Different form the previous models, a descriptor time delay system model based on square root B-spline approximation is first established. To enhance the robust performance for the tracking problem, the mixed H2 and H∞ performance is applied instead of the only H∞ performance. The novel mixed H2 and H∞ tracking problem is formulated as a optimization problem. Instead of the non-convex design algorithms, the improved linear-matrix-inequality (LMI) based convex algorithms are also proved for controller design. Furthermore, simulations on particle distribution control problems are given to demonstrate the efficiency of the proposed approach and encouraging results have obtained. Keyword: probability density function; non-Gaussian stochastic systems; PI controller; B-spline expansion; mixed H2 and H∞ performance