Constrained discrete-time PI controller design for output PDFs of stochastic systems with time delays

This article presents a new proportional-integral (PI) tracking control strategy for non-Gaussian stochastic systems based on a square root B-spline model for the output probability density functions (PDFs). Following the square root B-spline approximation to the measured output PDF, a non-linear discrete-time dynamical model can be established between the control input and the weights related to the PDFs. It is noted that the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics. For the non-linear discrete-time weight model including time-delay terms and exogenous disturbances, convex linear matrix inequality optimisation algorithms are used to design a generalised PI controller such that stabilisation, state constraint and tracking performance can be guaranteed simultaneously. Furthermore, in order to enhance the robustness, the peak-to-peak measure index is applied to optimise the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.