Abstract
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.
Acknowledgement
This work was supported by the NSF of China (Nos 60774013 and 60472065).