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

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.

PDF shaping control for non-Gaussian stochastic distribution systems with time-delay

“…e(r)dr (10) Thus, the concerned problem will be transformed to find gain matrices Kp, K] such that the system (6) …”

“…Defining a(t) = 81 (t) -8 2 (t) , so the dynamics for a(t) can be described as Combining with (35-36), it can be seen that constraint condition xT (t)ITx(t) :0; 1 can be satisfied (see [9][10]). …”

“…In order to achieve the good 978-1-4673-1487-9/12/$31.00 ©2012 IEEE tracking performance, Guo and Wang (see [6][7]) firstly designed the pseudo-PID controller for general non-Gaussian stochastic systems. Yi and Guo presented a novel two-step neural networks and fuzzy model control framework to identity the complex black-boxes model (see [8][9][10]). Zhang and Wang proposed a new PDF control algorithm based on networked control systems [11].…”

“…r > ° is the input time-delay. 10 (V(t)) as a kind of unknown model uncertainty, is a non-linear function satisfying the following globally Lipschitz condition 1 1!oCT-; (t)) -f o ( � (t)) 1 1 :,; II U o ( T-; (t) -� (t)) 1 1…”

Tolerant tracking controller design with guaranteed success rate of output SDC systems

“…However, the stochastic distribution control is different from traditional ones, it is generally encountered in industrial processes and with the purpose of controlling the shapes of the output probability density functions of non-Gaussian or dynamic stochastic systems. The virtues of controlling the output shapes of systems are already recognized in that and the shapes of PDFs contains integrated information which is related to both the stochastic dynamics of system and the PDF [2,4]. Furthermore, multiple additional information is contained in that shape of PDF.…”