Brief paper: Optimal probability density function control for NARMAX stochastic systems

Authors:
L. Guo;H. Wang;A. P. Wang
Affiliations:
School of Instrumentation and Opto-Electronic Engineering, Beihang University, Beijing 100083, China;Control Systems Centre, Manchester University, Manchester, M60 1QD, UK;Institute of Computer Science, Auhui University, Anhui, China
Venue:
Automatica (Journal of IFAC)
Year:
2008

Citing 2
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Abstract

This paper presents a new control strategy for a class of non-Gaussian stochastic systems so that the output probability density function (PDF) of the system can be made to follow a desired PDF. The system considered is represented by an Nonlinear AutoRegressive and Moving Average with eXogenous (NARMAX) inputs with input channel time-delay and non-Gaussian noise. A multi-step-ahead nonlinear cumulative cost function is used to improve tracking performance. For this purpose, a relationship between the PDFs of all the inputs and the PDFs of multiple-step-ahead output is formulated by constructing an auxiliary multivariate mapping. By minimizing this performance function, a new explicit predictive controller design algorithm is established with less conservatism than some previous results. Furthermore, an improved approach is developed to guarantee the local stability of the closed-loop system by tuning the weighting parameters recursively. Simulations are given to demonstrate the effectiveness of the proposed control algorithm and desired results have been obtained.