Open AccessMulti‐Step probabilistic sets in model predictive control for stochastic systems with multiplicative uncertainty
Author(s) -
Li Jiwei,
Li Dewei,
Xi Yugeng
Publication year - 2014
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2014.0229
Subject(s) - probabilistic logic , multiplicative noise , multiplicative function , control theory (sociology) , controller (irrigation) , model predictive control , mathematical optimization , probabilistic analysis of algorithms , mathematics , stability theory , stability (learning theory) , computer science , control (management) , artificial intelligence , machine learning , nonlinear system , physics , quantum mechanics , agronomy , biology , mathematical analysis , signal transfer function , digital signal processing , analog signal , computer hardware
This study designs a model predictive controller for linear, discrete‐time, stochastic systems with multiplicative noise and probabilistic constraints. The probabilistic invariance has shown its advantage in characterising the stochastic dynamics of the controlled state. Here multi‐step probabilistic sets strengthen probabilistic invariance to further satisfy infinite‐horizon probabilistic constraints. In addition, multi‐step probabilistic sets offer some degrees of freedom to enlarge the feasible region ensured by probabilistic invariance. The controller satisfies given constraints and guarantees closed‐loop mean‐square stability. Moreover, a simplified controller with lower on‐line computational burden is presented. Numerical examples show the performance of the proposed approach.