Open AccessH ∞ predictive control with probability constraints for linear stochastic systems
Author(s) -
Li Jiwei,
Li Dewei,
Xi Yugeng
Publication year - 2017
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.2016.0915
Subject(s) - probabilistic logic , model predictive control , control theory (sociology) , constraint (computer aided design) , constraint satisfaction , trajectory , mathematical optimization , scaling , computer science , control (management) , mathematics , artificial intelligence , physics , geometry , astronomy
This study develops stochastic model predictive control that guarantees the recursive feasibility of the closed‐loop H ∞ performance. Multi‐step sets with scaling parameters are proposed to contain the uncertain system trajectory. Meanwhile, by extending the probabilistic invariance to disturbed stochastic systems, we formulate probabilistic constraints as linear matrix inequalities. We show that the introduced scaling parameters enhance the feasibility of H ∞ predictive control and reduce the conservatism of the constraint satisfaction. The designed control algorithm is recursively feasible and stabilises the system in the mean‐square sense. A simplified algorithm further reduces much computational burden and makes the proposed approach more practical.