Open AccessAdaptive MPC for constrained systems with parameter uncertainty and additive disturbance
Author(s) -
Zhang Sixing,
Dai Li,
Xia Yuanqing
Publication year - 2019
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.2019.0273
Subject(s) - control theory (sociology) , model predictive control , constraint (computer aided design) , constraint satisfaction , stability (learning theory) , set (abstract data type) , controller (irrigation) , mathematical optimization , identification (biology) , computer science , state space , linear system , adaptive control , state (computer science) , mathematics , algorithm , control (management) , artificial intelligence , mathematical analysis , statistics , botany , geometry , machine learning , probabilistic logic , agronomy , biology , programming language
In this study, the authors propose an adaptive model predictive control (MPC) algorithm for constrained linear systems in state space subject to uncertain model parameters and disturbances. An iterative set membership identification algorithm is first presented to update the uncertain parameter set at each time step. Based on the shrunken uncertain parameter set, an MPC controller is then designed to robustly stabilise the uncertain systems subject to state and input constraints. The algorithm can efficiently reduce the size of the uncertain parameter set in min–max MPC setting, and therefore improve the control performance. The algorithm is proved to ensure constraint satisfaction, recursive feasibility and input‐to‐state practical stability of the closed‐loop system even in the presence of system uncertainties. A numerical example and a brief comparison with traditional min–max MPC are provided to demonstrate the efficiency of the proposed algorithm.