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Robust Constrained Model Predictive Control for Discrete‐Time Uncertain System in Takagi‐Sugeno's Form
Author(s) -
Xie Haofei,
Wang Jun,
Tang Xiaoming
Publication year - 2018
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1603
Subject(s) - control theory (sociology) , model predictive control , fuzzy logic , discrete time and continuous time , fuzzy control system , nonlinear system , continuous stirred tank reactor , controller (irrigation) , lyapunov function , mathematics , linear matrix inequality , mathematical optimization , compensation (psychology) , stability (learning theory) , computer science , control (management) , engineering , artificial intelligence , psychology , agronomy , statistics , physics , quantum mechanics , chemical engineering , machine learning , psychoanalysis , biology
In this paper, we investigate a robust constrained model predictive control synthesis approach for discrete‐time Takagi‐Sugeno's (T‐S) fuzzy system with structured uncertainty. The key idea is to determine, at each sampling time, a state feedback fuzzy predictive controller that minimizes the performance objective function in the infinite time horizon by solving a class of linear matrix inequalities (LMIs) optimization problem. To do this, the fuzzy predictive controller is designed on the basis of non‐parallel distributed compensation (non‐PDC) control law, relaxed stability conditions of the closed‐loop fuzzy system are developed by employing an extended nonquadratic Lyapunov function and introducing additional slack and collection matrices. In addition, the presented approach is capable of ensuring the robust asymptotic stability as well as the recursive feasibility of the closed‐loop fuzzy system. Simulations on a highly nonlinear continuous stirred tank reactor (CSTR) are eventually presented to demonstrate the effectiveness of the developed theoretical approach.