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Robust MPC for Linear Systems with Structured Time‐Varying Uncertainties and Saturating Actuator
Author(s) -
Zhang Langwen,
Xie Wei,
Wang Jingcheng
Publication year - 2017
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.1432
Subject(s) - control theory (sociology) , model predictive control , linear matrix inequality , convex optimization , optimization problem , linear system , nonlinear system , actuator , continuous stirred tank reactor , robust control , mathematics , mathematical optimization , engineering , computer science , control system , regular polygon , control (management) , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , chemical engineering , electrical engineering
In this paper, a synthesis of model predictive control (MPC) algorithm is presented for uncertain systems subject to structured time‐varying uncertainties and actuator saturation. The system matrices are not exactly known, but are affine functions of a time varying parameter vector. To deal with the nonlinear actuator saturation, a saturated linear feedback control law is expressed into a convex hull of a group of auxiliary linear feedback laws. At each time instant, a state feedback law is designed to ensure the robust stability of the closed‐loop system. The robust MPC controller design problem is formulated into solving a minimization problem of a worst‐case performance index with respect to model uncertainties. The design of controller is then cast into solving a feasibility of linear matrix inequality (LMI) optimization problem. Then, the result is further extended to saturation dependent robust MPC approach by introducing additional variables. A saturation dependent quadratic function is used to reduce the conservatism of controller design. To show the effectiveness, the proposed robust MPC algorithms are applied to a continuous‐time stirred tank reactor (CSTR) process.