Abstract
AbstractIn this paper, the problem of membership function‐dependent model predictive control (MFD‐MPC) of interval type‐2 Takagi–Sugeno (IT2 T‐S) fuzzy system is investigated. An online MFD‐MPC optimization problem is formulated to minimize an infinite horizon objective function subject to hard constraints on control input and system state. By using the variable dimension expansion method and dividing the operation domain of independent variables into several subdomains, a subregion‐based state feedback model predictive controller that offers more design flexibility is designed to stabilize the open‐loop fuzzy system. Based on descriptor system theory, the variable mismatching phenomenon between MFs and the coupling between plant, controller, and Lyapunov matrix are eliminated. Then, using the piecewise linear approximation technology, MFD sufficient conditions of low conservatism on guaranteeing recursive feasibility and the stability of IT2 closed‐loop fuzzy system are deduced by tightening terminal constraint set. Finally, a numerical example is provided to further explain the advance of the proposed method.
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