Relaxed Membership-Function-Dependent Model Predictive Control for Discrete-Time T–S Fuzzy System

The problem of membership-function-dependent model predictive control on an infinite horizon for discrete-time T-S fuzzy systems is investigated. To address this problem, an online local predictive control algorithm is designed based on pre-divided sub-regions of operation region of premise variables. The approximated values of membership functions are used to enlarge initial terminal set. Further, the normalized membership functions involved in approximation process, corresponding to vertices in subdomain, are handled by introducing auxiliary variables. Different from general membership-function-dependent results, this approach ensures that the constraint conditions can be satisfied in the form of the summation of all vertices within the subdomain rather than relying on a single vertex. Both conservatism and the cost function index for infinite horizon are significantly improved. An example of a continuous stirred-tank reactor is provided to confirm the effectiveness of the proposed relaxed online optimization algorithm.