Self‐Triggered Model Predictive Control for Interval Type‐2 T‐S Fuzzy Systems: A Co‐Design Approach

ABSTRACT In this article, the fuzzy model predictive control (FMPC) problem is investigated for a class of non‐linear systems in an interval type‐2 Takagi–Sugeno (IT2 T‐S) fuzzy form subject to hard constraints. To save transmission energy and reduce the calculation burden, a self‐triggering scheme is incorporated into the FMPC strategy, which gives rise to the so‐called self‐triggered FMPC strategy. Based on the characteristics of the self‐triggered FMPC strategy, the self‐triggering instants rather than sampling instants are employed to construct the corresponding quadratic function and time‐varying terminal constraint‐like (TC‐like) set. Then, to maximize triggering intervals and minimize the cost function, the fuzzy property and the self‐triggering instants are fully considered to formulate a “min‐max” problem over the infinite‐time horizon, through which the feedback gain and next triggering instant are co‐designed. Furthermore, the difference between the proposed quadratic functions of adjacent self‐triggering instants is established, which contributes greatly to finding a certain upper bound of the objective function over the infinite‐time horizon. Moreover, certain auxiliary optimization problems are developed for solvability and sufficient conditions are provided to ensure the asymptotic stability of the underlying IT2 T‐S fuzzy system. Finally, two simulation examples are utilized to illustrate the validity of the proposed self‐triggered IT2 T‐S FMPC strategy.