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.