Interval Type-2 Fuzzy Sampled-Data Optimal Control for Nonlinear Systems with Multiple Conditions

Abstract

The work is aimed at exploring the problem of interval type-2 (IT2) fuzzy sampled-data optimal control. Considering that the controlled system has multiple conditions such as nonlinearities, parameter uncertainties and missing data, the IT2 fuzzy system is utilized to model such the systems. By employing free-weighting matrix method, the effective control scheme formed by the linear matrix inequalities is acquired in the stable sense of Lyapunov–Krasovskii theory. And, the proposed sufficient conditions are relaxed by making the best of the attribute and boundary information of membership functions. Furthermore, the IT2 sampled-data fuzzy controller is devised, which makes the fuzzy closed-loop system keep asymptotical stability and satisfy the optimal control performance index. Finally, the fuzzy control scheme is fully verified by the inverted pendulum system.