Indirect Adaptive Interval Type-2 Fuzzy PI Sliding Mode Control for a Class of Uncertain\\ Nonlinear Systems

Controller design remains an elusive and challenging problem for uncertain nonlinear dynamics. Interval type-2 fuzzy logic systems (IT2FLS) in comparison with type-1 fuzzy logic systems claim to effectively handle system uncertainties especially in the presence of disturbances and noises, but lack a formal mechanism to guarantee performance. In contrast, adaptive sliding mode control (ASMC) provides a robust mechanism to provide system stability against parameter changes and uncertainties, but suffers from chattering phenomenon. In this paper, a stable indirect adaptive interval type-2 fuzzy PI sliding mode controller (AIT2FSMC) is investigated for a class of nonlinear systems in the presence of systemʹs unmodeled dynamics and external disturbances. The added Proportional Integral (PI) structure is used to further attenuate the chattering problem that is common in sliding mode control systems. The interval type-2 fuzzy adaptation law adjusts the consequent parameters of the rules based on a Lyapunov synthesis approach. Mathematical analysis proves the closed loop asymptotic stability, while benefiting from human expert knowledge to improve transient response of the system. Application to two nonlinear systems verifies the robustness of the proposed AIT2FSMC approach in the presence of uncertainties and bounded external disturbances, especially when disturbances have fast changes and large magnitudes.