Indirect Adaptive Interval Type-۲ Fuzzy PI Sliding Mode Control for a Class of Uncertain\ Nonlinear Systems

Controller design remains an elusive and challenging problem foruncertain nonlinear dynamics. Interval type-۲ fuzzy logic systems (IT۲FLS) incomparison with type-۱ fuzzy logic systems claim to effectively handle systemuncertainties especially in the presence of disturbances and noises, but lack aformal mechanism to guarantee performance. In contrast, adaptive sliding modecontrol (ASMC) provides a robust mechanism to provide system stability againstparameter changes and uncertainties, but suffers from chattering phenomenon.In this paper, a stable indirect adaptive interval type-۲ fuzzy PI sliding modecontroller (AIT۲FSMC) is investigated for a class of nonlinear systems in thepresence of system's unmodeled dynamics and external disturbances. The addedProportional Integral (PI) structure is used to further attenuate the chatteringproblem that is common in sliding mode control systems. The interval type-۲fuzzy adaptation law adjusts the consequent parameters of the rules based on aLyapunov synthesis approach. Mathematical analysis proves the closed loopasymptotic stability, while benefiting from human expert knowledge to improvetransient response of the system. Application to two nonlinear systems verifiesthe robustness of the proposed AIT۲FSMC approach in the presence ofuncertainties and bounded external disturbances, especially when disturbanceshave fast changes and large magnitudes.

Keywords:

Interval type-۲ fuzzy logic systems , Sliding mode control , Uncertainty , Adaptive PI control , Lyapunov theory , Nonlinear systems